# Properties

 Label 1232.2 Level 1232 Weight 2 Dimension 24020 Nonzero newspaces 32 Sturm bound 184320 Trace bound 11

## Defining parameters

 Level: $$N$$ = $$1232 = 2^{4} \cdot 7 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Sturm bound: $$184320$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1232))$$.

Total New Old
Modular forms 47760 24832 22928
Cusp forms 44401 24020 20381
Eisenstein series 3359 812 2547

## Trace form

 $$24020 q - 64 q^{2} - 50 q^{3} - 56 q^{4} - 78 q^{5} - 40 q^{6} - 57 q^{7} - 136 q^{8} - 14 q^{9} + O(q^{10})$$ $$24020 q - 64 q^{2} - 50 q^{3} - 56 q^{4} - 78 q^{5} - 40 q^{6} - 57 q^{7} - 136 q^{8} - 14 q^{9} - 56 q^{10} - 47 q^{11} - 152 q^{12} - 72 q^{13} - 84 q^{14} - 98 q^{15} - 88 q^{16} - 142 q^{17} - 48 q^{18} - 6 q^{19} - 40 q^{20} - 58 q^{21} - 176 q^{22} - 66 q^{23} - 56 q^{24} + 34 q^{25} - 40 q^{26} - 32 q^{27} - 60 q^{28} - 142 q^{29} - 72 q^{30} - 58 q^{31} - 24 q^{32} - 97 q^{33} - 120 q^{34} + q^{35} - 168 q^{36} + 18 q^{37} - 104 q^{38} + 72 q^{39} - 88 q^{40} + 72 q^{41} - 220 q^{42} - 36 q^{43} - 124 q^{44} - 120 q^{45} - 128 q^{46} + 46 q^{47} - 264 q^{48} - 187 q^{49} - 344 q^{50} + 34 q^{51} - 288 q^{52} - 166 q^{53} - 392 q^{54} - 30 q^{55} - 360 q^{56} - 190 q^{57} - 272 q^{58} - 114 q^{59} - 392 q^{60} - 238 q^{61} - 208 q^{62} - 124 q^{63} - 320 q^{64} - 166 q^{65} - 180 q^{66} - 166 q^{67} - 176 q^{68} - 130 q^{69} - 296 q^{70} - 74 q^{71} - 432 q^{72} - 126 q^{73} - 256 q^{74} - 20 q^{75} - 328 q^{76} - 138 q^{77} - 848 q^{78} - 58 q^{79} - 464 q^{80} - 212 q^{81} - 456 q^{82} - 48 q^{83} - 332 q^{84} - 398 q^{85} - 376 q^{86} - 122 q^{87} - 692 q^{88} - 98 q^{89} - 568 q^{90} - 235 q^{91} - 544 q^{92} - 254 q^{93} - 456 q^{94} - 262 q^{95} - 280 q^{96} - 328 q^{97} - 168 q^{98} - 350 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1232))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
1232.2.a $$\chi_{1232}(1, \cdot)$$ 1232.2.a.a 1 1
1232.2.a.b 1
1232.2.a.c 1
1232.2.a.d 1
1232.2.a.e 1
1232.2.a.f 1
1232.2.a.g 1
1232.2.a.h 1
1232.2.a.i 1
1232.2.a.j 1
1232.2.a.k 1
1232.2.a.l 1
1232.2.a.m 2
1232.2.a.n 2
1232.2.a.o 2
1232.2.a.p 2
1232.2.a.q 3
1232.2.a.r 3
1232.2.a.s 4
1232.2.c $$\chi_{1232}(617, \cdot)$$ None 0 1
1232.2.e $$\chi_{1232}(769, \cdot)$$ 1232.2.e.a 2 1
1232.2.e.b 4
1232.2.e.c 4
1232.2.e.d 4
1232.2.e.e 8
1232.2.e.f 24
1232.2.f $$\chi_{1232}(351, \cdot)$$ 1232.2.f.a 6 1
1232.2.f.b 6
1232.2.f.c 12
1232.2.f.d 12
1232.2.h $$\chi_{1232}(727, \cdot)$$ None 0 1
1232.2.j $$\chi_{1232}(111, \cdot)$$ 1232.2.j.a 16 1
1232.2.j.b 24
1232.2.l $$\chi_{1232}(967, \cdot)$$ None 0 1
1232.2.o $$\chi_{1232}(153, \cdot)$$ None 0 1
