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Properties

Label 55.2
Level 55
Weight 2
Dimension 79
Nonzero newspaces 6
Newform subspaces 9
Sturm bound 480
Trace bound 2

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Defining parameters

Level: N N = 55=5⋅11 55 = 5 \cdot 11
Weight: k k = 2 2
Nonzero newspaces: 6 6
Newform subspaces: 9 9
Sturm bound: 480480
Trace bound: 22

Dimensions

The following table gives the dimensions of various subspaces of M2(Γ1(55))M_{2}(\Gamma_1(55)).

Total New Old
Modular forms 160 135 25
Cusp forms 81 79 2
Eisenstein series 79 56 23

Trace form

79q−13q2−14q3−17q4−16q5−32q6−8q7−5q8−3q9−3q10−31q11−8q12−14q13−4q14+q15−q16+2q17+11q18+13q20+⋯−73q99+O(q100) 79 q - 13 q^{2} - 14 q^{3} - 17 q^{4} - 16 q^{5} - 32 q^{6} - 8 q^{7} - 5 q^{8} - 3 q^{9} - 3 q^{10} - 31 q^{11} - 8 q^{12} - 14 q^{13} - 4 q^{14} + q^{15} - q^{16} + 2 q^{17} + 11 q^{18} + 13 q^{20}+ \cdots - 73 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(Γ1(55))S_{2}^{\mathrm{new}}(\Gamma_1(55))

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
55.2.a χ55(1,⋅)\chi_{55}(1, \cdot) 55.2.a.a 1 1
55.2.a.b 2
55.2.b χ55(34,⋅)\chi_{55}(34, \cdot) 55.2.b.a 4 1
55.2.e χ55(32,⋅)\chi_{55}(32, \cdot) 55.2.e.a 4 2
55.2.e.b 4
55.2.g χ55(16,⋅)\chi_{55}(16, \cdot) 55.2.g.a 8 4
55.2.g.b 8
55.2.j χ55(4,⋅)\chi_{55}(4, \cdot) 55.2.j.a 16 4
55.2.l χ55(2,⋅)\chi_{55}(2, \cdot) 55.2.l.a 32 8

Decomposition of S2old(Γ1(55))S_{2}^{\mathrm{old}}(\Gamma_1(55)) into lower level spaces

S2old(Γ1(55))≅ S_{2}^{\mathrm{old}}(\Gamma_1(55)) \cong S2new(Γ1(1))S_{2}^{\mathrm{new}}(\Gamma_1(1))⊕4^{\oplus 4}⊕\oplusS2new(Γ1(5))S_{2}^{\mathrm{new}}(\Gamma_1(5))⊕2^{\oplus 2}⊕\oplusS2new(Γ1(11))S_{2}^{\mathrm{new}}(\Gamma_1(11))⊕2^{\oplus 2}