# Properties

 Label 1216.2 Level 1216 Weight 2 Dimension 25402 Nonzero newspaces 24 Sturm bound 184320 Trace bound 49

## Defining parameters

 Level: $$N$$ = $$1216 = 2^{6} \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Sturm bound: $$184320$$ Trace bound: $$49$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1216))$$.

Total New Old
Modular forms 47376 26150 21226
Cusp forms 44785 25402 19383
Eisenstein series 2591 748 1843

## Trace form

 $$25402 q - 128 q^{2} - 96 q^{3} - 128 q^{4} - 128 q^{5} - 128 q^{6} - 92 q^{7} - 128 q^{8} - 154 q^{9} + O(q^{10})$$ $$25402 q - 128 q^{2} - 96 q^{3} - 128 q^{4} - 128 q^{5} - 128 q^{6} - 92 q^{7} - 128 q^{8} - 154 q^{9} - 128 q^{10} - 88 q^{11} - 128 q^{12} - 112 q^{13} - 128 q^{14} - 84 q^{15} - 128 q^{16} - 208 q^{17} - 128 q^{18} - 94 q^{19} - 272 q^{20} - 136 q^{21} - 144 q^{22} - 92 q^{23} - 208 q^{24} - 182 q^{25} - 208 q^{26} - 108 q^{27} - 208 q^{28} - 160 q^{29} - 288 q^{30} - 140 q^{31} - 208 q^{32} - 148 q^{33} - 208 q^{34} - 100 q^{35} - 288 q^{36} - 144 q^{37} - 176 q^{38} - 200 q^{39} - 208 q^{40} - 160 q^{41} - 208 q^{42} - 72 q^{43} - 144 q^{44} - 120 q^{45} - 128 q^{46} - 60 q^{47} - 128 q^{48} - 206 q^{49} - 80 q^{50} - 148 q^{51} - 32 q^{52} - 80 q^{53} - 220 q^{55} - 16 q^{56} - 164 q^{57} - 128 q^{58} - 232 q^{59} + 64 q^{60} - 112 q^{61} - 64 q^{62} - 228 q^{63} + 64 q^{64} - 348 q^{65} + 32 q^{66} - 272 q^{67} - 32 q^{68} - 104 q^{69} + 64 q^{70} - 220 q^{71} + 16 q^{72} - 160 q^{73} - 16 q^{74} - 208 q^{75} - 72 q^{76} - 280 q^{77} - 80 q^{78} - 156 q^{79} - 208 q^{80} - 230 q^{81} - 288 q^{82} - 96 q^{83} - 352 q^{84} - 144 q^{85} - 336 q^{86} - 92 q^{87} - 288 q^{88} - 256 q^{89} - 416 q^{90} - 84 q^{91} - 432 q^{92} - 208 q^{93} - 320 q^{94} - 120 q^{95} - 544 q^{96} - 176 q^{97} - 400 q^{98} - 144 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1216))$$

