Properties

Label 8.9
Level 8
Weight 9
Dimension 7
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 36
Trace bound 0

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(8))\).

Total New Old
Modular forms 19 9 10
Cusp forms 13 7 6
Eisenstein series 6 2 4

Trace form

\( 7 q + 2 q^{2} - 2 q^{3} - 332 q^{4} - 740 q^{6} - 2728 q^{8} + 10933 q^{9} - 4080 q^{10} + 19774 q^{11} - 18632 q^{12} - 51744 q^{14} + 86032 q^{16} - 38642 q^{17} + 181510 q^{18} - 167554 q^{19} - 216480 q^{20}+ \cdots + 445152506 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(8))\)

We only show spaces with odd 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
8.9.c \(\chi_{8}(7, \cdot)\) None 0 1
8.9.d \(\chi_{8}(3, \cdot)\) 8.9.d.a 1 1
8.9.d.b 6

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)