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Properties

Label 10.7
Level 10
Weight 7
Dimension 6
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 42
Trace bound 0

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Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(42\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(10))\).

Total New Old
Modular forms 22 6 16
Cusp forms 14 6 8
Eisenstein series 8 0 8

Trace form

\( 6 q + 8 q^{2} - 64 q^{3} + 180 q^{5} + 224 q^{6} - 696 q^{7} - 256 q^{8} + 2280 q^{10} + 472 q^{11} - 2048 q^{12} - 4614 q^{13} + 3320 q^{15} - 6144 q^{16} + 17554 q^{17} + 12152 q^{18} - 9920 q^{20} - 46408 q^{21}+ \cdots - 1286072 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.7.c \(\chi_{10}(3, \cdot)\) 10.7.c.a 2 2
10.7.c.b 4

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 1}\)