= Dimension of level-one modular forms
{title2=$\dim M_k=\lfloor k/12\rfloor+1-\mathbf1_{k\equiv2\pmod{12}}$}
For even nonnegative weight, the displayed dimension follows from <multiplication by the modular discriminant> and the constant-coefficient map. Every nonnegative even weight except two has a product $E_4^aE_6^b$ of <Eisenstein series> with constant term one, so $\dim M_k=1+\dim M_{k-12}$ for even $k\geq4$. The initial dimensions are one in weight zero and zero in weight two; negative and odd weights have no nonzero level-one <modular forms>.
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