Properties

Label 64.2.a
Level $64$
Weight $2$
Character orbit 64.a
Rep. character $\chi_{64}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $16$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 64.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(64))\).

Total New Old
Modular forms 14 3 11
Cusp forms 3 1 2
Eisenstein series 11 2 9

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)Dim
\(-\)\(1\)

Trace form

\( q + 2 q^{5} - 3 q^{9} + O(q^{10}) \) \( q + 2 q^{5} - 3 q^{9} - 6 q^{13} + 2 q^{17} - q^{25} + 10 q^{29} + 2 q^{37} + 10 q^{41} - 6 q^{45} - 7 q^{49} - 14 q^{53} + 10 q^{61} - 12 q^{65} - 6 q^{73} + 9 q^{81} + 4 q^{85} + 10 q^{89} + 18 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(64))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
64.2.a.a 64.a 1.a $1$ $0.511$ \(\Q\) \(\Q(\sqrt{-1}) \) 32.2.a.a \(0\) \(0\) \(2\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q+2q^{5}-3q^{9}-6q^{13}+2q^{17}-q^{25}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(64))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(64)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)