Forget "no" and "not" for a second - they seem related, but it is a false comparison.
Instead, think about
"There is" vs. "There is not". These are related expressions but one is positive and one is negative.
Things are simple when the (reflexive) subject of the sentence is expressed positively.
For example, suppose the subject is "life".
There is (life on Mars).
There is not (life on Mars).
The complication is that sometimes the subject is expressed negatively.
Suppose the subject was "no life".
The verb-positive sentence remains the same.
There is (no life on Mars).
The verb-negative sentence has to change, though, because English (unlike Spanish) has rules against double negatives.
It is incorrect to say:
There is not (no life on Mars).
Instead, we say
There is not (any life on Mars).
Other examples of a negative subject becoming positive because the verb is negative:
There is no reason to agree with him. There is not any reason to agree with him.
There is no way out of this situation. There is not a way out of this situation.
There is no one alive who remembers him. There is not anyone alive who remembers him.
In each case, the "not" in "There is not" is part of the verb, making the verb negative, whereas the "no" is part of the subject, making the subject negative. So you can't really compare "there is no" with "there is not" - just remember that in English, you are not allowed to have both the verb and subject expressed negatively.
You can say either one, but they have different effects.
"She is not a student" is a simple statement of fact. "She is no student" is usually an emphatic statement, which only really makes sense when you're denying somebody else's implication that she's a student. For example, if one professor says, "A student asked me a question about [some crackpot theory] after yesterday's lecture," another professor might say, "She's no student! She's just some woman who slips into lectures so she can ask her crazy questions." You could also use it figuratively, to mean that she's such a bad student that she doesn't deserve the name: "Mary? Ha! She's no student. I mean, she pays her fees and comes to lectures but have you ever seen her actually study anything? I haven't!"
Best Answer
Both are grammatically correct, but it depends on the situation which one would be appropriate.
Generally speaking, we use the plural with everything except one, and no counts as not one.
There are, however, two exceptions. The first is if there could only possibly be one or zero. For example, when talking about the moon, we use the singular:
So, if there were a university committee which normally had one student representative, it would be OK to say
The second is when we want to be emphatic: we can use the singular to emphasize that there was not one single.... So, if the teacher was disappointed to find that no student turned up, he or she could say
Here is an idiomatic expression that is a good example of the use of the singular for emphasis:
Here is an example using almost the same phrasing as the question: