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Properties

Label 237.2
Level 237
Weight 2
Dimension 1481
Nonzero newspaces 8
Newform subspaces 15
Sturm bound 8320
Trace bound 1

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Defining parameters

Level: \( N \) = \( 237 = 3 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 15 \)
Sturm bound: \(8320\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(237))\).

Total New Old
Modular forms 2236 1637 599
Cusp forms 1925 1481 444
Eisenstein series 311 156 155

Trace form

\( 1481 q - 3 q^{2} - 40 q^{3} - 85 q^{4} - 6 q^{5} - 42 q^{6} - 86 q^{7} - 15 q^{8} - 40 q^{9} + O(q^{10}) \) \( 1481 q - 3 q^{2} - 40 q^{3} - 85 q^{4} - 6 q^{5} - 42 q^{6} - 86 q^{7} - 15 q^{8} - 40 q^{9} - 96 q^{10} - 12 q^{11} - 46 q^{12} - 92 q^{13} - 24 q^{14} - 45 q^{15} - 109 q^{16} - 18 q^{17} - 42 q^{18} - 98 q^{19} - 42 q^{20} - 47 q^{21} - 114 q^{22} - 24 q^{23} - 54 q^{24} - 109 q^{25} - 42 q^{26} - 40 q^{27} - 134 q^{28} - 30 q^{29} - 57 q^{30} - 110 q^{31} - 63 q^{32} - 51 q^{33} - 132 q^{34} - 48 q^{35} - 46 q^{36} - 116 q^{37} - 60 q^{38} - 53 q^{39} - 168 q^{40} - 42 q^{41} - 63 q^{42} - 122 q^{43} - 84 q^{44} - 45 q^{45} - 150 q^{46} - 48 q^{47} - 70 q^{48} - 135 q^{49} - 93 q^{50} - 57 q^{51} - 176 q^{52} - 54 q^{53} - 42 q^{54} - 150 q^{55} - 120 q^{56} - 59 q^{57} - 168 q^{58} - 60 q^{59} - 81 q^{60} - 140 q^{61} - 96 q^{62} - 34 q^{63} + 107 q^{64} + 72 q^{65} + 81 q^{66} + 36 q^{67} + 186 q^{68} + 93 q^{69} + 402 q^{70} + 84 q^{71} + 102 q^{72} + 4 q^{73} + 198 q^{74} + 86 q^{75} + 510 q^{76} + 138 q^{77} + 114 q^{78} + 311 q^{79} + 594 q^{80} - 40 q^{81} + 108 q^{82} + 150 q^{83} + 269 q^{84} + 126 q^{85} + 180 q^{86} + 9 q^{87} + 522 q^{88} + 66 q^{89} + 21 q^{90} + 122 q^{91} + 144 q^{92} + 20 q^{93} + 90 q^{94} + 36 q^{95} + 54 q^{96} - 72 q^{97} - 171 q^{98} - 51 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(237))\)

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
237.2.a \(\chi_{237}(1, \cdot)\) 237.2.a.a 2 1
237.2.a.b 4
237.2.a.c 7
237.2.b \(\chi_{237}(236, \cdot)\) 237.2.b.a 24 1
237.2.e \(\chi_{237}(55, \cdot)\) 237.2.e.a 12 2
237.2.e.b 14
237.2.h \(\chi_{237}(56, \cdot)\) 237.2.h.a 2 2
237.2.h.b 48
237.2.i \(\chi_{237}(10, \cdot)\) 237.2.i.a 72 12
237.2.i.b 96
237.2.l \(\chi_{237}(14, \cdot)\) 237.2.l.a 288 12
237.2.m \(\chi_{237}(4, \cdot)\) 237.2.m.a 144 24
237.2.m.b 168
237.2.n \(\chi_{237}(29, \cdot)\) 237.2.n.a 24 24
237.2.n.b 576

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(237))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(237)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(79))\)\(^{\oplus 2}\)