 Hecke eigenform (source code)

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= Hecke eigenform
{c}
{title2=$T_nf=a_n(f)f$}

A Hecke eigenform is a nonzero <modular form> that is an <eigenvector> for every <Hecke operator>. A cuspidal eigenform has nonzero first <Fourier coefficient>: $a_1(T_nf)=a_n(f)$ proves this. Normalize $a_1=1$, and then $T_nf=a_n(f)f$. The <Hecke multiplication relations> give multiplicativity and the prime-power recurrence of the coefficients.

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