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Properties

Label 287.2
Level 287
Weight 2
Dimension 3019
Nonzero newspaces 16
Newform subspaces 30
Sturm bound 13440
Trace bound 3

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Defining parameters

Level: \( N \) = \( 287 = 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 30 \)
Sturm bound: \(13440\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(287))\).

Total New Old
Modular forms 3600 3411 189
Cusp forms 3121 3019 102
Eisenstein series 479 392 87

Trace form

\( 3019 q - 83 q^{2} - 84 q^{3} - 87 q^{4} - 86 q^{5} - 92 q^{6} - 101 q^{7} - 215 q^{8} - 93 q^{9} + O(q^{10}) \) \( 3019 q - 83 q^{2} - 84 q^{3} - 87 q^{4} - 86 q^{5} - 92 q^{6} - 101 q^{7} - 215 q^{8} - 93 q^{9} - 98 q^{10} - 92 q^{11} - 108 q^{12} - 94 q^{13} - 103 q^{14} - 224 q^{15} - 111 q^{16} - 98 q^{17} - 119 q^{18} - 100 q^{19} - 122 q^{20} - 104 q^{21} - 236 q^{22} - 104 q^{23} - 140 q^{24} - 111 q^{25} - 122 q^{26} - 120 q^{27} - 107 q^{28} - 230 q^{29} - 72 q^{30} - 72 q^{31} - 3 q^{32} - 8 q^{33} - 34 q^{34} - 66 q^{35} - 11 q^{36} + 2 q^{37} - 60 q^{38} + 24 q^{39} + 110 q^{40} - 81 q^{41} - 52 q^{42} - 204 q^{43} + 76 q^{44} + 2 q^{45} - 72 q^{46} - 8 q^{47} + 76 q^{48} - 61 q^{49} - 193 q^{50} - 32 q^{51} - 38 q^{52} - 94 q^{53} - 120 q^{54} - 152 q^{55} - 115 q^{56} - 280 q^{57} - 170 q^{58} - 140 q^{59} - 248 q^{60} - 142 q^{61} - 176 q^{62} - 113 q^{63} - 327 q^{64} - 144 q^{65} - 64 q^{66} - 28 q^{67} - 6 q^{68} - 16 q^{69} + 82 q^{70} - 112 q^{71} + 85 q^{72} + 6 q^{73} + 46 q^{74} + 116 q^{75} + 380 q^{76} - 32 q^{77} + 32 q^{78} + 214 q^{80} + 179 q^{81} + 277 q^{82} - 84 q^{83} + 152 q^{84} + 32 q^{85} + 188 q^{86} - 40 q^{87} + 140 q^{88} - 10 q^{89} + 286 q^{90} + 46 q^{91} - 128 q^{92} - 48 q^{93} + 136 q^{94} - 40 q^{95} + 68 q^{96} - 18 q^{97} - 3 q^{98} - 236 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(287))\)

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
287.2.a \(\chi_{287}(1, \cdot)\) 287.2.a.a 2 1
287.2.a.b 2
287.2.a.c 3
287.2.a.d 3
287.2.a.e 5
287.2.a.f 6
287.2.c \(\chi_{287}(204, \cdot)\) 287.2.c.a 10 1
287.2.c.b 12
287.2.e \(\chi_{287}(165, \cdot)\) 287.2.e.a 4 2
287.2.e.b 4
287.2.e.c 10
287.2.e.d 34
287.2.f \(\chi_{287}(50, \cdot)\) 287.2.f.a 40 2
287.2.h \(\chi_{287}(57, \cdot)\) 287.2.h.a 4 4
287.2.h.b 4
287.2.h.c 40
287.2.h.d 40
287.2.j \(\chi_{287}(81, \cdot)\) 287.2.j.a 52 2
287.2.l \(\chi_{287}(27, \cdot)\) 287.2.l.a 104 4
287.2.n \(\chi_{287}(64, \cdot)\) 287.2.n.a 88 4
287.2.r \(\chi_{287}(9, \cdot)\) 287.2.r.a 4 4
287.2.r.b 4
287.2.r.c 96
287.2.s \(\chi_{287}(16, \cdot)\) 287.2.s.a 208 8
287.2.u \(\chi_{287}(8, \cdot)\) 287.2.u.a 160 8
287.2.w \(\chi_{287}(3, \cdot)\) 287.2.w.a 208 8
287.2.z \(\chi_{287}(4, \cdot)\) 287.2.z.a 208 8
287.2.bb \(\chi_{287}(6, \cdot)\) 287.2.bb.a 416 16
287.2.bc \(\chi_{287}(2, \cdot)\) 287.2.bc.a 416 16
287.2.be \(\chi_{287}(12, \cdot)\) 287.2.be.a 832 32

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(287))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(287)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 2}\)