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Properties

Label 258.2
Level 258
Weight 2
Dimension 463
Nonzero newspaces 8
Newform subspaces 38
Sturm bound 7392
Trace bound 5

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Defining parameters

Level: \( N \) = \( 258 = 2 \cdot 3 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 38 \)
Sturm bound: \(7392\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(258))\).

Total New Old
Modular forms 2016 463 1553
Cusp forms 1681 463 1218
Eisenstein series 335 0 335

Trace form

\( 463 q + q^{2} + q^{3} + q^{4} + 6 q^{5} + q^{6} + 8 q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( 463 q + q^{2} + q^{3} + q^{4} + 6 q^{5} + q^{6} + 8 q^{7} + q^{8} + q^{9} + 6 q^{10} + 12 q^{11} + q^{12} + 14 q^{13} + 8 q^{14} + 6 q^{15} + q^{16} + 18 q^{17} + q^{18} + 20 q^{19} + 6 q^{20} + 8 q^{21} + 12 q^{22} + 24 q^{23} + q^{24} + 31 q^{25} + 14 q^{26} + q^{27} + 8 q^{28} + 30 q^{29} + 6 q^{30} + 4 q^{31} + q^{32} - 72 q^{33} - 108 q^{34} - 120 q^{35} - 13 q^{36} - 130 q^{37} - 148 q^{38} - 84 q^{39} + 6 q^{40} - 42 q^{41} - 76 q^{42} - 377 q^{43} - 72 q^{44} - 78 q^{45} - 144 q^{46} - 36 q^{47} + q^{48} - 139 q^{49} - 137 q^{50} - 66 q^{51} - 98 q^{52} - 114 q^{53} + q^{54} - 96 q^{55} + 8 q^{56} + 6 q^{57} + 30 q^{58} + 60 q^{59} + 6 q^{60} + 62 q^{61} + 32 q^{62} + 8 q^{63} + q^{64} + 84 q^{65} + 12 q^{66} + 68 q^{67} + 18 q^{68} - 18 q^{69} + 48 q^{70} - 12 q^{71} + q^{72} - 10 q^{73} + 38 q^{74} - 116 q^{75} + 20 q^{76} - 156 q^{77} + 14 q^{78} - 88 q^{79} + 6 q^{80} - 167 q^{81} + 42 q^{82} - 84 q^{83} + 8 q^{84} - 60 q^{85} + 43 q^{86} - 180 q^{87} + 12 q^{88} - 78 q^{89} + 6 q^{90} - 56 q^{91} + 24 q^{92} - 136 q^{93} + 48 q^{94} - 48 q^{95} + q^{96} - 154 q^{97} + 57 q^{98} - 135 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(258))\)

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
258.2.a \(\chi_{258}(1, \cdot)\) 258.2.a.a 1 1
258.2.a.b 1
258.2.a.c 1
258.2.a.d 1
258.2.a.e 1
258.2.a.f 1
258.2.a.g 1
258.2.d \(\chi_{258}(257, \cdot)\) 258.2.d.a 2 1
258.2.d.b 2
258.2.d.c 6
258.2.d.d 6
258.2.e \(\chi_{258}(49, \cdot)\) 258.2.e.a 2 2
258.2.e.b 2
258.2.e.c 2
258.2.e.d 2
258.2.e.e 2
258.2.e.f 2
258.2.e.g 4
258.2.f \(\chi_{258}(179, \cdot)\) 258.2.f.a 2 2
258.2.f.b 2
258.2.f.c 4
258.2.f.d 4
258.2.f.e 8
258.2.f.f 8
258.2.i \(\chi_{258}(97, \cdot)\) 258.2.i.a 6 6
258.2.i.b 6
258.2.i.c 6
258.2.i.d 6
258.2.i.e 12
258.2.j \(\chi_{258}(65, \cdot)\) 258.2.j.a 48 6
258.2.j.b 48
258.2.m \(\chi_{258}(13, \cdot)\) 258.2.m.a 12 12
258.2.m.b 12
258.2.m.c 24
258.2.m.d 24
258.2.m.e 24
258.2.p \(\chi_{258}(5, \cdot)\) 258.2.p.a 84 12
258.2.p.b 84

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(258))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(258)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(86))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(129))\)\(^{\oplus 2}\)