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Properties

Label 8.19
Level 8
Weight 19
Dimension 17
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 76
Trace bound 0

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Defining parameters

Level: N N = 8=23 8 = 2^{3}
Weight: k k = 19 19
Nonzero newspaces: 1 1
Newform subspaces: 2 2
Sturm bound: 7676
Trace bound: 00

Dimensions

The following table gives the dimensions of various subspaces of M19(Γ1(8))M_{19}(\Gamma_1(8)).

Total New Old
Modular forms 39 19 20
Cusp forms 33 17 16
Eisenstein series 6 2 4

Trace form

17q−86q2−2q3−182188q4−13676516q6+170697016q8+1937102443q9−1569837600q10−2825920882q11+3908201752q12+26163923904q14−123600598768q16−56596854238q17+⋯−68 ⁣⋯ ⁣74q99+O(q100) 17 q - 86 q^{2} - 2 q^{3} - 182188 q^{4} - 13676516 q^{6} + 170697016 q^{8} + 1937102443 q^{9} - 1569837600 q^{10} - 2825920882 q^{11} + 3908201752 q^{12} + 26163923904 q^{14} - 123600598768 q^{16} - 56596854238 q^{17}+ \cdots - 68\!\cdots\!74 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S19new(Γ1(8))S_{19}^{\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 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
8.19.c χ8(7,⋅)\chi_{8}(7, \cdot) None 0 1
8.19.d χ8(3,⋅)\chi_{8}(3, \cdot) 8.19.d.a 1 1
8.19.d.b 16

Decomposition of S19old(Γ1(8))S_{19}^{\mathrm{old}}(\Gamma_1(8)) into lower level spaces

S19old(Γ1(8))≅ S_{19}^{\mathrm{old}}(\Gamma_1(8)) \cong S19new(Γ1(1))S_{19}^{\mathrm{new}}(\Gamma_1(1))⊕4^{\oplus 4}⊕\oplusS19new(Γ1(2))S_{19}^{\mathrm{new}}(\Gamma_1(2))⊕3^{\oplus 3}⊕\oplusS19new(Γ1(4))S_{19}^{\mathrm{new}}(\Gamma_1(4))⊕2^{\oplus 2}