Properties

Label 230.4
Level 230
Weight 4
Dimension 1446
Nonzero newspaces 6
Newform subspaces 19
Sturm bound 12672
Trace bound 1

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Defining parameters

Level: \( N \) = \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 19 \)
Sturm bound: \(12672\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(230))\).

Total New Old
Modular forms 4928 1446 3482
Cusp forms 4576 1446 3130
Eisenstein series 352 0 352

Trace form

\( 1446q - 4q^{2} + 16q^{3} + 8q^{4} + 10q^{5} + 16q^{6} + 8q^{7} - 16q^{8} - 166q^{9} + O(q^{10}) \) \( 1446q - 4q^{2} + 16q^{3} + 8q^{4} + 10q^{5} + 16q^{6} + 8q^{7} - 16q^{8} - 166q^{9} - 100q^{10} + 88q^{11} + 64q^{12} + 116q^{13} + 224q^{14} - 588q^{15} - 96q^{16} - 484q^{17} + 28q^{18} + 400q^{19} + 232q^{20} + 2368q^{21} + 920q^{22} + 1804q^{23} + 192q^{24} + 954q^{25} + 576q^{26} + 424q^{27} - 320q^{28} - 340q^{29} - 1256q^{30} - 1992q^{31} - 64q^{32} - 3680q^{33} - 776q^{34} - 2430q^{35} + 72q^{36} - 2308q^{37} + 400q^{38} - 568q^{39} + 240q^{40} + 1008q^{41} - 128q^{42} + 3368q^{43} - 544q^{44} + 3060q^{45} - 32q^{46} + 4192q^{47} + 256q^{48} + 6342q^{49} + 700q^{50} + 2888q^{51} + 464q^{52} - 928q^{53} - 6728q^{54} - 7676q^{55} - 4640q^{56} - 17704q^{57} - 3336q^{58} - 10820q^{59} - 88q^{60} - 1860q^{61} + 2824q^{62} + 8656q^{63} + 128q^{64} + 9684q^{65} + 11744q^{66} + 7856q^{67} + 5456q^{68} + 15784q^{69} + 4848q^{70} + 17288q^{71} + 4336q^{72} + 3500q^{73} + 8712q^{74} - 378q^{75} + 1760q^{76} - 784q^{77} - 4760q^{78} - 12812q^{79} - 1248q^{80} - 18126q^{81} - 8280q^{82} - 18052q^{83} - 6992q^{84} - 5998q^{85} - 13496q^{86} + 7932q^{87} - 192q^{88} + 160q^{89} - 2580q^{90} + 6296q^{91} - 528q^{92} + 2432q^{93} + 2624q^{94} + 23232q^{95} + 256q^{96} + 25816q^{97} + 15212q^{98} + 34028q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(230))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
230.4.a \(\chi_{230}(1, \cdot)\) 230.4.a.a 1 1
230.4.a.b 1
230.4.a.c 1
230.4.a.d 1
230.4.a.e 1
230.4.a.f 2
230.4.a.g 3
230.4.a.h 4
230.4.a.i 4
230.4.a.j 4
230.4.b \(\chi_{230}(139, \cdot)\) 230.4.b.a 14 1
230.4.b.b 18
230.4.e \(\chi_{230}(137, \cdot)\) 230.4.e.a 72 2
230.4.g \(\chi_{230}(31, \cdot)\) 230.4.g.a 50 10
230.4.g.b 60
230.4.g.c 60
230.4.g.d 70
230.4.j \(\chi_{230}(9, \cdot)\) 230.4.j.a 360 10
230.4.l \(\chi_{230}(7, \cdot)\) 230.4.l.a 720 20

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(230))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(230)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 2}\)