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Properties

Label 1152.2
Level 1152
Weight 2
Dimension 16200
Nonzero newspaces 20
Sturm bound 147456
Trace bound 33

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Defining parameters

Level: \( N \) = \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(147456\)
Trace bound: \(33\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1152))\).

Total New Old
Modular forms 38144 16632 21512
Cusp forms 35585 16200 19385
Eisenstein series 2559 432 2127

Trace form

\( 16200 q - 48 q^{2} - 48 q^{3} - 48 q^{4} - 48 q^{5} - 64 q^{6} - 36 q^{7} - 48 q^{8} - 80 q^{9} + O(q^{10}) \) \( 16200 q - 48 q^{2} - 48 q^{3} - 48 q^{4} - 48 q^{5} - 64 q^{6} - 36 q^{7} - 48 q^{8} - 80 q^{9} - 144 q^{10} - 36 q^{11} - 64 q^{12} - 48 q^{13} - 48 q^{14} - 48 q^{15} - 48 q^{16} - 72 q^{17} - 64 q^{18} - 108 q^{19} - 48 q^{20} - 64 q^{21} - 48 q^{22} - 44 q^{23} - 64 q^{24} - 76 q^{25} - 48 q^{26} - 48 q^{27} - 144 q^{28} - 64 q^{29} - 64 q^{30} - 56 q^{31} - 48 q^{32} - 128 q^{33} - 48 q^{34} - 60 q^{35} - 64 q^{36} - 160 q^{37} - 48 q^{38} - 48 q^{39} - 48 q^{40} - 76 q^{41} - 64 q^{42} - 44 q^{43} - 48 q^{44} - 64 q^{45} - 144 q^{46} - 24 q^{47} - 64 q^{48} - 44 q^{49} - 48 q^{51} + 48 q^{52} - 16 q^{53} - 64 q^{54} - 76 q^{55} + 64 q^{56} - 80 q^{57} + 96 q^{58} - 4 q^{59} - 64 q^{60} + 16 q^{61} + 48 q^{62} - 48 q^{63} + 48 q^{64} + 16 q^{65} - 64 q^{66} + 4 q^{67} + 48 q^{68} - 40 q^{69} + 144 q^{70} - 4 q^{71} - 64 q^{72} - 116 q^{73} + 64 q^{74} - 8 q^{75} + 80 q^{76} + 68 q^{77} - 64 q^{78} + 24 q^{79} - 32 q^{81} - 144 q^{82} + 84 q^{83} - 64 q^{84} + 88 q^{85} - 48 q^{86} + 64 q^{87} - 48 q^{88} + 132 q^{89} - 64 q^{90} + 36 q^{91} - 48 q^{92} + 32 q^{93} - 48 q^{94} + 144 q^{95} - 64 q^{96} + 96 q^{97} - 48 q^{98} + 80 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1152))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1152.2.a \(\chi_{1152}(1, \cdot)\) 1152.2.a.a 1 1
1152.2.a.b 1
1152.2.a.c 1
1152.2.a.d 1
1152.2.a.e 1
1152.2.a.f 1
1152.2.a.g 1
1152.2.a.h 1
1152.2.a.i 1
1152.2.a.j 1
1152.2.a.k 1
1152.2.a.l 1
1152.2.a.m 1
1152.2.a.n 1
1152.2.a.o 1
1152.2.a.p 1
1152.2.a.q 1
1152.2.a.r 1
1152.2.a.s 1
1152.2.a.t 1
1152.2.c \(\chi_{1152}(1151, \cdot)\) 1152.2.c.a 4 1
1152.2.c.b 4
1152.2.c.c 4
1152.2.c.d 4
1152.2.d \(\chi_{1152}(577, \cdot)\) 1152.2.d.a 2 1
1152.2.d.b 2
1152.2.d.c 2
1152.2.d.d 2
1152.2.d.e 2
1152.2.d.f 2
1152.2.d.g 4
1152.2.d.h 4
1152.2.f \(\chi_{1152}(575, \cdot)\) 1152.2.f.a 4 1
1152.2.f.b 4
1152.2.f.c 4
1152.2.f.d 4
1152.2.i \(\chi_{1152}(385, \cdot)\) 1152.2.i.a 2 2
1152.2.i.b 2
1152.2.i.c 2
1152.2.i.d 2
1152.2.i.e 10
1152.2.i.f 10
1152.2.i.g 10
1152.2.i.h 10
1152.2.i.i 12
1152.2.i.j 12
1152.2.i.k 12
1152.2.i.l 12
1152.2.k \(\chi_{1152}(289, \cdot)\) 1152.2.k.a 2 2
1152.2.k.b 2
1152.2.k.c 8
1152.2.k.d 8
1152.2.k.e 8
1152.2.k.f 8
1152.2.l \(\chi_{1152}(287, \cdot)\) 1152.2.l.a 16 2
1152.2.l.b 16
1152.2.p \(\chi_{1152}(191, \cdot)\) 1152.2.p.a 4 2
1152.2.p.b 4
1152.2.p.c 8
1152.2.p.d 16
1152.2.p.e 16
1152.2.p.f 24
1152.2.p.g 24
1152.2.r \(\chi_{1152}(193, \cdot)\) 1152.2.r.a 4 2
1152.2.r.b 4
1152.2.r.c 4
1152.2.r.d 4
1152.2.r.e 16
1152.2.r.f 16
1152.2.r.g 24
1152.2.r.h 24
1152.2.s \(\chi_{1152}(383, \cdot)\) 1152.2.s.a 24 2
1152.2.s.b 24
1152.2.s.c 24
1152.2.s.d 24
1152.2.v \(\chi_{1152}(145, \cdot)\) 1152.2.v.a 4 4
1152.2.v.b 8
1152.2.v.c 32
1152.2.v.d 32
1152.2.w \(\chi_{1152}(143, \cdot)\) 1152.2.w.a 32 4
1152.2.w.b 32
1152.2.y \(\chi_{1152}(95, \cdot)\) n/a 176 4
1152.2.bb \(\chi_{1152}(97, \cdot)\) n/a 176 4
1152.2.bd \(\chi_{1152}(73, \cdot)\) None 0 8
1152.2.be \(\chi_{1152}(71, \cdot)\) None 0 8
1152.2.bg \(\chi_{1152}(49, \cdot)\) n/a 368 8
1152.2.bj \(\chi_{1152}(47, \cdot)\) n/a 368 8
1152.2.bl \(\chi_{1152}(37, \cdot)\) n/a 1264 16
1152.2.bm \(\chi_{1152}(35, \cdot)\) n/a 1024 16
1152.2.bp \(\chi_{1152}(23, \cdot)\) None 0 16
1152.2.bq \(\chi_{1152}(25, \cdot)\) None 0 16
1152.2.bs \(\chi_{1152}(11, \cdot)\) n/a 6080 32
1152.2.bv \(\chi_{1152}(13, \cdot)\) n/a 6080 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1152))\) into lower level spaces

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