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Properties

Label 6.7
Level 6
Weight 7
Dimension 2
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 14
Trace bound 0

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Defining parameters

Level: N N = 6=2⋅3 6 = 2 \cdot 3
Weight: k k = 7 7
Nonzero newspaces: 1 1
Newform subspaces: 1 1
Sturm bound: 1414
Trace bound: 00

Dimensions

The following table gives the dimensions of various subspaces of M7(Γ1(6))M_{7}(\Gamma_1(6)).

Total New Old
Modular forms 8 2 6
Cusp forms 4 2 2
Eisenstein series 4 0 4

Trace form

2q+42q3−64q4−192q6+4q7+306q9+1920q10−1344q12−5900q13+5760q15+2048q16−8064q18+10516q19+84q21+384q22+6144q24−26350q25+⋯+48384q99+O(q100) 2 q + 42 q^{3} - 64 q^{4} - 192 q^{6} + 4 q^{7} + 306 q^{9} + 1920 q^{10} - 1344 q^{12} - 5900 q^{13} + 5760 q^{15} + 2048 q^{16} - 8064 q^{18} + 10516 q^{19} + 84 q^{21} + 384 q^{22} + 6144 q^{24} - 26350 q^{25}+ \cdots + 48384 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S7new(Γ1(6))S_{7}^{\mathrm{new}}(\Gamma_1(6))

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space Sknew(N,χ) S_k^{\mathrm{new}}(N, \chi) we list available newforms together with their dimension.

Label χ\chi Newforms Dimension χ\chi degree
6.7.b χ6(5,⋅)\chi_{6}(5, \cdot) 6.7.b.a 2 1

Decomposition of S7old(Γ1(6))S_{7}^{\mathrm{old}}(\Gamma_1(6)) into lower level spaces

S7old(Γ1(6))≅ S_{7}^{\mathrm{old}}(\Gamma_1(6)) \cong S7new(Γ1(1))S_{7}^{\mathrm{new}}(\Gamma_1(1))⊕4^{\oplus 4}⊕\oplusS7new(Γ1(2))S_{7}^{\mathrm{new}}(\Gamma_1(2))⊕2^{\oplus 2}⊕\oplusS7new(Γ1(3))S_{7}^{\mathrm{new}}(\Gamma_1(3))⊕2^{\oplus 2}