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Properties

Label 74.8
Level 74
Weight 8
Dimension 397
Nonzero newspaces 6
Newform subspaces 11
Sturm bound 2736
Trace bound 1

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Defining parameters

Level: N N = 74=2⋅37 74 = 2 \cdot 37
Weight: k k = 8 8
Nonzero newspaces: 6 6
Newform subspaces: 11 11
Sturm bound: 27362736
Trace bound: 11

Dimensions

The following table gives the dimensions of various subspaces of M8(Γ1(74))M_{8}(\Gamma_1(74)).

Total New Old
Modular forms 1233 397 836
Cusp forms 1161 397 764
Eisenstein series 72 0 72

Trace form

397q+16q2−24q3−128q4+420q5+192q6−2032q7+1024q8+4086q9−3360q10−2184q11−1536q12−2764q13+16256q14+5040q15−8192q16+⋯+124970652q99+O(q100) 397 q + 16 q^{2} - 24 q^{3} - 128 q^{4} + 420 q^{5} + 192 q^{6} - 2032 q^{7} + 1024 q^{8} + 4086 q^{9} - 3360 q^{10} - 2184 q^{11} - 1536 q^{12} - 2764 q^{13} + 16256 q^{14} + 5040 q^{15} - 8192 q^{16}+ \cdots + 124970652 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S8new(Γ1(74))S_{8}^{\mathrm{new}}(\Gamma_1(74))

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
74.8.a χ74(1,⋅)\chi_{74}(1, \cdot) 74.8.a.a 4 1
74.8.a.b 4
74.8.a.c 6
74.8.a.d 7
74.8.b χ74(73,⋅)\chi_{74}(73, \cdot) 74.8.b.a 24 1
74.8.c χ74(47,⋅)\chi_{74}(47, \cdot) 74.8.c.a 22 2
74.8.c.b 24
74.8.e χ74(11,⋅)\chi_{74}(11, \cdot) 74.8.e.a 48 2
74.8.f χ74(7,⋅)\chi_{74}(7, \cdot) 74.8.f.a 60 6
74.8.f.b 66
74.8.h χ74(3,⋅)\chi_{74}(3, \cdot) 74.8.h.a 132 6

Decomposition of S8old(Γ1(74))S_{8}^{\mathrm{old}}(\Gamma_1(74)) into lower level spaces

S8old(Γ1(74))≅ S_{8}^{\mathrm{old}}(\Gamma_1(74)) \cong S8new(Γ1(1))S_{8}^{\mathrm{new}}(\Gamma_1(1))⊕4^{\oplus 4}⊕\oplusS8new(Γ1(2))S_{8}^{\mathrm{new}}(\Gamma_1(2))⊕2^{\oplus 2}⊕\oplusS8new(Γ1(37))S_{8}^{\mathrm{new}}(\Gamma_1(37))⊕2^{\oplus 2}