Properties

Label 1176.4
Level 1176
Weight 4
Dimension 45509
Nonzero newspaces 24
Sturm bound 301056
Trace bound 8

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Defining parameters

Level: \( N \) = \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(301056\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1176))\).

Total New Old
Modular forms 114336 45897 68439
Cusp forms 111456 45509 65947
Eisenstein series 2880 388 2492

Trace form

\( 45509q + 2q^{2} - 29q^{3} - 40q^{4} + 14q^{5} - 44q^{6} - 72q^{7} - 76q^{8} - 191q^{9} + O(q^{10}) \) \( 45509q + 2q^{2} - 29q^{3} - 40q^{4} + 14q^{5} - 44q^{6} - 72q^{7} - 76q^{8} - 191q^{9} - 24q^{10} + 140q^{11} - 86q^{12} + 238q^{13} + 192q^{15} - 156q^{16} + 158q^{17} + 136q^{18} + 676q^{19} + 2144q^{20} - 168q^{21} + 700q^{22} - 168q^{23} - 578q^{24} - 1621q^{25} - 2944q^{26} - 449q^{27} - 2664q^{28} - 138q^{29} - 2298q^{30} - 2056q^{31} - 1088q^{32} + 644q^{33} + 768q^{34} + 1044q^{35} - 2q^{36} + 1542q^{37} + 5200q^{38} + 384q^{39} + 1924q^{40} + 518q^{41} - 1332q^{42} + 5172q^{43} - 6240q^{44} + 714q^{45} - 2492q^{46} + 2280q^{47} + 2146q^{48} - 612q^{49} + 6170q^{50} - 1468q^{51} + 10972q^{52} - 3658q^{53} + 6664q^{54} - 13396q^{55} + 4620q^{56} - 5788q^{57} + 5888q^{58} - 9628q^{59} + 1734q^{60} - 2234q^{61} + 700q^{62} + 186q^{63} - 4516q^{64} + 3268q^{65} - 7870q^{66} + 15004q^{67} - 9144q^{68} + 3336q^{69} - 7512q^{70} + 11248q^{71} - 8678q^{72} + 5522q^{73} + 1568q^{74} + 2785q^{75} + 1804q^{76} + 468q^{77} + 6762q^{78} - 2152q^{79} - 2112q^{80} + 13933q^{81} - 5432q^{82} + 6628q^{83} + 8928q^{84} - 2812q^{85} - 760q^{86} + 7308q^{87} - 2636q^{88} - 3466q^{89} + 12882q^{90} - 12108q^{91} - 4728q^{92} - 11352q^{93} - 21252q^{94} - 38632q^{95} - 21350q^{96} + 7994q^{97} - 5964q^{98} - 16540q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1176))\)

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
1176.4.a \(\chi_{1176}(1, \cdot)\) 1176.4.a.a 1 1
1176.4.a.b 1
1176.4.a.c 1
1176.4.a.d 1
1176.4.a.e 1
1176.4.a.f 1
1176.4.a.g 1
1176.4.a.h 1
1176.4.a.i 1
1176.4.a.j 1
1176.4.a.k 1
1176.4.a.l 1
1176.4.a.m 1
1176.4.a.n 1
1176.4.a.o 1
1176.4.a.p 2
1176.4.a.q 2
1176.4.a.r 2
1176.4.a.s 2
1176.4.a.t 2
1176.4.a.u 2
1176.4.a.v 2
1176.4.a.w 2
1176.4.a.x 3
1176.4.a.y 3
1176.4.a.z 4
1176.4.a.ba 4
1176.4.a.bb 4
1176.4.a.bc 4
1176.4.a.bd 4
1176.4.a.be 4
1176.4.b \(\chi_{1176}(391, \cdot)\) None 0 1
1176.4.c \(\chi_{1176}(589, \cdot)\) n/a 246 1
1176.4.h \(\chi_{1176}(1079, \cdot)\) None 0 1
1176.4.i \(\chi_{1176}(293, \cdot)\) n/a 472 1
1176.4.j \(\chi_{1176}(491, \cdot)\) n/a 482 1
1176.4.k \(\chi_{1176}(881, \cdot)\) n/a 120 1
1176.4.p \(\chi_{1176}(979, \cdot)\) n/a 240 1
1176.4.q \(\chi_{1176}(361, \cdot)\) n/a 120 2
1176.4.t \(\chi_{1176}(19, \cdot)\) n/a 480 2
1176.4.u \(\chi_{1176}(521, \cdot)\) n/a 240 2
1176.4.v \(\chi_{1176}(275, \cdot)\) n/a 944 2
1176.4.ba \(\chi_{1176}(509, \cdot)\) n/a 944 2
1176.4.bb \(\chi_{1176}(263, \cdot)\) None 0 2
1176.4.bc \(\chi_{1176}(373, \cdot)\) n/a 480 2
1176.4.bd \(\chi_{1176}(31, \cdot)\) None 0 2
1176.4.bg \(\chi_{1176}(169, \cdot)\) n/a 504 6
1176.4.bh \(\chi_{1176}(139, \cdot)\) n/a 2016 6
1176.4.bm \(\chi_{1176}(41, \cdot)\) n/a 1008 6
1176.4.bn \(\chi_{1176}(155, \cdot)\) n/a 4008 6
1176.4.bo \(\chi_{1176}(125, \cdot)\) n/a 4008 6
1176.4.bp \(\chi_{1176}(71, \cdot)\) None 0 6
1176.4.bu \(\chi_{1176}(85, \cdot)\) n/a 2016 6
1176.4.bv \(\chi_{1176}(55, \cdot)\) None 0 6
1176.4.bw \(\chi_{1176}(25, \cdot)\) n/a 1008 12
1176.4.bz \(\chi_{1176}(103, \cdot)\) None 0 12
1176.4.ca \(\chi_{1176}(37, \cdot)\) n/a 4032 12
1176.4.cb \(\chi_{1176}(23, \cdot)\) None 0 12
1176.4.cc \(\chi_{1176}(5, \cdot)\) n/a 8016 12
1176.4.ch \(\chi_{1176}(11, \cdot)\) n/a 8016 12
1176.4.ci \(\chi_{1176}(17, \cdot)\) n/a 2016 12
1176.4.cj \(\chi_{1176}(115, \cdot)\) n/a 4032 12

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1176))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1176)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(588))\)\(^{\oplus 2}\)