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Properties

Label 555.4
Level 555
Weight 4
Dimension 22328
Nonzero newspaces 30
Sturm bound 87552
Trace bound 8

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Defining parameters

Level: \( N \) = \( 555 = 3 \cdot 5 \cdot 37 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(87552\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(555))\).

Total New Old
Modular forms 33408 22744 10664
Cusp forms 32256 22328 9928
Eisenstein series 1152 416 736

Trace form

\( 22328 q - 8 q^{2} - 24 q^{3} - 24 q^{4} - 12 q^{5} - 108 q^{6} - 32 q^{7} + 72 q^{8} + O(q^{10}) \) \( 22328 q - 8 q^{2} - 24 q^{3} - 24 q^{4} - 12 q^{5} - 108 q^{6} - 32 q^{7} + 72 q^{8} + 84 q^{10} + 112 q^{11} - 252 q^{12} - 400 q^{13} - 528 q^{14} - 402 q^{15} - 824 q^{16} - 80 q^{17} + 372 q^{18} + 440 q^{19} + 872 q^{20} + 1068 q^{21} + 968 q^{22} + 576 q^{23} + 540 q^{24} - 280 q^{25} - 3128 q^{26} - 2088 q^{27} - 10104 q^{28} - 3016 q^{29} - 2718 q^{30} - 184 q^{31} + 4376 q^{32} + 1716 q^{33} + 9704 q^{34} + 4712 q^{35} + 5136 q^{36} + 7236 q^{37} + 5680 q^{38} + 3732 q^{39} + 6676 q^{40} + 4184 q^{41} + 252 q^{42} - 1840 q^{43} - 7216 q^{44} - 306 q^{45} - 16552 q^{46} - 5792 q^{47} - 9996 q^{48} - 11892 q^{49} - 1436 q^{50} + 780 q^{51} - 360 q^{52} - 224 q^{53} + 396 q^{54} - 60 q^{55} - 2028 q^{57} - 12208 q^{58} - 20720 q^{59} - 14940 q^{60} - 17388 q^{61} - 21864 q^{62} - 10812 q^{63} - 11088 q^{64} - 1214 q^{65} + 5868 q^{66} + 4144 q^{67} + 18272 q^{68} + 14940 q^{69} + 27168 q^{70} + 20672 q^{71} + 40284 q^{72} + 26840 q^{73} + 45424 q^{74} + 19644 q^{75} + 45640 q^{76} + 21024 q^{77} + 28596 q^{78} + 15352 q^{79} + 10268 q^{80} + 3240 q^{81} - 7464 q^{82} - 5184 q^{83} - 23676 q^{84} - 17850 q^{85} - 50600 q^{86} - 22068 q^{87} - 53760 q^{88} - 28308 q^{89} - 25896 q^{90} - 36952 q^{91} - 21480 q^{92} + 17244 q^{93} - 6904 q^{94} - 6608 q^{95} + 30036 q^{96} - 5040 q^{97} - 808 q^{98} + 1908 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(555))\)

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
555.4.a \(\chi_{555}(1, \cdot)\) 555.4.a.a 1 1
555.4.a.b 1
555.4.a.c 7
555.4.a.d 7
555.4.a.e 8
555.4.a.f 9
555.4.a.g 9
555.4.a.h 10
555.4.a.i 10
555.4.a.j 10
555.4.c \(\chi_{555}(334, \cdot)\) n/a 108 1
555.4.e \(\chi_{555}(406, \cdot)\) 555.4.e.a 38 1
555.4.e.b 38
555.4.g \(\chi_{555}(184, \cdot)\) n/a 112 1
555.4.i \(\chi_{555}(121, \cdot)\) n/a 152 2
555.4.j \(\chi_{555}(43, \cdot)\) n/a 228 2
555.4.m \(\chi_{555}(179, \cdot)\) n/a 448 2
555.4.n \(\chi_{555}(332, \cdot)\) n/a 448 2
555.4.o \(\chi_{555}(38, \cdot)\) n/a 432 2
555.4.s \(\chi_{555}(191, \cdot)\) n/a 304 2
555.4.t \(\chi_{555}(253, \cdot)\) n/a 228 2
555.4.x \(\chi_{555}(64, \cdot)\) n/a 224 2
555.4.z \(\chi_{555}(196, \cdot)\) n/a 152 2
555.4.bb \(\chi_{555}(454, \cdot)\) n/a 232 2
555.4.bc \(\chi_{555}(16, \cdot)\) n/a 456 6
555.4.bd \(\chi_{555}(82, \cdot)\) n/a 456 4
555.4.bg \(\chi_{555}(236, \cdot)\) n/a 608 4
555.4.bh \(\chi_{555}(122, \cdot)\) n/a 896 4
555.4.bi \(\chi_{555}(47, \cdot)\) n/a 896 4
555.4.bm \(\chi_{555}(14, \cdot)\) n/a 896 4
555.4.bn \(\chi_{555}(193, \cdot)\) n/a 456 4
555.4.bp \(\chi_{555}(4, \cdot)\) n/a 672 6
555.4.bs \(\chi_{555}(34, \cdot)\) n/a 696 6
555.4.bt \(\chi_{555}(136, \cdot)\) n/a 456 6
555.4.bx \(\chi_{555}(22, \cdot)\) n/a 1368 12
555.4.bz \(\chi_{555}(56, \cdot)\) n/a 1824 12
555.4.ca \(\chi_{555}(59, \cdot)\) n/a 2688 12
555.4.cc \(\chi_{555}(53, \cdot)\) n/a 2688 12
555.4.cf \(\chi_{555}(62, \cdot)\) n/a 2688 12
555.4.ch \(\chi_{555}(13, \cdot)\) n/a 1368 12

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(555))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(555)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(185))\)\(^{\oplus 2}\)