# Properties

 Label 1248.1 Level 1248 Weight 1 Dimension 32 Nonzero newspaces 4 Newform subspaces 4 Sturm bound 86016 Trace bound 13

## Defining parameters

 Level: $$N$$ = $$1248 = 2^{5} \cdot 3 \cdot 13$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$4$$ Newform subspaces: $$4$$ Sturm bound: $$86016$$ Trace bound: $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1248))$$.

Total New Old
Modular forms 1716 252 1464
Cusp forms 180 32 148
Eisenstein series 1536 220 1316

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 24 0 8 0

## Trace form

 $$32q - 8q^{9} + O(q^{10})$$ $$32q - 8q^{9} - 16q^{12} + 8q^{21} - 16q^{22} - 4q^{33} - 4q^{37} + 4q^{39} + 4q^{45} - 4q^{49} + 8q^{55} - 4q^{61} + 8q^{69} + 8q^{73} + 16q^{75} + 12q^{81} - 4q^{85} - 4q^{93} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1248))$$

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
1248.1.b $$\chi_{1248}(1169, \cdot)$$ 1248.1.b.a 4 1
1248.1.e $$\chi_{1248}(79, \cdot)$$ None 0 1
1248.1.f $$\chi_{1248}(833, \cdot)$$ None 0 1
1248.1.i $$\chi_{1248}(415, \cdot)$$ None 0 1
1248.1.k $$\chi_{1248}(703, \cdot)$$ None 0 1
1248.1.l $$\chi_{1248}(545, \cdot)$$ 1248.1.l.a 4 1
1248.1.o $$\chi_{1248}(1039, \cdot)$$ None 0 1
1248.1.p $$\chi_{1248}(209, \cdot)$$ None 0 1
1248.1.s $$\chi_{1248}(551, \cdot)$$ None 0 2
1248.1.t $$\chi_{1248}(265, \cdot)$$ None 0 2
1248.1.w $$\chi_{1248}(521, \cdot)$$ None 0 2
1248.1.y $$\chi_{1248}(103, \cdot)$$ None 0 2
1248.1.z $$\chi_{1248}(1009, \cdot)$$ None 0 2
1248.1.ba $$\chi_{1248}(385, \cdot)$$ None 0 2
1248.1.bd $$\chi_{1248}(671, \cdot)$$ None 0 2
1248.1.be $$\chi_{1248}(47, \cdot)$$ None 0 2
1248.1.bi $$\chi_{1248}(233, \cdot)$$ None 0 2
1248.1.bk $$\chi_{1248}(391, \cdot)$$ None 0 2
1248.1.bl $$\chi_{1248}(73, \cdot)$$ None 0 2
1248.1.bo $$\chi_{1248}(359, \cdot)$$ None 0 2
1248.1.bp $$\chi_{1248}(127, \cdot)$$ None 0 2
1248.1.bs $$\chi_{1248}(737, \cdot)$$ 1248.1.bs.a 8 2
1248.1.bt $$\chi_{1248}(367, \cdot)$$ None 0 2
1248.1.bw $$\chi_{1248}(17, \cdot)$$ None 0 2
1248.1.bx $$\chi_{1248}(113, \cdot)$$ None 0 2
1248.1.by $$\chi_{1248}(751, \cdot)$$ None 0 2
1248.1.cb $$\chi_{1248}(257, \cdot)$$ None 0 2
1248.1.cc $$\chi_{1248}(607, \cdot)$$ None 0 2
1248.1.ce $$\chi_{1248}(83, \cdot)$$ None 0 4
1248.1.cg $$\chi_{1248}(421, \cdot)$$ None 0 4
1248.1.cj $$\chi_{1248}(235, \cdot)$$ None 0 4
1248.1.cl $$\chi_{1248}(259, \cdot)$$ None 0 4
1248.1.cm $$\chi_{1248}(77, \cdot)$$ 1248.1.cm.a 16 4
1248.1.co $$\chi_{1248}(53, \cdot)$$ None 0 4
1248.1.cr $$\chi_{1248}(395, \cdot)$$ None 0 4
1248.1.ct $$\chi_{1248}(109, \cdot)$$ None 0 4
1248.1.cv $$\chi_{1248}(457, \cdot)$$ None 0 4
1248.1.cw $$\chi_{1248}(71, \cdot)$$ None 0 4
1248.1.cy $$\chi_{1248}(55, \cdot)$$ None 0 4
1248.1.da $$\chi_{1248}(329, \cdot)$$ None 0 4
1248.1.de $$\chi_{1248}(431, \cdot)$$ None 0 4
1248.1.df $$\chi_{1248}(383, \cdot)$$ None 0 4
1248.1.di $$\chi_{1248}(97, \cdot)$$ None 0 4
1248.1.dj $$\chi_{1248}(145, \cdot)$$ None 0 4
1248.1.dk $$\chi_{1248}(199, \cdot)$$ None 0 4
1248.1.dm $$\chi_{1248}(185, \cdot)$$ None 0 4
1248.1.do $$\chi_{1248}(119, \cdot)$$ None 0 4
1248.1.dr $$\chi_{1248}(409, \cdot)$$ None 0 4
1248.1.ds $$\chi_{1248}(37, \cdot)$$ None 0 8
1248.1.du $$\chi_{1248}(323, \cdot)$$ None 0 8
1248.1.dw $$\chi_{1248}(101, \cdot)$$ None 0 8
1248.1.dy $$\chi_{1248}(29, \cdot)$$ None 0 8
1248.1.eb $$\chi_{1248}(139, \cdot)$$ None 0 8
1248.1.ed $$\chi_{1248}(43, \cdot)$$ None 0 8
1248.1.ef $$\chi_{1248}(349, \cdot)$$ None 0 8
1248.1.eh $$\chi_{1248}(11, \cdot)$$ None 0 8

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1248))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1248)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(156))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(208))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(312))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(416))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(624))$$$$^{\oplus 2}$$