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Properties

Label 308.2
Level 308
Weight 2
Dimension 1494
Nonzero newspaces 16
Newform subspaces 29
Sturm bound 11520
Trace bound 5

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Defining parameters

Level: \( N \) = \( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 29 \)
Sturm bound: \(11520\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(308))\).

Total New Old
Modular forms 3180 1670 1510
Cusp forms 2581 1494 1087
Eisenstein series 599 176 423

Trace form

\( 1494 q - 14 q^{2} + 2 q^{3} - 14 q^{4} - 22 q^{5} - 20 q^{6} + 13 q^{7} - 44 q^{8} - 12 q^{9} + O(q^{10}) \) \( 1494 q - 14 q^{2} + 2 q^{3} - 14 q^{4} - 22 q^{5} - 20 q^{6} + 13 q^{7} - 44 q^{8} - 12 q^{9} - 42 q^{10} + 7 q^{11} - 64 q^{12} - 38 q^{13} - 48 q^{14} - 12 q^{15} - 78 q^{16} - 32 q^{17} - 76 q^{18} - 32 q^{19} - 70 q^{20} - 90 q^{21} - 92 q^{22} - 4 q^{23} - 56 q^{24} - 64 q^{25} - 46 q^{26} + 20 q^{27} + 4 q^{28} - 90 q^{29} - 18 q^{30} - 14 q^{31} - 24 q^{32} - 29 q^{33} - 15 q^{35} - 18 q^{36} - 114 q^{37} - 6 q^{38} - 6 q^{39} + 26 q^{40} - 94 q^{41} - 4 q^{42} + 36 q^{43} + 32 q^{44} - 192 q^{45} + 6 q^{46} - 8 q^{47} + 90 q^{48} - 23 q^{49} - 36 q^{50} - 4 q^{51} - 10 q^{52} - 88 q^{53} + 6 q^{54} - 2 q^{55} - 98 q^{56} - 94 q^{57} - 78 q^{58} - 22 q^{59} - 86 q^{60} - 26 q^{61} - 170 q^{62} - 70 q^{63} - 188 q^{64} - 182 q^{65} - 144 q^{66} - 104 q^{67} - 150 q^{68} - 272 q^{69} - 62 q^{70} - 160 q^{71} - 90 q^{72} - 182 q^{73} - 86 q^{74} - 222 q^{75} - 176 q^{77} - 128 q^{78} - 126 q^{79} + 58 q^{80} - 260 q^{81} + 16 q^{82} - 88 q^{83} - 20 q^{84} - 150 q^{85} + 116 q^{86} - 62 q^{87} + 122 q^{88} - 128 q^{89} + 70 q^{90} - 39 q^{91} - 48 q^{92} - 96 q^{93} + 90 q^{94} + 14 q^{95} + 18 q^{96} + 20 q^{97} - 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(308))\)

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
308.2.a \(\chi_{308}(1, \cdot)\) 308.2.a.a 1 1
308.2.a.b 2
308.2.a.c 3
308.2.c \(\chi_{308}(153, \cdot)\) 308.2.c.a 4 1
308.2.c.b 4
308.2.d \(\chi_{308}(43, \cdot)\) 308.2.d.a 18 1
308.2.d.b 18
308.2.f \(\chi_{308}(111, \cdot)\) 308.2.f.a 40 1
308.2.i \(\chi_{308}(177, \cdot)\) 308.2.i.a 6 2
308.2.i.b 6
308.2.j \(\chi_{308}(113, \cdot)\) 308.2.j.a 4 4
308.2.j.b 8
308.2.j.c 12
308.2.l \(\chi_{308}(199, \cdot)\) 308.2.l.a 80 2
308.2.n \(\chi_{308}(219, \cdot)\) 308.2.n.a 4 2
308.2.n.b 4
308.2.n.c 80
308.2.q \(\chi_{308}(241, \cdot)\) 308.2.q.a 16 2
308.2.t \(\chi_{308}(27, \cdot)\) 308.2.t.a 8 4
308.2.t.b 8
308.2.t.c 160
308.2.v \(\chi_{308}(127, \cdot)\) 308.2.v.a 72 4
308.2.v.b 72
308.2.w \(\chi_{308}(13, \cdot)\) 308.2.w.a 32 4
308.2.y \(\chi_{308}(9, \cdot)\) 308.2.y.a 16 8
308.2.y.b 48
308.2.z \(\chi_{308}(17, \cdot)\) 308.2.z.a 64 8
308.2.bc \(\chi_{308}(39, \cdot)\) 308.2.bc.a 352 8
308.2.be \(\chi_{308}(3, \cdot)\) 308.2.be.a 352 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(308))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(308)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 1}\)