Properties

Label 64.2
Level 64
Weight 2
Dimension 61
Nonzero newspaces 4
Newform subspaces 4
Sturm bound 512
Trace bound 3

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Defining parameters

Level: \( N \) = \( 64 = 2^{6} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 4 \)
Sturm bound: \(512\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(64))\).

Total New Old
Modular forms 164 83 81
Cusp forms 93 61 32
Eisenstein series 71 22 49

Trace form

\( 61 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 13 q^{9} - 8 q^{10} - 10 q^{11} - 8 q^{12} - 16 q^{13} - 8 q^{14} - 12 q^{15} - 8 q^{16} - 22 q^{17} - 8 q^{18} - 14 q^{19} - 8 q^{20}+ \cdots + 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)

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
64.2.a \(\chi_{64}(1, \cdot)\) 64.2.a.a 1 1
64.2.b \(\chi_{64}(33, \cdot)\) 64.2.b.a 2 1
64.2.e \(\chi_{64}(17, \cdot)\) 64.2.e.a 2 2
64.2.g \(\chi_{64}(9, \cdot)\) None 0 4
64.2.i \(\chi_{64}(5, \cdot)\) 64.2.i.a 56 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(64))\) into lower level spaces

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