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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

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

Display 100 coefficients 10 coefficients

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 available 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

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