Properties

Label 230.6
Level 230
Weight 6
Dimension 2410
Nonzero newspaces 6
Sturm bound 19008
Trace bound 1

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Defining parameters

Level: \( N \) = \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(19008\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(230))\).

Total New Old
Modular forms 8096 2410 5686
Cusp forms 7744 2410 5334
Eisenstein series 352 0 352

Trace form

\( 2410q + 8q^{2} - 8q^{3} - 32q^{4} - 170q^{5} + 160q^{6} + 624q^{7} + 128q^{8} - 1306q^{9} + O(q^{10}) \) \( 2410q + 8q^{2} - 8q^{3} - 32q^{4} - 170q^{5} + 160q^{6} + 624q^{7} + 128q^{8} - 1306q^{9} + 360q^{10} + 1480q^{11} - 128q^{12} - 228q^{13} - 3136q^{14} - 10902q^{15} - 2560q^{16} + 14048q^{17} + 32776q^{18} + 14284q^{19} + 448q^{20} - 50348q^{21} - 27920q^{22} - 43712q^{23} - 4608q^{24} - 16814q^{25} + 8064q^{26} + 99532q^{27} + 51520q^{28} + 38864q^{29} + 57136q^{30} + 25764q^{31} + 2048q^{32} - 213620q^{33} - 37616q^{34} - 20670q^{35} - 14880q^{36} + 178036q^{37} + 34720q^{38} + 190808q^{39} + 640q^{40} + 6144q^{41} - 22784q^{42} - 145040q^{43} + 4736q^{44} - 149340q^{45} - 9920q^{46} - 235064q^{47} - 2048q^{48} + 5226q^{49} + 22600q^{50} + 48248q^{51} - 3648q^{52} + 232736q^{53} - 357200q^{54} - 12784q^{55} + 44800q^{56} + 492044q^{57} + 280528q^{58} + 277180q^{59} + 39968q^{60} + 645300q^{61} + 246928q^{62} + 113572q^{63} - 8192q^{64} - 265194q^{65} - 487360q^{66} - 399008q^{67} - 436288q^{68} - 1183556q^{69} - 551328q^{70} - 864220q^{71} - 50048q^{72} - 22820q^{73} + 237744q^{74} + 220104q^{75} - 105600q^{76} + 1425548q^{77} + 740560q^{78} + 1990404q^{79} + 119808q^{80} + 1852542q^{81} + 295984q^{82} + 462248q^{83} - 77504q^{84} - 749566q^{85} - 1085360q^{86} - 949428q^{87} - 105984q^{88} - 614816q^{89} - 53880q^{90} - 1227448q^{91} - 50304q^{92} - 235936q^{93} + 316544q^{94} + 2580102q^{95} + 40960q^{96} + 1604980q^{97} - 16216q^{98} - 48640q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(230))\)

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
230.6.a \(\chi_{230}(1, \cdot)\) 230.6.a.a 1 1
230.6.a.b 2
230.6.a.c 3
230.6.a.d 3
230.6.a.e 3
230.6.a.f 5
230.6.a.g 5
230.6.a.h 6
230.6.a.i 6
230.6.b \(\chi_{230}(139, \cdot)\) 230.6.b.a 26 1
230.6.b.b 30
230.6.e \(\chi_{230}(137, \cdot)\) n/a 120 2
230.6.g \(\chi_{230}(31, \cdot)\) n/a 400 10
230.6.j \(\chi_{230}(9, \cdot)\) n/a 600 10
230.6.l \(\chi_{230}(7, \cdot)\) n/a 1200 20

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(230))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(230)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 2}\)