Properties

Label 10.34
Level 10
Weight 34
Dimension 27
Nonzero newspaces 2
Newform subspaces 5
Sturm bound 204
Trace bound 1

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Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 34 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 5 \)
Sturm bound: \(204\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{34}(\Gamma_1(10))\).

Total New Old
Modular forms 103 27 76
Cusp forms 95 27 68
Eisenstein series 8 0 8

Trace form

\( 27 q - 65536 q^{2} + 74568256 q^{3} - 21474836480 q^{4} - 147433460545 q^{5} - 15356278341632 q^{6} + 22560918015772 q^{7} - 281474976710656 q^{8} - 16\!\cdots\!65 q^{9} - 36\!\cdots\!40 q^{10} - 63\!\cdots\!76 q^{11}+ \cdots - 27\!\cdots\!80 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{34}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.34.a \(\chi_{10}(1, \cdot)\) 10.34.a.a 2 1
10.34.a.b 3
10.34.a.c 3
10.34.a.d 3
10.34.b \(\chi_{10}(9, \cdot)\) 10.34.b.a 16 1

Decomposition of \(S_{34}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{34}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{34}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 1}\)