# Properties

 Label 1560.1 Level 1560 Weight 1 Dimension 64 Nonzero newspaces 4 Newform subspaces 18 Sturm bound 129024 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$4$$ Newform subspaces: $$18$$ Sturm bound: $$129024$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1560))$$.

Total New Old
Modular forms 2616 328 2288
Cusp forms 312 64 248
Eisenstein series 2304 264 2040

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 64 0 0 0

## Trace form

 $$64 q + O(q^{10})$$ $$64 q + 4 q^{10} - 8 q^{12} - 24 q^{16} - 8 q^{22} + 12 q^{27} - 8 q^{30} - 8 q^{31} + 16 q^{34} - 8 q^{39} + 4 q^{40} - 12 q^{42} - 16 q^{43} + 16 q^{46} - 8 q^{49} + 8 q^{52} - 8 q^{55} - 8 q^{66} + 12 q^{75} - 16 q^{79} - 16 q^{81} - 8 q^{82} - 8 q^{88} + 8 q^{90} - 8 q^{94} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1560))$$

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
1560.1.c $$\chi_{1560}(259, \cdot)$$ None 0 1
1560.1.d $$\chi_{1560}(701, \cdot)$$ None 0 1
1560.1.f $$\chi_{1560}(391, \cdot)$$ None 0 1
1560.1.i $$\chi_{1560}(209, \cdot)$$ None 0 1
1560.1.j $$\chi_{1560}(1481, \cdot)$$ None 0 1
1560.1.m $$\chi_{1560}(1039, \cdot)$$ None 0 1
1560.1.o $$\chi_{1560}(989, \cdot)$$ None 0 1
1560.1.p $$\chi_{1560}(1171, \cdot)$$ None 0 1
1560.1.s $$\chi_{1560}(79, \cdot)$$ None 0 1
1560.1.t $$\chi_{1560}(521, \cdot)$$ None 0 1
1560.1.v $$\chi_{1560}(571, \cdot)$$ None 0 1
1560.1.y $$\chi_{1560}(389, \cdot)$$ 1560.1.y.a 1 1
1560.1.y.b 1
1560.1.y.c 1
1560.1.y.d 1
1560.1.y.e 2
1560.1.y.f 2
1560.1.z $$\chi_{1560}(1301, \cdot)$$ None 0 1
1560.1.bc $$\chi_{1560}(859, \cdot)$$ None 0 1
1560.1.be $$\chi_{1560}(1169, \cdot)$$ None 0 1
1560.1.bf $$\chi_{1560}(1351, \cdot)$$ None 0 1
1560.1.bj $$\chi_{1560}(343, \cdot)$$ None 0 2
1560.1.bk $$\chi_{1560}(317, \cdot)$$ None 0 2
1560.1.bl $$\chi_{1560}(307, \cdot)$$ None 0 2
1560.1.bm $$\chi_{1560}(593, \cdot)$$ None 0 2
1560.1.bp $$\chi_{1560}(443, \cdot)$$ None 0 2
1560.1.bs $$\chi_{1560}(623, \cdot)$$ None 0 2
1560.1.bt $$\chi_{1560}(337, \cdot)$$ None 0 2
1560.1.bw $$\chi_{1560}(157, \cdot)$$ None 0 2
1560.1.bx $$\chi_{1560}(421, \cdot)$$ None 0 2
1560.1.ca $$\chi_{1560}(1201, \cdot)$$ None 0 2
1560.1.cc $$\chi_{1560}(239, \cdot)$$ None 0 2
1560.1.cd $$\chi_{1560}(1019, \cdot)$$ None 0 2
1560.1.cf $$\chi_{1560}(551, \cdot)$$ None 0 2
1560.1.ci $$\chi_{1560}(1331, \cdot)$$ None 0 2
1560.1.ck $$\chi_{1560}(109, \cdot)$$ None 0 2
1560.1.cl $$\chi_{1560}(889, \cdot)$$ None 0 2
1560.1.co $$\chi_{1560}(313, \cdot)$$ None 0 2
1560.1.cp $$\chi_{1560}(493, \cdot)$$ None 0 2
1560.1.cs $$\chi_{1560}(467, \cdot)$$ 1560.1.cs.a 4 2
1560.1.cs.b 4
1560.1.cs.c 8
1560.1.cs.d 8
1560.1.cs.e 8
1560.1.cs.f 8
