Properties

Label 8.22
Level 8
Weight 22
Dimension 25
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 88
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 22 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(88\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(8))\).

Total New Old
Modular forms 45 27 18
Cusp forms 39 25 14
Eisenstein series 6 2 4

Trace form

\( 25 q + 286 q^{2} - 8668 q^{3} + 409876 q^{4} - 22003634 q^{5} + 118236748 q^{6} + 1305710568 q^{7} + 3649699336 q^{8} - 32845074403 q^{9} - 51269339528 q^{10} + 13471294636 q^{11} + 65316900136 q^{12} - 356632250986 q^{13}+ \cdots + 81\!\cdots\!44 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(8))\)

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
8.22.a \(\chi_{8}(1, \cdot)\) 8.22.a.a 2 1
8.22.a.b 3
8.22.b \(\chi_{8}(5, \cdot)\) 8.22.b.a 20 1

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)