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Properties

Label 1152.5
Level 1152
Weight 5
Dimension 65448
Nonzero newspaces 20
Sturm bound 368640
Trace bound 33

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Defining parameters

Level: \( N \) = \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(368640\)
Trace bound: \(33\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(1152))\).

Total New Old
Modular forms 148736 65880 82856
Cusp forms 146176 65448 80728
Eisenstein series 2560 432 2128

Trace form

\( 65448 q - 48 q^{2} - 48 q^{3} - 48 q^{4} - 48 q^{5} - 64 q^{6} - 36 q^{7} - 48 q^{8} - 80 q^{9} + O(q^{10}) \) \( 65448 q - 48 q^{2} - 48 q^{3} - 48 q^{4} - 48 q^{5} - 64 q^{6} - 36 q^{7} - 48 q^{8} - 80 q^{9} - 144 q^{10} - 36 q^{11} - 64 q^{12} - 48 q^{13} - 48 q^{14} - 48 q^{15} - 48 q^{16} - 72 q^{17} - 64 q^{18} - 108 q^{19} - 48 q^{20} - 64 q^{21} - 48 q^{22} + 1116 q^{23} - 64 q^{24} - 1404 q^{25} - 48 q^{26} - 48 q^{27} - 144 q^{28} - 1776 q^{29} - 64 q^{30} - 40 q^{31} - 48 q^{32} - 128 q^{33} - 48 q^{34} + 5148 q^{35} - 64 q^{36} + 3504 q^{37} - 48 q^{38} - 48 q^{39} - 48 q^{40} - 2940 q^{41} - 64 q^{42} - 5604 q^{43} - 48 q^{44} - 64 q^{45} - 144 q^{46} - 48 q^{47} - 64 q^{48} - 9676 q^{49} - 43104 q^{50} - 48 q^{51} - 18000 q^{52} + 1872 q^{53} - 64 q^{54} + 11668 q^{55} + 49344 q^{56} - 80 q^{57} + 65472 q^{58} + 13020 q^{59} - 64 q^{60} + 15056 q^{61} + 11760 q^{62} - 48 q^{63} - 24528 q^{64} - 16176 q^{65} - 64 q^{66} - 18916 q^{67} - 53328 q^{68} - 712 q^{69} - 122352 q^{70} - 20004 q^{71} - 64 q^{72} - 29620 q^{73} - 33312 q^{74} - 5048 q^{75} + 28240 q^{76} - 10044 q^{77} - 64 q^{78} - 50208 q^{79} + 105216 q^{80} - 30560 q^{81} - 144 q^{82} + 31644 q^{83} - 64 q^{84} + 72152 q^{85} - 48 q^{86} + 98512 q^{87} - 48 q^{88} + 163524 q^{89} - 64 q^{90} + 95508 q^{91} - 48 q^{92} + 34880 q^{93} - 48 q^{94} - 24 q^{95} - 64 q^{96} - 73056 q^{97} - 48 q^{98} - 93232 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(1152))\)

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
1152.5.b \(\chi_{1152}(703, \cdot)\) 1152.5.b.a 2 1
1152.5.b.b 2
1152.5.b.c 2
1152.5.b.d 2
1152.5.b.e 4
1152.5.b.f 4
1152.5.b.g 4
1152.5.b.h 4
1152.5.b.i 4
1152.5.b.j 4
1152.5.b.k 8
1152.5.b.l 8
1152.5.b.m 16
1152.5.b.n 16
1152.5.e \(\chi_{1152}(1025, \cdot)\) 1152.5.e.a 8 1
1152.5.e.b 8
1152.5.e.c 8
1152.5.e.d 8
1152.5.e.e 8
1152.5.e.f 8
1152.5.e.g 8
1152.5.e.h 8
1152.5.g \(\chi_{1152}(127, \cdot)\) 1152.5.g.a 8 1
1152.5.g.b 8
1152.5.g.c 16
1152.5.g.d 16
1152.5.g.e 16
1152.5.g.f 16
1152.5.h \(\chi_{1152}(449, \cdot)\) 1152.5.h.a 4 1
1152.5.h.b 4
1152.5.h.c 8
1152.5.h.d 8
1152.5.h.e 8
1152.5.h.f 16
1152.5.h.g 16
1152.5.j \(\chi_{1152}(161, \cdot)\) n/a 128 2
1152.5.m \(\chi_{1152}(415, \cdot)\) n/a 156 2
1152.5.n \(\chi_{1152}(65, \cdot)\) n/a 384 2
1152.5.o \(\chi_{1152}(511, \cdot)\) n/a 384 2
1152.5.q \(\chi_{1152}(257, \cdot)\) n/a 384 2
1152.5.t \(\chi_{1152}(319, \cdot)\) n/a 384 2
1152.5.u \(\chi_{1152}(271, \cdot)\) n/a 316 4
1152.5.x \(\chi_{1152}(17, \cdot)\) n/a 256 4
1152.5.z \(\chi_{1152}(31, \cdot)\) n/a 752 4
1152.5.ba \(\chi_{1152}(353, \cdot)\) n/a 752 4
1152.5.bc \(\chi_{1152}(89, \cdot)\) None 0 8
1152.5.bf \(\chi_{1152}(55, \cdot)\) None 0 8
1152.5.bh \(\chi_{1152}(79, \cdot)\) n/a 1520 8
1152.5.bi \(\chi_{1152}(113, \cdot)\) n/a 1520 8
1152.5.bk \(\chi_{1152}(19, \cdot)\) n/a 5104 16
1152.5.bn \(\chi_{1152}(53, \cdot)\) n/a 4096 16
1152.5.bo \(\chi_{1152}(7, \cdot)\) None 0 16
1152.5.br \(\chi_{1152}(41, \cdot)\) None 0 16
1152.5.bt \(\chi_{1152}(5, \cdot)\) n/a 24512 32
1152.5.bu \(\chi_{1152}(43, \cdot)\) n/a 24512 32

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(1152))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(1152)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 14}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 15}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 7}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(576))\)\(^{\oplus 2}\)