Properties

Label 1176.2
Level 1176
Weight 2
Dimension 15041
Nonzero newspaces 24
Sturm bound 150528
Trace bound 8

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Defining parameters

Level: \( N \) = \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(150528\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1176))\).

Total New Old
Modular forms 39072 15429 23643
Cusp forms 36193 15041 21152
Eisenstein series 2879 388 2491

Trace form

\( 15041q - 2q^{2} - 33q^{3} - 64q^{4} - 2q^{5} - 28q^{6} - 72q^{7} + 4q^{8} - 75q^{9} + O(q^{10}) \) \( 15041q - 2q^{2} - 33q^{3} - 64q^{4} - 2q^{5} - 28q^{6} - 72q^{7} + 4q^{8} - 75q^{9} - 56q^{10} - 20q^{11} - 22q^{12} - 26q^{13} - 72q^{15} - 60q^{16} - 26q^{17} - 36q^{18} - 60q^{19} + 64q^{20} + 4q^{22} + 72q^{23} + 30q^{24} - 57q^{25} + 112q^{26} + 3q^{27} + 24q^{28} + 6q^{29} + 62q^{30} + 48q^{31} + 128q^{32} + 4q^{33} + 104q^{34} + 36q^{35} - 26q^{36} + 30q^{37} + 80q^{38} + 48q^{39} + 68q^{40} - 2q^{41} - 72q^{42} - 76q^{43} - 96q^{44} + 82q^{45} - 188q^{46} + 120q^{47} - 158q^{48} - 108q^{49} - 170q^{50} + 108q^{51} - 260q^{52} + 70q^{53} - 216q^{54} + 76q^{55} - 84q^{56} - 52q^{57} - 192q^{58} + 148q^{59} - 234q^{60} - 2q^{61} - 220q^{62} + 18q^{63} - 292q^{64} + 20q^{65} - 214q^{66} + 12q^{67} - 120q^{68} - 40q^{69} - 120q^{70} + 32q^{71} - 246q^{72} - 214q^{73} + 16q^{74} - 115q^{75} - 84q^{76} - 36q^{77} - 214q^{78} - 144q^{79} - 47q^{81} - 96q^{82} + 68q^{83} - 144q^{84} + 20q^{85} - 8q^{86} - 12q^{87} - 44q^{88} + 94q^{89} - 262q^{90} - 12q^{91} - 24q^{92} + 112q^{93} - 180q^{94} + 88q^{95} - 294q^{96} + 194q^{97} - 84q^{98} - 156q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1176))\)

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
1176.2.a \(\chi_{1176}(1, \cdot)\) 1176.2.a.a 1 1
1176.2.a.b 1
1176.2.a.c 1
1176.2.a.d 1
1176.2.a.e 1
1176.2.a.f 1
1176.2.a.g 1
1176.2.a.h 1
1176.2.a.i 1
1176.2.a.j 2
1176.2.a.k 2
1176.2.a.l 2
1176.2.a.m 2
1176.2.a.n 2
1176.2.a.o 2
1176.2.b \(\chi_{1176}(391, \cdot)\) None 0 1
1176.2.c \(\chi_{1176}(589, \cdot)\) 1176.2.c.a 2 1
1176.2.c.b 4
1176.2.c.c 8
1176.2.c.d 12
1176.2.c.e 16
1176.2.c.f 16
1176.2.c.g 24
1176.2.h \(\chi_{1176}(1079, \cdot)\) None 0 1
1176.2.i \(\chi_{1176}(293, \cdot)\) n/a 152 1
1176.2.j \(\chi_{1176}(491, \cdot)\) n/a 154 1
1176.2.k \(\chi_{1176}(881, \cdot)\) 1176.2.k.a 16 1
1176.2.k.b 24
1176.2.p \(\chi_{1176}(979, \cdot)\) 1176.2.p.a 32 1
1176.2.p.b 48
1176.2.q \(\chi_{1176}(361, \cdot)\) 1176.2.q.a 2 2
1176.2.q.b 2
1176.2.q.c 2
1176.2.q.d 2
1176.2.q.e 2
1176.2.q.f 2
1176.2.q.g 2
1176.2.q.h 2
1176.2.q.i 2
1176.2.q.j 2
1176.2.q.k 4
1176.2.q.l 4
1176.2.q.m 4
1176.2.q.n 4
1176.2.q.o 4
1176.2.t \(\chi_{1176}(19, \cdot)\) n/a 160 2
1176.2.u \(\chi_{1176}(521, \cdot)\) 1176.2.u.a 16 2
1176.2.u.b 16
1176.2.u.c 48
1176.2.v \(\chi_{1176}(275, \cdot)\) n/a 304 2
1176.2.ba \(\chi_{1176}(509, \cdot)\) n/a 304 2
1176.2.bb \(\chi_{1176}(263, \cdot)\) None 0 2
1176.2.bc \(\chi_{1176}(373, \cdot)\) n/a 160 2
1176.2.bd \(\chi_{1176}(31, \cdot)\) None 0 2
1176.2.bg \(\chi_{1176}(169, \cdot)\) n/a 168 6
1176.2.bh \(\chi_{1176}(139, \cdot)\) n/a 672 6
1176.2.bm \(\chi_{1176}(41, \cdot)\) n/a 336 6
1176.2.bn \(\chi_{1176}(155, \cdot)\) n/a 1320 6
1176.2.bo \(\chi_{1176}(125, \cdot)\) n/a 1320 6
1176.2.bp \(\chi_{1176}(71, \cdot)\) None 0 6
1176.2.bu \(\chi_{1176}(85, \cdot)\) n/a 672 6
1176.2.bv \(\chi_{1176}(55, \cdot)\) None 0 6
1176.2.bw \(\chi_{1176}(25, \cdot)\) n/a 336 12
1176.2.bz \(\chi_{1176}(103, \cdot)\) None 0 12
1176.2.ca \(\chi_{1176}(37, \cdot)\) n/a 1344 12
1176.2.cb \(\chi_{1176}(23, \cdot)\) None 0 12
1176.2.cc \(\chi_{1176}(5, \cdot)\) n/a 2640 12
1176.2.ch \(\chi_{1176}(11, \cdot)\) n/a 2640 12
1176.2.ci \(\chi_{1176}(17, \cdot)\) n/a 672 12
1176.2.cj \(\chi_{1176}(115, \cdot)\) n/a 1344 12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1176))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1176)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(588))\)\(^{\oplus 2}\)