# Properties

 Label 2816.2 Level 2816 Weight 2 Dimension 135000 Nonzero newspaces 24 Sturm bound 983040 Trace bound 129

## Defining parameters

 Level: $$N$$ = $$2816 = 2^{8} \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Sturm bound: $$983040$$ Trace bound: $$129$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2816))$$.

Total New Old
Modular forms 249280 136872 112408
Cusp forms 242241 135000 107241
Eisenstein series 7039 1872 5167

## Trace form

 $$135000 q - 256 q^{2} - 192 q^{3} - 256 q^{4} - 256 q^{5} - 256 q^{6} - 192 q^{7} - 256 q^{8} - 320 q^{9} + O(q^{10})$$ $$135000 q - 256 q^{2} - 192 q^{3} - 256 q^{4} - 256 q^{5} - 256 q^{6} - 192 q^{7} - 256 q^{8} - 320 q^{9} - 256 q^{10} - 216 q^{11} - 576 q^{12} - 256 q^{13} - 256 q^{14} - 192 q^{15} - 256 q^{16} - 384 q^{17} - 256 q^{18} - 192 q^{19} - 256 q^{20} - 256 q^{21} - 288 q^{22} - 432 q^{23} - 256 q^{24} - 320 q^{25} - 256 q^{26} - 192 q^{27} - 256 q^{28} - 256 q^{29} - 256 q^{30} - 176 q^{31} - 256 q^{32} - 504 q^{33} - 576 q^{34} - 192 q^{35} - 256 q^{36} - 256 q^{37} - 256 q^{38} - 192 q^{39} - 256 q^{40} - 320 q^{41} - 256 q^{42} - 192 q^{43} - 288 q^{44} - 528 q^{45} - 256 q^{46} - 192 q^{47} - 256 q^{48} - 328 q^{49} - 256 q^{50} - 128 q^{51} - 256 q^{52} - 192 q^{53} - 256 q^{54} - 152 q^{55} - 576 q^{56} - 192 q^{57} - 256 q^{58} - 64 q^{59} - 256 q^{60} - 128 q^{61} - 256 q^{62} - 48 q^{63} - 256 q^{64} - 448 q^{65} - 288 q^{66} - 272 q^{67} - 256 q^{68} - 128 q^{69} - 256 q^{70} - 64 q^{71} - 256 q^{72} - 192 q^{73} - 256 q^{74} - 64 q^{75} - 256 q^{76} - 256 q^{77} - 576 q^{78} - 128 q^{79} - 256 q^{80} - 312 q^{81} - 256 q^{82} - 192 q^{83} - 256 q^{84} - 176 q^{85} - 256 q^{86} - 192 q^{87} - 288 q^{88} - 720 q^{89} - 256 q^{90} - 192 q^{91} - 256 q^{92} - 352 q^{93} - 256 q^{94} - 176 q^{95} - 256 q^{96} - 448 q^{97} - 256 q^{98} - 192 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2816))$$

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
2816.2.a $$\chi_{2816}(1, \cdot)$$ 2816.2.a.a 2 1
2816.2.a.b 2
2816.2.a.c 2
2816.2.a.d 2
2816.2.a.e 2
2816.2.a.f 2
2816.2.a.g 2
2816.2.a.h 2
2816.2.a.i 3
2816.2.a.j 3
2816.2.a.k 3
2816.2.a.l 3
2816.2.a.m 4
2816.2.a.n 4
2816.2.a.o 5
2816.2.a.p 5
2816.2.a.q 5
2816.2.a.r 5
2816.2.a.s 6
2816.2.a.t 6
2816.2.a.u 6
2816.2.a.v 6
2816.2.c $$\chi_{2816}(1409, \cdot)$$ 2816.2.c.a 2 1
2816.2.c.b 2
2816.2.c.c 2
2816.2.c.d 2
2816.2.c.e 2
2816.2.c.f 2
2816.2.c.g 2
2816.2.c.h 2
2816.2.c.i 2
2816.2.c.j 2
2816.2.c.k 2
2816.2.c.l 2
2816.2.c.m 2
2816.2.c.n 2
2816.2.c.o 4
2816.2.c.p 4
2816.2.c.q 4
2816.2.c.r 4
2816.2.c.s 4
2816.2.c.t 4
2816.2.c.u 4
2816.2.c.v 4
2816.2.c.w 4
2816.2.c.x 4
2816.2.c.y 6
2816.2.c.z 6
2816.2.e $$\chi_{2816}(2815, \cdot)$$ 2816.2.e.a 2 1
2816.2.e.b 2
2816.2.e.c 4
2816.2.e.d 4
2816.2.e.e 4
2816.2.e.f 4
2816.2.e.g 6
2816.2.e.h 6
2816.2.e.i 6
2816.2.e.j 6
2816.2.e.k 8
2816.2.e.l 8
2816.2.e.m 8
2816.2.e.n 8
2816.2.e.o 16
2816.2.g $$\chi_{2816}(1407, \cdot)$$ 2816.2.g.a 4 1
2816.2.g.b 8
2816.2.g.c 8
2816.2.g.d 12
2816.2.g.e 12
2816.2.g.f 12
2816.2.g.g 12
2816.2.g.h 12
2816.2.g.i 12
2816.2.i $$\chi_{2816}(703, \cdot)$$ n/a 192 2
2816.2.j $$\chi_{2816}(705, \cdot)$$ n/a 160 2
2816.2.m $$\chi_{2816}(257, \cdot)$$ n/a 368 4
2816.2.n $$\chi_{2816}(353, \cdot)$$ n/a 320 4
2816.2.q $$\chi_{2816}(351, \cdot)$$ n/a 368 4
2816.2.s $$\chi_{2816}(127, \cdot)$$ n/a 368 4
2816.2.u $$\chi_{2816}(255, \cdot)$$ n/a 368 4
2816.2.w $$\chi_{2816}(641, \cdot)$$ n/a 368 4
2816.2.z $$\chi_{2816}(177, \cdot)$$ n/a 640 8
2816.2.bb $$\chi_{2816}(175, \cdot)$$ n/a 752 8
2816.2.be $$\chi_{2816}(449, \cdot)$$ n/a 768 8
2816.2.bf $$\chi_{2816}(63, \cdot)$$ n/a 768 8
2816.2.bg $$\chi_{2816}(89, \cdot)$$ None 0 16
2816.2.bh $$\chi_{2816}(87, \cdot)$$ None 0 16
2816.2.bk $$\chi_{2816}(95, \cdot)$$ n/a 1472 16
2816.2.bn $$\chi_{2816}(97, \cdot)$$ n/a 1472 16
2816.2.bo $$\chi_{2816}(45, \cdot)$$ n/a 10240 32
2816.2.bp $$\chi_{2816}(43, \cdot)$$ n/a 12224 32
2816.2.bs $$\chi_{2816}(79, \cdot)$$ n/a 3008 32
2816.2.bu $$\chi_{2816}(49, \cdot)$$ n/a 3008 32
2816.2.by $$\chi_{2816}(9, \cdot)$$ None 0 64
2816.2.bz $$\chi_{2816}(7, \cdot)$$ None 0 64
2816.2.cc $$\chi_{2816}(19, \cdot)$$ n/a 48896 128
2816.2.cd $$\chi_{2816}(5, \cdot)$$ n/a 48896 128

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2816))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2816)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(176))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(256))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(352))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(704))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1408))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2816))$$$$^{\oplus 1}$$