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
1216.2.a $$\chi_{1216}(1, \cdot)$$ 1216.2.a.a 1 1
1216.2.a.b 1
1216.2.a.c 1
1216.2.a.d 1
1216.2.a.e 1
1216.2.a.f 1
1216.2.a.g 1
1216.2.a.h 1
1216.2.a.i 1
1216.2.a.j 1
1216.2.a.k 1
1216.2.a.l 1
1216.2.a.m 1
1216.2.a.n 1
1216.2.a.o 1
1216.2.a.p 1
1216.2.a.q 1
1216.2.a.r 1
1216.2.a.s 2
1216.2.a.t 2
1216.2.a.u 3
1216.2.a.v 3
1216.2.a.w 4
1216.2.a.x 4
1216.2.b $$\chi_{1216}(607, \cdot)$$ 1216.2.b.a 4 1
1216.2.b.b 4
1216.2.b.c 4
1216.2.b.d 8
1216.2.b.e 8
1216.2.b.f 12
1216.2.c $$\chi_{1216}(609, \cdot)$$ 1216.2.c.a 2 1
1216.2.c.b 2
1216.2.c.c 2
1216.2.c.d 2
1216.2.c.e 4
1216.2.c.f 4
1216.2.c.g 4
1216.2.c.h 8
1216.2.c.i 8
1216.2.h $$\chi_{1216}(1215, \cdot)$$ 1216.2.h.a 2 1
1216.2.h.b 4
1216.2.h.c 4
1216.2.h.d 8
1216.2.h.e 20
1216.2.i $$\chi_{1216}(577, \cdot)$$ 1216.2.i.a 2 2
1216.2.i.b 2
1216.2.i.c 2
1216.2.i.d 2
1216.2.i.e 2
1216.2.i.f 2
1216.2.i.g 2
1216.2.i.h 2
1216.2.i.i 2
1216.2.i.j 2
1216.2.i.k 4
1216.2.i.l 4
1216.2.i.m 6
1216.2.i.n 6
1216.2.i.o 8
1216.2.i.p 8
1216.2.i.q 8
1216.2.i.r 12
1216.2.k $$\chi_{1216}(305, \cdot)$$ 1216.2.k.a 4 2
1216.2.k.b 68
1216.2.m $$\chi_{1216}(303, \cdot)$$ 1216.2.m.a 76 2
1216.2.n $$\chi_{1216}(255, \cdot)$$ 1216.2.n.a 2 2
1216.2.n.b 2
1216.2.n.c 4
1216.2.n.d 6
1216.2.n.e 6
1216.2.n.f 16
1216.2.n.g 40
1216.2.s $$\chi_{1216}(31, \cdot)$$ 1216.2.s.a 4 2
1216.2.s.b 4
1216.2.s.c 4
1216.2.s.d 4
1216.2.s.e 4
1216.2.s.f 4
1216.2.s.g 12
1216.2.s.h 12
1216.2.s.i 32
1216.2.t $$\chi_{1216}(353, \cdot)$$ 1216.2.t.a 8 2
1216.2.t.b 8
1216.2.t.c 16
1216.2.t.d 24
1216.2.t.e 24
1216.2.u $$\chi_{1216}(151, \cdot)$$ None 0 4
1216.2.v $$\chi_{1216}(153, \cdot)$$ None 0 4
1216.2.y $$\chi_{1216}(321, \cdot)$$ n/a 228 6
1216.2.z $$\chi_{1216}(49, \cdot)$$ n/a 152 4
1216.2.bb $$\chi_{1216}(335, \cdot)$$ n/a 152 4
1216.2.bd $$\chi_{1216}(77, \cdot)$$ n/a 1152 8
1216.2.be $$\chi_{1216}(75, \cdot)$$ n/a 1264 8
1216.2.bj $$\chi_{1216}(161, \cdot)$$ n/a 240 6
1216.2.bl $$\chi_{1216}(223, \cdot)$$ n/a 240 6
1216.2.bm $$\chi_{1216}(127, \cdot)$$ n/a 228 6
1216.2.bq $$\chi_{1216}(121, \cdot)$$ None 0 8
1216.2.br $$\chi_{1216}(103, \cdot)$$ None 0 8
1216.2.bs $$\chi_{1216}(15, \cdot)$$ n/a 456 12
1216.2.bu $$\chi_{1216}(17, \cdot)$$ n/a 456 12
1216.2.bw $$\chi_{1216}(27, \cdot)$$ n/a 2528 16
1216.2.bx $$\chi_{1216}(45, \cdot)$$ n/a 2528 16
1216.2.ca $$\chi_{1216}(9, \cdot)$$ None 0 24
1216.2.cb $$\chi_{1216}(71, \cdot)$$ None 0 24
1216.2.cg $$\chi_{1216}(5, \cdot)$$ n/a 7584 48
1216.2.ch $$\chi_{1216}(3, \cdot)$$ n/a 7584 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1216))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1216)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(304))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(608))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1216))$$$$^{\oplus 1}$$