1560.1.ct $$\chi_{1560}(287, \cdot)$$ None 0 2
1560.1.cv $$\chi_{1560}(437, \cdot)$$ None 0 2
1560.1.cw $$\chi_{1560}(463, \cdot)$$ None 0 2
1560.1.db $$\chi_{1560}(473, \cdot)$$ None 0 2
1560.1.dc $$\chi_{1560}(187, \cdot)$$ None 0 2
1560.1.dd $$\chi_{1560}(511, \cdot)$$ None 0 2
1560.1.de $$\chi_{1560}(329, \cdot)$$ None 0 2
1560.1.dg $$\chi_{1560}(139, \cdot)$$ None 0 2
1560.1.dj $$\chi_{1560}(341, \cdot)$$ None 0 2
1560.1.dk $$\chi_{1560}(1109, \cdot)$$ 1560.1.dk.a 4 2
1560.1.dk.b 4
1560.1.dn $$\chi_{1560}(1291, \cdot)$$ None 0 2
1560.1.dp $$\chi_{1560}(1121, \cdot)$$ None 0 2
1560.1.dq $$\chi_{1560}(679, \cdot)$$ None 0 2
1560.1.dt $$\chi_{1560}(211, \cdot)$$ None 0 2
1560.1.du $$\chi_{1560}(29, \cdot)$$ 1560.1.du.a 2 2
1560.1.du.b 2
1560.1.du.c 2
1560.1.du.d 2
1560.1.dw $$\chi_{1560}(199, \cdot)$$ None 0 2
1560.1.dz $$\chi_{1560}(641, \cdot)$$ None 0 2
1560.1.ea $$\chi_{1560}(809, \cdot)$$ None 0 2
1560.1.ed $$\chi_{1560}(991, \cdot)$$ None 0 2
1560.1.ef $$\chi_{1560}(101, \cdot)$$ None 0 2
1560.1.eg $$\chi_{1560}(979, \cdot)$$ None 0 2
1560.1.ei $$\chi_{1560}(137, \cdot)$$ None 0 4
1560.1.ej $$\chi_{1560}(67, \cdot)$$ None 0 4
1560.1.eo $$\chi_{1560}(557, \cdot)$$ None 0 4
1560.1.ep $$\chi_{1560}(487, \cdot)$$ None 0 4
1560.1.er $$\chi_{1560}(263, \cdot)$$ None 0 4
1560.1.es $$\chi_{1560}(563, \cdot)$$ None 0 4
1560.1.ev $$\chi_{1560}(277, \cdot)$$ None 0 4
1560.1.ew $$\chi_{1560}(217, \cdot)$$ None 0 4
1560.1.ey $$\chi_{1560}(409, \cdot)$$ None 0 4
1560.1.fb $$\chi_{1560}(349, \cdot)$$ None 0 4
1560.1.fd $$\chi_{1560}(11, \cdot)$$ None 0 4
1560.1.fe $$\chi_{1560}(71, \cdot)$$ None 0 4
1560.1.fg $$\chi_{1560}(59, \cdot)$$ None 0 4
1560.1.fj $$\chi_{1560}(119, \cdot)$$ None 0 4
1560.1.fl $$\chi_{1560}(241, \cdot)$$ None 0 4
1560.1.fm $$\chi_{1560}(301, \cdot)$$ None 0 4
1560.1.fo $$\chi_{1560}(133, \cdot)$$ None 0 4
1560.1.fr $$\chi_{1560}(433, \cdot)$$ None 0 4
1560.1.fs $$\chi_{1560}(23, \cdot)$$ None 0 4
1560.1.fv $$\chi_{1560}(107, \cdot)$$ None 0 4
1560.1.fy $$\chi_{1560}(427, \cdot)$$ None 0 4
1560.1.fz $$\chi_{1560}(617, \cdot)$$ None 0 4
1560.1.ga $$\chi_{1560}(7, \cdot)$$ None 0 4
1560.1.gb $$\chi_{1560}(197, \cdot)$$ None 0 4

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1560))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1560)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(156))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(195))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(260))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(312))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(520))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(780))$$$$^{\oplus 2}$$