Properties

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

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Defining parameters

Level: \( N \) = \( 155 = 5 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newforms: \( 25 \)
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

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

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

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