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Properties

Label 267.2
Level 267
Weight 2
Dimension 1891
Nonzero newspaces 8
Newform subspaces 16
Sturm bound 10560
Trace bound 2

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Defining parameters

Level: \( N \) = \( 267 = 3 \cdot 89 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 16 \)
Sturm bound: \(10560\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(267))\).

Total New Old
Modular forms 2816 2067 749
Cusp forms 2465 1891 574
Eisenstein series 351 176 175

Trace form

\( 1891 q - 3 q^{2} - 45 q^{3} - 95 q^{4} - 6 q^{5} - 47 q^{6} - 96 q^{7} - 15 q^{8} - 45 q^{9} + O(q^{10}) \) \( 1891 q - 3 q^{2} - 45 q^{3} - 95 q^{4} - 6 q^{5} - 47 q^{6} - 96 q^{7} - 15 q^{8} - 45 q^{9} - 106 q^{10} - 12 q^{11} - 51 q^{12} - 102 q^{13} - 24 q^{14} - 50 q^{15} - 119 q^{16} - 18 q^{17} - 47 q^{18} - 108 q^{19} - 42 q^{20} - 52 q^{21} - 124 q^{22} - 24 q^{23} - 59 q^{24} - 119 q^{25} - 42 q^{26} - 45 q^{27} - 144 q^{28} - 30 q^{29} - 62 q^{30} - 120 q^{31} - 63 q^{32} - 56 q^{33} - 142 q^{34} - 48 q^{35} - 51 q^{36} - 126 q^{37} - 60 q^{38} - 58 q^{39} - 178 q^{40} - 42 q^{41} - 68 q^{42} - 132 q^{43} - 84 q^{44} - 50 q^{45} - 160 q^{46} - 48 q^{47} - 75 q^{48} - 145 q^{49} - 93 q^{50} - 62 q^{51} - 186 q^{52} - 54 q^{53} - 47 q^{54} - 160 q^{55} - 120 q^{56} - 64 q^{57} - 178 q^{58} - 60 q^{59} - 86 q^{60} - 150 q^{61} - 96 q^{62} - 52 q^{63} - 215 q^{64} - 84 q^{65} - 80 q^{66} - 156 q^{67} - 126 q^{68} - 68 q^{69} - 232 q^{70} - 72 q^{71} + 73 q^{72} - 74 q^{73} + 106 q^{74} + 145 q^{75} + 300 q^{76} + 80 q^{77} + 178 q^{78} + 8 q^{79} + 474 q^{80} + 175 q^{81} + 138 q^{82} + 180 q^{83} + 516 q^{84} + 68 q^{85} + 220 q^{86} + 146 q^{87} + 348 q^{88} + 263 q^{89} + 422 q^{90} + 152 q^{91} + 360 q^{92} + 144 q^{93} + 120 q^{94} + 144 q^{95} + 509 q^{96} + 78 q^{97} + 181 q^{98} + 164 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(267))\)

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
267.2.a \(\chi_{267}(1, \cdot)\) 267.2.a.a 1 1
267.2.a.b 1
267.2.a.c 3
267.2.a.d 3
267.2.a.e 3
267.2.a.f 4
267.2.d \(\chi_{267}(88, \cdot)\) 267.2.d.a 16 1
267.2.f \(\chi_{267}(34, \cdot)\) 267.2.f.a 28 2
267.2.g \(\chi_{267}(77, \cdot)\) 267.2.g.a 4 4
267.2.g.b 4
267.2.g.c 104
267.2.i \(\chi_{267}(4, \cdot)\) 267.2.i.a 80 10
267.2.i.b 80
267.2.j \(\chi_{267}(22, \cdot)\) 267.2.j.a 160 10
267.2.m \(\chi_{267}(10, \cdot)\) 267.2.m.a 280 20
267.2.p \(\chi_{267}(14, \cdot)\) 267.2.p.a 1120 40

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(267))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(267)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(89))\)\(^{\oplus 2}\)