Properties

Label 8.8
Level 8
Weight 8
Dimension 8
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 32
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(32\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 17 10 7
Cusp forms 11 8 3
Eisenstein series 6 2 4

Trace form

\( 8 q + 6 q^{2} - 40 q^{3} + 116 q^{4} + 348 q^{5} + 268 q^{6} - 2368 q^{7} + 1512 q^{8} + 1700 q^{9} - 1656 q^{10} - 5688 q^{11} - 4088 q^{12} - 4660 q^{13} + 12048 q^{14} + 43680 q^{15} + 35344 q^{16} - 25968 q^{17}+ \cdots - 11495192 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

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
8.8.a \(\chi_{8}(1, \cdot)\) 8.8.a.a 1 1
8.8.a.b 1
8.8.b \(\chi_{8}(5, \cdot)\) 8.8.b.a 6 1

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

\( S_{8}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)