Properties

Label 155.2
Level 155
Weight 2
Dimension 789
Nonzero newspaces 12
Newform subspaces 25
Sturm bound 3840
Trace bound 2

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Defining parameters

Level: \( N \) = \( 155 = 5 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 25 \)
Sturm bound: \(3840\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(155))\).

Total New Old
Modular forms 1080 965 115
Cusp forms 841 789 52
Eisenstein series 239 176 63

Trace form

\( 789 q - 33 q^{2} - 34 q^{3} - 37 q^{4} - 46 q^{5} - 102 q^{6} - 38 q^{7} - 45 q^{8} - 43 q^{9} + O(q^{10}) \) \( 789 q - 33 q^{2} - 34 q^{3} - 37 q^{4} - 46 q^{5} - 102 q^{6} - 38 q^{7} - 45 q^{8} - 43 q^{9} - 48 q^{10} - 102 q^{11} - 58 q^{12} - 44 q^{13} - 54 q^{14} - 49 q^{15} - 121 q^{16} - 48 q^{17} - 69 q^{18} - 50 q^{19} - 52 q^{20} - 112 q^{21} - 6 q^{22} - 24 q^{23} + 30 q^{24} - 36 q^{25} - 72 q^{26} + 20 q^{27} + 74 q^{28} + 18 q^{30} - 61 q^{31} + 57 q^{32} - 18 q^{33} + 36 q^{34} - 23 q^{35} - 21 q^{36} + 22 q^{37} - 30 q^{38} - 16 q^{39} - 102 q^{41} - 66 q^{42} - 64 q^{43} - 114 q^{44} - 58 q^{45} - 162 q^{46} - 78 q^{47} - 64 q^{48} - 27 q^{49} + 27 q^{50} + 18 q^{51} + 22 q^{52} - 24 q^{53} + 180 q^{54} + 3 q^{55} + 60 q^{56} + 70 q^{57} + 90 q^{58} - 30 q^{59} + 182 q^{60} + 58 q^{61} + 57 q^{62} + 76 q^{63} + 83 q^{64} + 31 q^{65} + 216 q^{66} - 38 q^{67} + 54 q^{68} + 54 q^{69} + 66 q^{70} - 42 q^{71} + 105 q^{72} - 44 q^{73} + 6 q^{74} + 56 q^{75} + 20 q^{76} + 24 q^{77} + 72 q^{78} - 40 q^{79} + 74 q^{80} - 91 q^{81} - 36 q^{82} + 96 q^{83} + 106 q^{84} - 3 q^{85} + 18 q^{86} - 30 q^{87} + 150 q^{88} + 30 q^{89} + 141 q^{90} - 72 q^{91} + 192 q^{92} + 86 q^{93} - 84 q^{94} + 55 q^{95} + 108 q^{96} + 2 q^{97} + 159 q^{98} - 36 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(155))\)

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

Label \(\chi\) Newforms Dimension \(\chi\) degree
155.2.a \(\chi_{155}(1, \cdot)\) 155.2.a.a 1 1
155.2.a.b 1
155.2.a.c 1
155.2.a.d 4
155.2.a.e 4
155.2.b \(\chi_{155}(94, \cdot)\) 155.2.b.a 4 1
155.2.b.b 10
155.2.e \(\chi_{155}(36, \cdot)\) 155.2.e.a 2 2
155.2.e.b 2
155.2.e.c 8
155.2.e.d 8
155.2.f \(\chi_{155}(92, \cdot)\) 155.2.f.a 12 2
155.2.f.b 16
155.2.h \(\chi_{155}(16, \cdot)\) 155.2.h.a 24 4
155.2.h.b 24
155.2.j \(\chi_{155}(129, \cdot)\) 155.2.j.a 28 2
155.2.n \(\chi_{155}(4, \cdot)\) 155.2.n.a 56 4
155.2.p \(\chi_{155}(37, \cdot)\) 155.2.p.a 4 4
155.2.p.b 4
155.2.p.c 48
155.2.q \(\chi_{155}(41, \cdot)\) 155.2.q.a 40 8
155.2.q.b 40
155.2.r \(\chi_{155}(23, \cdot)\) 155.2.r.a 112 8
155.2.u \(\chi_{155}(9, \cdot)\) 155.2.u.a 112 8
155.2.x \(\chi_{155}(3, \cdot)\) 155.2.x.a 224 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(155))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(155)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 2}\)