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Properties

Label 230.5
Level 230
Weight 5
Dimension 1928
Nonzero newspaces 6
Sturm bound 15840
Trace bound 1

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Defining parameters

Level: \( N \) = \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(15840\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(230))\).

Total New Old
Modular forms 6512 1928 4584
Cusp forms 6160 1928 4232
Eisenstein series 352 0 352

Trace form

\( 1928 q - 40 q^{3} + 120 q^{5} + 128 q^{6} - 40 q^{7} + O(q^{10}) \) \( 1928 q - 40 q^{3} + 120 q^{5} + 128 q^{6} - 40 q^{7} - 320 q^{10} - 336 q^{11} - 320 q^{12} + 120 q^{13} + 2886 q^{15} + 512 q^{16} + 60 q^{17} - 5760 q^{18} - 3828 q^{19} - 1584 q^{20} - 7348 q^{21} - 2560 q^{22} + 2340 q^{23} + 6812 q^{25} + 9024 q^{26} + 18500 q^{27} + 5600 q^{28} + 2772 q^{29} - 3328 q^{30} - 5300 q^{31} - 23180 q^{33} + 11040 q^{35} - 64 q^{36} - 5000 q^{37} - 1920 q^{38} - 22176 q^{39} - 2560 q^{40} - 22512 q^{41} + 4480 q^{42} - 15752 q^{43} - 12800 q^{45} - 2176 q^{46} + 12600 q^{47} + 2560 q^{48} + 43296 q^{49} + 9600 q^{50} + 56272 q^{51} + 960 q^{52} + 24504 q^{53} + 54208 q^{54} + 43188 q^{55} + 10752 q^{56} - 31756 q^{57} - 21120 q^{58} - 106656 q^{59} + 64 q^{60} - 75872 q^{61} - 62016 q^{62} - 126500 q^{63} - 71142 q^{65} - 65280 q^{66} - 29024 q^{67} - 16320 q^{68} + 30140 q^{69} + 20736 q^{70} + 75924 q^{71} + 55296 q^{72} + 78960 q^{73} + 118272 q^{74} + 172390 q^{75} + 10240 q^{76} + 173580 q^{77} + 85440 q^{78} + 64240 q^{79} - 3456 q^{80} - 72504 q^{81} - 34304 q^{82} - 152124 q^{83} - 61952 q^{84} - 139860 q^{85} - 90816 q^{86} - 107104 q^{87} + 20480 q^{88} - 15312 q^{89} - 18880 q^{90} - 31056 q^{91} - 12960 q^{92} - 4240 q^{93} - 164610 q^{95} - 8192 q^{96} - 144468 q^{97} - 92160 q^{98} + 52404 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(230))\)

We only show spaces with odd 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
230.5.c \(\chi_{230}(229, \cdot)\) 230.5.c.a 48 1
230.5.d \(\chi_{230}(91, \cdot)\) 230.5.d.a 32 1
230.5.f \(\chi_{230}(47, \cdot)\) 230.5.f.a 44 2
230.5.f.b 44
230.5.h \(\chi_{230}(11, \cdot)\) n/a 320 10
230.5.i \(\chi_{230}(19, \cdot)\) n/a 480 10
230.5.k \(\chi_{230}(3, \cdot)\) n/a 960 20

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(230))\) into lower level spaces

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