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Properties

Label 576.5
Level 576
Weight 5
Dimension 16317
Nonzero newspaces 16
Sturm bound 92160
Trace bound 25

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Defining parameters

Level: \( N \) = \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(92160\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(576))\).

Total New Old
Modular forms 37440 16515 20925
Cusp forms 36288 16317 19971
Eisenstein series 1152 198 954

Trace form

\( 16317 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 32 q^{6} - 16 q^{7} - 24 q^{8} - 40 q^{9} + O(q^{10}) \) \( 16317 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 32 q^{6} - 16 q^{7} - 24 q^{8} - 40 q^{9} - 72 q^{10} - 114 q^{11} - 32 q^{12} - 376 q^{13} - 24 q^{14} - 24 q^{15} - 24 q^{16} + 438 q^{17} - 32 q^{18} + 650 q^{19} - 24 q^{20} - 32 q^{21} - 2688 q^{22} - 1176 q^{23} - 32 q^{24} + 689 q^{25} + 5376 q^{26} - 24 q^{27} + 5568 q^{28} + 1704 q^{29} - 32 q^{30} - 28 q^{31} - 2544 q^{32} - 348 q^{33} - 7104 q^{34} - 6360 q^{35} - 32 q^{36} - 9960 q^{37} - 7584 q^{38} + 2664 q^{39} + 336 q^{40} + 16098 q^{41} - 32 q^{42} + 16206 q^{43} + 8400 q^{44} + 8224 q^{45} - 72 q^{46} - 12 q^{47} - 32 q^{48} - 11467 q^{49} + 21504 q^{50} - 13784 q^{51} + 8952 q^{52} - 30264 q^{53} - 32 q^{54} + 11724 q^{55} - 24720 q^{56} - 4520 q^{57} - 32784 q^{58} + 43854 q^{59} - 32 q^{60} + 24840 q^{61} - 5544 q^{62} + 9580 q^{63} + 12120 q^{64} + 7044 q^{65} - 32 q^{66} - 45778 q^{67} + 26616 q^{68} + 616 q^{69} + 61128 q^{70} - 59916 q^{71} - 32 q^{72} - 18010 q^{73} + 16608 q^{74} + 2800 q^{75} - 14168 q^{76} + 21588 q^{77} + 108496 q^{78} + 100332 q^{79} + 134544 q^{80} + 30408 q^{81} + 15528 q^{82} - 3858 q^{83} - 115840 q^{84} - 47928 q^{85} - 255552 q^{86} - 49304 q^{87} - 213384 q^{88} - 151134 q^{89} - 223232 q^{90} - 35764 q^{91} - 239424 q^{92} - 34976 q^{93} - 53880 q^{94} + 12 q^{95} + 51920 q^{96} + 54670 q^{97} + 228864 q^{98} + 46568 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(576))\)

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
576.5.b \(\chi_{576}(415, \cdot)\) 576.5.b.a 4 1
576.5.b.b 4
576.5.b.c 4
576.5.b.d 4
576.5.b.e 4
576.5.b.f 4
576.5.b.g 8
576.5.b.h 8
576.5.e \(\chi_{576}(449, \cdot)\) 576.5.e.a 2 1
576.5.e.b 2
576.5.e.c 2
576.5.e.d 2
576.5.e.e 2
576.5.e.f 2
576.5.e.g 2
576.5.e.h 2
576.5.e.i 2
576.5.e.j 2
576.5.e.k 4
576.5.e.l 4
576.5.e.m 4
576.5.g \(\chi_{576}(127, \cdot)\) 576.5.g.a 1 1
576.5.g.b 1
576.5.g.c 1
576.5.g.d 2
576.5.g.e 2
576.5.g.f 2
576.5.g.g 2
576.5.g.h 2
576.5.g.i 2
576.5.g.j 4
576.5.g.k 4
576.5.g.l 4
576.5.g.m 4
576.5.g.n 4
576.5.g.o 4
576.5.h \(\chi_{576}(161, \cdot)\) 576.5.h.a 8 1
576.5.h.b 24
576.5.j \(\chi_{576}(17, \cdot)\) 576.5.j.a 64 2
576.5.m \(\chi_{576}(271, \cdot)\) 576.5.m.a 14 2
576.5.m.b 32
576.5.m.c 32
576.5.n \(\chi_{576}(353, \cdot)\) n/a 192 2
576.5.o \(\chi_{576}(319, \cdot)\) n/a 188 2
576.5.q \(\chi_{576}(65, \cdot)\) n/a 188 2
576.5.t \(\chi_{576}(31, \cdot)\) n/a 192 2
576.5.u \(\chi_{576}(55, \cdot)\) None 0 4
576.5.x \(\chi_{576}(89, \cdot)\) None 0 4
576.5.z \(\chi_{576}(79, \cdot)\) n/a 376 4
576.5.ba \(\chi_{576}(113, \cdot)\) n/a 376 4
576.5.bc \(\chi_{576}(53, \cdot)\) n/a 1024 8
576.5.bf \(\chi_{576}(19, \cdot)\) n/a 1272 8
576.5.bh \(\chi_{576}(7, \cdot)\) None 0 8
576.5.bi \(\chi_{576}(41, \cdot)\) None 0 8
576.5.bk \(\chi_{576}(43, \cdot)\) n/a 6112 16
576.5.bn \(\chi_{576}(5, \cdot)\) n/a 6112 16

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(576))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(576)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 15}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 7}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 2}\)