Properties

Label 64.8
Level 64
Weight 8
Dimension 493
Nonzero newspaces 4
Newform subspaces 15
Sturm bound 2048
Trace bound 1

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Defining parameters

Level: \( N \) = \( 64 = 2^{6} \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 15 \)
Sturm bound: \(2048\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(64))\).

Total New Old
Modular forms 932 515 417
Cusp forms 860 493 367
Eisenstein series 72 22 50

Trace form

\( 493 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 2197 q^{9} - 8 q^{10} - 1210 q^{11} - 8 q^{12} - 7072 q^{13} - 8 q^{14} + 26996 q^{15} - 8 q^{16} - 5830 q^{17} - 8 q^{18} - 60590 q^{19}+ \cdots - 18797518 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(64))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
64.8.a \(\chi_{64}(1, \cdot)\) 64.8.a.a 1 1
64.8.a.b 1
64.8.a.c 1
64.8.a.d 1
64.8.a.e 1
64.8.a.f 1
64.8.a.g 1
64.8.a.h 2
64.8.a.i 2
64.8.a.j 2
64.8.b \(\chi_{64}(33, \cdot)\) 64.8.b.a 2 1
64.8.b.b 4
64.8.b.c 8
64.8.e \(\chi_{64}(17, \cdot)\) 64.8.e.a 26 2
64.8.g \(\chi_{64}(9, \cdot)\) None 0 4
64.8.i \(\chi_{64}(5, \cdot)\) 64.8.i.a 440 8

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(64))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(64)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 7}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)