are newforms
as long as the coefficients are multiplicative.
A weight k newform can be written as a linear
combination of products of 
and 
where
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All cuspforms on are newforms
as long as the coefficients are multiplicative.
A weight k newform can be written as a linear
combination of products of and
where
and
The weight must be a positive even integer.
The number of cusp forms of weight k is [k/12] if
k is not congruent to 2 mod 12 and is [k/12]-1 if
is congruent to 2 mod 12.