## 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

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

## 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

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