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Properties

Label 142.2
Level 142
Weight 2
Dimension 209
Nonzero newspaces 4
Newform subspaces 13
Sturm bound 2520
Trace bound 1

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Defining parameters

Level: \( N \) = \( 142 = 2 \cdot 71 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 13 \)
Sturm bound: \(2520\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(142))\).

Total New Old
Modular forms 700 209 491
Cusp forms 561 209 352
Eisenstein series 139 0 139

Trace form

\( 209 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} + O(q^{10}) \) \( 209 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} - 6 q^{10} - 12 q^{11} - 4 q^{12} - 14 q^{13} - 8 q^{14} - 24 q^{15} - q^{16} - 18 q^{17} - 13 q^{18} - 20 q^{19} - 6 q^{20} - 32 q^{21} - 12 q^{22} - 24 q^{23} - 4 q^{24} - 31 q^{25} - 14 q^{26} - 40 q^{27} - 8 q^{28} - 30 q^{29} - 24 q^{30} - 32 q^{31} - q^{32} - 48 q^{33} - 18 q^{34} - 48 q^{35} - 13 q^{36} - 38 q^{37} - 20 q^{38} - 56 q^{39} - 6 q^{40} - 42 q^{41} - 32 q^{42} - 44 q^{43} - 12 q^{44} - 78 q^{45} - 24 q^{46} - 48 q^{47} - 4 q^{48} - 57 q^{49} - 31 q^{50} - 72 q^{51} - 14 q^{52} - 54 q^{53} - 40 q^{54} - 72 q^{55} - 8 q^{56} + 130 q^{57} + 40 q^{58} + 80 q^{59} + 116 q^{60} + 8 q^{61} + 108 q^{62} + 176 q^{63} - q^{64} + 56 q^{65} + 232 q^{66} + 212 q^{67} + 52 q^{68} + 254 q^{69} + 92 q^{70} + 139 q^{71} - 13 q^{72} + 136 q^{73} + 102 q^{74} + 226 q^{75} + 50 q^{76} + 184 q^{77} + 224 q^{78} + 60 q^{79} - 6 q^{80} + 159 q^{81} + 98 q^{82} - 14 q^{83} + 108 q^{84} + 32 q^{85} + 26 q^{86} + 90 q^{87} - 12 q^{88} - 90 q^{89} - 78 q^{90} - 112 q^{91} - 24 q^{92} - 128 q^{93} - 48 q^{94} - 120 q^{95} - 4 q^{96} - 98 q^{97} - 57 q^{98} - 156 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(142))\)

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
142.2.a \(\chi_{142}(1, \cdot)\) 142.2.a.a 1 1
142.2.a.b 1
142.2.a.c 1
142.2.a.d 1
142.2.a.e 1
142.2.c \(\chi_{142}(5, \cdot)\) 142.2.c.a 4 4
142.2.c.b 8
142.2.c.c 12
142.2.d \(\chi_{142}(37, \cdot)\) 142.2.d.a 6 6
142.2.d.b 12
142.2.d.c 18
142.2.g \(\chi_{142}(3, \cdot)\) 142.2.g.a 72 24
142.2.g.b 72

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(142))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(142)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(71))\)\(^{\oplus 2}\)