Properties

Label 141.2
Level 141
Weight 2
Dimension 505
Nonzero newspaces 4
Newform subspaces 11
Sturm bound 2944
Trace bound 1

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Defining parameters

Level: \( N \) = \( 141 = 3 \cdot 47 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 11 \)
Sturm bound: \(2944\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(141))\).

Total New Old
Modular forms 828 597 231
Cusp forms 645 505 140
Eisenstein series 183 92 91

Trace form

\( 505q - 3q^{2} - 24q^{3} - 53q^{4} - 6q^{5} - 26q^{6} - 54q^{7} - 15q^{8} - 24q^{9} + O(q^{10}) \) \( 505q - 3q^{2} - 24q^{3} - 53q^{4} - 6q^{5} - 26q^{6} - 54q^{7} - 15q^{8} - 24q^{9} - 64q^{10} - 12q^{11} - 30q^{12} - 60q^{13} - 24q^{14} - 29q^{15} - 77q^{16} - 18q^{17} - 26q^{18} - 66q^{19} - 42q^{20} - 31q^{21} - 82q^{22} - 24q^{23} - 38q^{24} - 77q^{25} - 42q^{26} - 24q^{27} - 102q^{28} - 30q^{29} - 41q^{30} - 78q^{31} - 63q^{32} - 35q^{33} - 100q^{34} - 2q^{35} + 62q^{36} - 38q^{37} + 32q^{38} + 32q^{39} + 140q^{40} + 96q^{41} + 91q^{42} - 44q^{43} + 100q^{44} + 86q^{45} + 112q^{46} + 45q^{47} + 153q^{48} - 11q^{49} + 91q^{50} + 74q^{51} + 40q^{52} - 8q^{53} + 112q^{54} + 20q^{55} + 156q^{56} + 26q^{57} - 44q^{58} - 14q^{59} + 27q^{60} - 62q^{61} - 96q^{62} - 31q^{63} - 173q^{64} - 84q^{65} - 59q^{66} - 114q^{67} - 126q^{68} - 47q^{69} - 190q^{70} - 72q^{71} - 38q^{72} - 120q^{73} - 114q^{74} - 54q^{75} - 94q^{76} - 4q^{77} + 73q^{78} + 58q^{79} + 136q^{80} - 24q^{81} + 242q^{82} + 8q^{83} + 197q^{84} + 214q^{85} + 236q^{86} + 39q^{87} + 326q^{88} + 94q^{89} + 51q^{90} + 302q^{91} + 246q^{92} + 60q^{93} + 365q^{94} + 248q^{95} + 236q^{96} + 40q^{97} + 243q^{98} + 57q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(141))\)

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
141.2.a \(\chi_{141}(1, \cdot)\) 141.2.a.a 1 1
141.2.a.b 1
141.2.a.c 1
141.2.a.d 1
141.2.a.e 1
141.2.a.f 2
141.2.c \(\chi_{141}(140, \cdot)\) 141.2.c.a 4 1
141.2.c.b 10
141.2.e \(\chi_{141}(4, \cdot)\) 141.2.e.a 88 22
141.2.e.b 88
141.2.g \(\chi_{141}(5, \cdot)\) 141.2.g.a 308 22

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(141))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(141)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(47))\)\(^{\oplus 2}\)