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Properties

Label 2312.4
Level 2312
Weight 4
Dimension 278231
Nonzero newspaces 18
Sturm bound 1331712
Trace bound 4

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Defining parameters

Level: \( N \) = \( 2312 = 2^{3} \cdot 17^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(1331712\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2312))\).

Total New Old
Modular forms 501792 279705 222087
Cusp forms 496992 278231 218761
Eisenstein series 4800 1474 3326

Trace form

\( 278231 q - 242 q^{2} - 244 q^{3} - 252 q^{4} - 2 q^{5} - 212 q^{6} - 232 q^{7} - 200 q^{8} - 493 q^{9} + O(q^{10}) \) \( 278231 q - 242 q^{2} - 244 q^{3} - 252 q^{4} - 2 q^{5} - 212 q^{6} - 232 q^{7} - 200 q^{8} - 493 q^{9} - 296 q^{10} - 284 q^{11} - 296 q^{12} + 22 q^{13} - 224 q^{14} - 120 q^{15} - 224 q^{16} - 512 q^{17} - 462 q^{18} - 196 q^{19} - 128 q^{20} - 96 q^{21} - 324 q^{22} - 600 q^{23} - 352 q^{24} + 985 q^{25} + 40 q^{26} + 344 q^{27} - 144 q^{28} - 322 q^{29} - 352 q^{30} - 1680 q^{31} - 592 q^{32} - 2248 q^{33} - 256 q^{34} - 2496 q^{35} - 228 q^{36} - 1506 q^{37} - 436 q^{38} - 1080 q^{39} - 16 q^{40} + 102 q^{41} - 464 q^{42} + 2548 q^{43} - 72 q^{44} + 3982 q^{45} + 64 q^{46} + 960 q^{47} - 432 q^{48} - 805 q^{49} - 266 q^{50} - 256 q^{51} - 1024 q^{52} - 3674 q^{53} - 17912 q^{54} - 9032 q^{55} - 10960 q^{56} - 2328 q^{57} - 6232 q^{58} - 1388 q^{59} + 3664 q^{60} + 2950 q^{61} + 7600 q^{62} + 13048 q^{63} + 10896 q^{64} + 2060 q^{65} + 26632 q^{66} + 6348 q^{67} + 11536 q^{68} + 12704 q^{69} + 21680 q^{70} + 5624 q^{71} + 19272 q^{72} - 26 q^{73} + 5848 q^{74} + 3412 q^{75} - 968 q^{76} - 3264 q^{77} - 17568 q^{78} - 8064 q^{79} - 21520 q^{80} - 7821 q^{81} - 22980 q^{82} - 12756 q^{83} - 32592 q^{84} + 2604 q^{85} - 2788 q^{86} + 11112 q^{87} + 96 q^{88} + 6046 q^{89} - 4184 q^{90} + 1440 q^{91} + 1584 q^{92} - 3072 q^{93} - 912 q^{94} - 10552 q^{95} - 688 q^{96} - 4154 q^{97} + 318 q^{98} - 14300 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2312))\)

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
2312.4.a \(\chi_{2312}(1, \cdot)\) 2312.4.a.a 1 1
2312.4.a.b 2
2312.4.a.c 3
2312.4.a.d 3
2312.4.a.e 4
2312.4.a.f 6
2312.4.a.g 6
2312.4.a.h 6
2312.4.a.i 6
2312.4.a.j 6
2312.4.a.k 8
2312.4.a.l 14
2312.4.a.m 14
2312.4.a.n 18
2312.4.a.o 18
2312.4.a.p 18
2312.4.a.q 18
2312.4.a.r 24
2312.4.a.s 28
2312.4.b \(\chi_{2312}(577, \cdot)\) n/a 202 1
2312.4.c \(\chi_{2312}(1157, \cdot)\) n/a 798 1
2312.4.h \(\chi_{2312}(1733, \cdot)\) n/a 796 1
2312.4.i \(\chi_{2312}(829, \cdot)\) n/a 1592 2
2312.4.k \(\chi_{2312}(905, \cdot)\) n/a 404 2
2312.4.n \(\chi_{2312}(977, \cdot)\) n/a 812 4
2312.4.o \(\chi_{2312}(733, \cdot)\) n/a 3184 4
2312.4.r \(\chi_{2312}(447, \cdot)\) None 0 8
2312.4.s \(\chi_{2312}(75, \cdot)\) n/a 6368 8
2312.4.u \(\chi_{2312}(137, \cdot)\) n/a 3680 16
2312.4.v \(\chi_{2312}(101, \cdot)\) n/a 14656 16
2312.4.ba \(\chi_{2312}(69, \cdot)\) n/a 14656 16
2312.4.bb \(\chi_{2312}(33, \cdot)\) n/a 3680 16
2312.4.bd \(\chi_{2312}(81, \cdot)\) n/a 7360 32
2312.4.bf \(\chi_{2312}(13, \cdot)\) n/a 29312 32
2312.4.bh \(\chi_{2312}(53, \cdot)\) n/a 58624 64
2312.4.bi \(\chi_{2312}(9, \cdot)\) n/a 14656 64
2312.4.bl \(\chi_{2312}(3, \cdot)\) n/a 117248 128
2312.4.bm \(\chi_{2312}(7, \cdot)\) None 0 128

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2312))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2312)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(578))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1156))\)\(^{\oplus 2}\)