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Properties

Label 42.4
Level 42
Weight 4
Dimension 34
Nonzero newspaces 4
Newform subspaces 7
Sturm bound 384
Trace bound 3

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Defining parameters

Level: N N = 42=2⋅3⋅7 42 = 2 \cdot 3 \cdot 7
Weight: k k = 4 4
Nonzero newspaces: 4 4
Newform subspaces: 7 7
Sturm bound: 384384
Trace bound: 33

Dimensions

The following table gives the dimensions of various subspaces of M4(Γ1(42))M_{4}(\Gamma_1(42)).

Total New Old
Modular forms 168 34 134
Cusp forms 120 34 86
Eisenstein series 48 0 48

Trace form

34q+4q2−6q3−8q4+36q5+24q6+112q7+16q8−60q9−48q10−108q11−24q12−64q13−32q14+288q15−32q16+264q17−132q18+⋯−468q99+O(q100) 34 q + 4 q^{2} - 6 q^{3} - 8 q^{4} + 36 q^{5} + 24 q^{6} + 112 q^{7} + 16 q^{8} - 60 q^{9} - 48 q^{10} - 108 q^{11} - 24 q^{12} - 64 q^{13} - 32 q^{14} + 288 q^{15} - 32 q^{16} + 264 q^{17} - 132 q^{18}+ \cdots - 468 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S4new(Γ1(42))S_{4}^{\mathrm{new}}(\Gamma_1(42))

We only show spaces with even 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
42.4.a χ42(1,⋅)\chi_{42}(1, \cdot) 42.4.a.a 1 1
42.4.a.b 1
42.4.d χ42(41,⋅)\chi_{42}(41, \cdot) 42.4.d.a 8 1
42.4.e χ42(25,⋅)\chi_{42}(25, \cdot) 42.4.e.a 2 2
42.4.e.b 2
42.4.e.c 4
42.4.f χ42(5,⋅)\chi_{42}(5, \cdot) 42.4.f.a 16 2

Decomposition of S4old(Γ1(42))S_{4}^{\mathrm{old}}(\Gamma_1(42)) into lower level spaces

S4old(Γ1(42))≅ S_{4}^{\mathrm{old}}(\Gamma_1(42)) \cong S4new(Γ1(1))S_{4}^{\mathrm{new}}(\Gamma_1(1))⊕8^{\oplus 8}⊕\oplusS4new(Γ1(2))S_{4}^{\mathrm{new}}(\Gamma_1(2))⊕4^{\oplus 4}⊕\oplusS4new(Γ1(3))S_{4}^{\mathrm{new}}(\Gamma_1(3))⊕4^{\oplus 4}⊕\oplusS4new(Γ1(6))S_{4}^{\mathrm{new}}(\Gamma_1(6))⊕2^{\oplus 2}⊕\oplusS4new(Γ1(7))S_{4}^{\mathrm{new}}(\Gamma_1(7))⊕4^{\oplus 4}⊕\oplusS4new(Γ1(14))S_{4}^{\mathrm{new}}(\Gamma_1(14))⊕2^{\oplus 2}⊕\oplusS4new(Γ1(21))S_{4}^{\mathrm{new}}(\Gamma_1(21))⊕2^{\oplus 2}