Properties

Label 35.10
Level 35
Weight 10
Dimension 364
Nonzero newspaces 6
Newform subspaces 11
Sturm bound 960
Trace bound 2

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Defining parameters

Level: \( N \) = \( 35 = 5 \cdot 7 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 11 \)
Sturm bound: \(960\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(35))\).

Total New Old
Modular forms 456 396 60
Cusp forms 408 364 44
Eisenstein series 48 32 16

Trace form

\( 364 q + 30 q^{2} - 622 q^{3} + 1538 q^{4} - 4391 q^{5} + 18772 q^{6} - 8684 q^{7} - 76710 q^{8} + 86488 q^{9} + 190986 q^{10} - 323682 q^{11} - 617024 q^{12} + 733792 q^{13} + 848202 q^{14} + 281354 q^{15}+ \cdots + 15798283616 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(35))\)

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
35.10.a \(\chi_{35}(1, \cdot)\) 35.10.a.a 1 1
35.10.a.b 2
35.10.a.c 4
35.10.a.d 5
35.10.a.e 6
35.10.b \(\chi_{35}(29, \cdot)\) 35.10.b.a 26 1
35.10.e \(\chi_{35}(11, \cdot)\) 35.10.e.a 22 2
35.10.e.b 26
35.10.f \(\chi_{35}(13, \cdot)\) 35.10.f.a 68 2
35.10.j \(\chi_{35}(4, \cdot)\) 35.10.j.a 68 2
35.10.k \(\chi_{35}(3, \cdot)\) 35.10.k.a 136 4

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(35))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(35)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)