1232.2.q $$\chi_{1232}(177, \cdot)$$ 1232.2.q.a 2 2
1232.2.q.b 2
1232.2.q.c 2
1232.2.q.d 2
1232.2.q.e 2
1232.2.q.f 4
1232.2.q.g 4
1232.2.q.h 4
1232.2.q.i 6
1232.2.q.j 6
1232.2.q.k 6
1232.2.q.l 6
1232.2.q.m 6
1232.2.q.n 8
1232.2.q.o 10
1232.2.q.p 10
1232.2.r $$\chi_{1232}(43, \cdot)$$ n/a 288 2
1232.2.s $$\chi_{1232}(419, \cdot)$$ n/a 320 2
1232.2.x $$\chi_{1232}(461, \cdot)$$ n/a 376 2
1232.2.y $$\chi_{1232}(309, \cdot)$$ n/a 240 2
1232.2.z $$\chi_{1232}(113, \cdot)$$ n/a 144 4
1232.2.ba $$\chi_{1232}(857, \cdot)$$ None 0 2
1232.2.be $$\chi_{1232}(815, \cdot)$$ 1232.2.be.a 24 2
1232.2.be.b 28
1232.2.be.c 28
1232.2.bg $$\chi_{1232}(263, \cdot)$$ None 0 2
1232.2.bi $$\chi_{1232}(527, \cdot)$$ 1232.2.bi.a 32 2
1232.2.bi.b 32
1232.2.bi.c 32
1232.2.bk $$\chi_{1232}(199, \cdot)$$ None 0 2
1232.2.bl $$\chi_{1232}(793, \cdot)$$ None 0 2
1232.2.bn $$\chi_{1232}(241, \cdot)$$ 1232.2.bn.a 12 2
1232.2.bn.b 16
1232.2.bn.c 16
1232.2.bn.d 48
1232.2.bq $$\chi_{1232}(41, \cdot)$$ None 0 4
1232.2.bt $$\chi_{1232}(183, \cdot)$$ None 0 4
1232.2.bv $$\chi_{1232}(223, \cdot)$$ n/a 192 4
1232.2.bx $$\chi_{1232}(279, \cdot)$$ None 0 4
1232.2.bz $$\chi_{1232}(127, \cdot)$$ n/a 144 4
1232.2.ca $$\chi_{1232}(321, \cdot)$$ n/a 184 4
1232.2.cc $$\chi_{1232}(169, \cdot)$$ None 0 4
1232.2.cg $$\chi_{1232}(243, \cdot)$$ n/a 640 4
1232.2.ch $$\chi_{1232}(219, \cdot)$$ n/a 752 4
1232.2.ci $$\chi_{1232}(221, \cdot)$$ n/a 640 4
1232.2.cj $$\chi_{1232}(285, \cdot)$$ n/a 752 4
1232.2.cm $$\chi_{1232}(81, \cdot)$$ n/a 368 8
1232.2.cn $$\chi_{1232}(141, \cdot)$$ n/a 1152 8
1232.2.co $$\chi_{1232}(13, \cdot)$$ n/a 1504 8
1232.2.ct $$\chi_{1232}(27, \cdot)$$ n/a 1504 8
1232.2.cu $$\chi_{1232}(211, \cdot)$$ n/a 1152 8
1232.2.cw $$\chi_{1232}(17, \cdot)$$ n/a 368 8
1232.2.cy $$\chi_{1232}(9, \cdot)$$ None 0 8
1232.2.cz $$\chi_{1232}(103, \cdot)$$ None 0 8
1232.2.db $$\chi_{1232}(79, \cdot)$$ n/a 384 8
1232.2.dd $$\chi_{1232}(39, \cdot)$$ None 0 8
1232.2.df $$\chi_{1232}(31, \cdot)$$ n/a 384 8
1232.2.dj $$\chi_{1232}(73, \cdot)$$ None 0 8
1232.2.dm $$\chi_{1232}(61, \cdot)$$ n/a 3008 16
1232.2.dn $$\chi_{1232}(37, \cdot)$$ n/a 3008 16
1232.2.do $$\chi_{1232}(51, \cdot)$$ n/a 3008 16
1232.2.dp $$\chi_{1232}(3, \cdot)$$ n/a 3008 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1232))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1232)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(154))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(176))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(308))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(616))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1232))$$$$^{\oplus 1}$$