## Defining parameters

 Level: $$N$$ = $$1512 = 2^{3} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$9$$ Newform subspaces: $$20$$ Sturm bound: $$124416$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1512))$$.

Total New Old
Modular forms 2422 388 2034
Cusp forms 262 68 194
Eisenstein series 2160 320 1840

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 56 8 4 0

## Trace form

 $$68q - 6q^{4} + O(q^{10})$$ $$68q - 6q^{4} + 8q^{10} + 2q^{11} + 2q^{14} - 12q^{15} - 2q^{16} - 4q^{17} - 6q^{19} + 4q^{22} - 16q^{23} + 2q^{25} - 4q^{26} + 2q^{28} - 10q^{31} + 4q^{35} + 6q^{40} - 4q^{41} - 4q^{43} + 4q^{44} - 2q^{49} - 16q^{50} - 16q^{55} + 6q^{56} + 10q^{58} - 2q^{61} - 12q^{64} - 14q^{65} - 4q^{67} - 2q^{68} + 22q^{70} + 24q^{72} - 2q^{73} + 2q^{74} + 4q^{76} - 12q^{78} - 4q^{79} - 12q^{81} - 4q^{83} + 8q^{85} - 8q^{88} + 4q^{89} - 8q^{91} + 20q^{92} + 8q^{95} + 4q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1512))$$

We only show spaces with odd 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
1512.1.d $$\chi_{1512}(1457, \cdot)$$ None 0 1
1512.1.e $$\chi_{1512}(755, \cdot)$$ 1512.1.e.a 1 1
1512.1.e.b 1
1512.1.e.c 1
1512.1.e.d 1
1512.1.f $$\chi_{1512}(433, \cdot)$$ None 0 1
1512.1.g $$\chi_{1512}(379, \cdot)$$ None 0 1
1512.1.l $$\chi_{1512}(1189, \cdot)$$ 1512.1.l.a 4 1
1512.1.m $$\chi_{1512}(1135, \cdot)$$ None 0 1
1512.1.n $$\chi_{1512}(701, \cdot)$$ None 0 1
1512.1.o $$\chi_{1512}(1511, \cdot)$$ None 0 1
1512.1.u $$\chi_{1512}(395, \cdot)$$ None 0 2
1512.1.v $$\chi_{1512}(737, \cdot)$$ None 0 2
1512.1.ba $$\chi_{1512}(667, \cdot)$$ 1512.1.ba.a 4 2
1512.1.bb $$\chi_{1512}(577, \cdot)$$ None 0 2
1512.1.bc $$\chi_{1512}(215, \cdot)$$ None 0 2
1512.1.bd $$\chi_{1512}(53, \cdot)$$ 1512.1.bd.a 2 2
1512.1.bd.b 2
1512.1.bd.c 2
1512.1.bd.d 2
1512.1.bg $$\chi_{1512}(197, \cdot)$$ None 0 2
1512.1.bh $$\chi_{1512}(143, \cdot)$$ None 0 2
1512.1.bi $$\chi_{1512}(989, \cdot)$$ None 0 2
1512.1.bj $$\chi_{1512}(503, \cdot)$$ None 0 2
1512.1.bn $$\chi_{1512}(181, \cdot)$$ 1512.1.bn.a 2 2
1512.1.bn.b 2
1512.1.bn.c 4
1512.1.bo $$\chi_{1512}(415, \cdot)$$ None 0 2
1512.1.bp $$\chi_{1512}(829, \cdot)$$ None 0 2
1512.1.bq $$\chi_{1512}(127, \cdot)$$ None 0 2
1512.1.bv $$\chi_{1512}(487, \cdot)$$ None 0 2
1512.1.bw $$\chi_{1512}(325, \cdot)$$ 1512.1.bw.a 4 2
1512.1.bw.b 4
1512.1.bx $$\chi_{1512}(163, \cdot)$$ None 0 2
1512.1.by $$\chi_{1512}(649, \cdot)$$ None 0 2
1512.1.cd $$\chi_{1512}(937, \cdot)$$ None 0 2
1512.1.ce $$\chi_{1512}(235, \cdot)$$ 1512.1.ce.a 4 2
1512.1.cf $$\chi_{1512}(73, \cdot)$$ None 0 2
1512.1.cg $$\chi_{1512}(883, \cdot)$$ None 0 2
1512.1.cl $$\chi_{1512}(449, \cdot)$$ None 0 2
1512.1.cm $$\chi_{1512}(899, \cdot)$$ None 0 2
1512.1.cn $$\chi_{1512}(233, \cdot)$$ None 0 2
1512.1.co $$\chi_{1512}(251, \cdot)$$ None 0 2
1512.1.ct $$\chi_{1512}(971, \cdot)$$ None 0 2
1512.1.cu $$\chi_{1512}(809, \cdot)$$ 1512.1.cu.a 4 2
1512.1.cv $$\chi_{1512}(1423, \cdot)$$ None 0 2
1512.1.cw $$\chi_{1512}(397, \cdot)$$ None 0 2
1512.1.da $$\chi_{1512}(1151, \cdot)$$ None 0 2
1512.1.db $$\chi_{1512}(557, \cdot)$$ None 0 2
1512.1.df $$\chi_{1512}(241, \cdot)$$ None 0 6
1512.1.dh $$\chi_{1512}(149, \cdot)$$ None 0 6
1512.1.dk $$\chi_{1512}(137, \cdot)$$ None 0 6
1512.1.dm $$\chi_{1512}(229, \cdot)$$ None 0 6
1512.1.do $$\chi_{1512}(67, \cdot)$$ None 0 6
1512.1.dp $$\chi_{1512}(167, \cdot)$$ None 0 6
1512.1.dq $$\chi_{1512}(43, \cdot)$$ None 0 6
1512.1.ds $$\chi_{1512}(47, \cdot)$$ None 0 6
1512.1.dt $$\chi_{1512}(59, \cdot)$$ None 0 6
1512.1.dw $$\chi_{1512}(295, \cdot)$$ None 0 6
1512.1.dy $$\chi_{1512}(83, \cdot)$$ None 0 6
1512.1.dz $$\chi_{1512}(79, \cdot)$$ None 0 6
1512.1.ec $$\chi_{1512}(61, \cdot)$$ None 0 6
1512.1.ed $$\chi_{1512}(113, \cdot)$$ None 0 6
1512.1.ef $$\chi_{1512}(13, \cdot)$$ 1512.1.ef.a 6 6
1512.1.ef.b 6
1512.1.ef.c 12
1512.1.ei $$\chi_{1512}(65, \cdot)$$ None 0 6
1512.1.ej $$\chi_{1512}(221, \cdot)$$ None 0 6
1512.1.em $$\chi_{1512}(97, \cdot)$$ None 0 6
1512.1.eo $$\chi_{1512}(29, \cdot)$$ None 0 6
1512.1.ep $$\chi_{1512}(313, \cdot)$$ None 0 6
1512.1.er $$\chi_{1512}(151, \cdot)$$ None 0 6
1512.1.et $$\chi_{1512}(131, \cdot)$$ None 0 6
1512.1.ev $$\chi_{1512}(383, \cdot)$$ None 0 6
1512.1.ex $$\chi_{1512}(403, \cdot)$$ None 0 6

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1512))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1512)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(189))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(216))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(252))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(504))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(756))$$$$^{\oplus 2}$$