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

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

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

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