# Properties

 Label 2496.1 Level 2496 Weight 1 Dimension 126 Nonzero newspaces 12 Newform subspaces 30 Sturm bound 344064 Trace bound 25

## Defining parameters

 Level: $$N$$ = $$2496 = 2^{6} \cdot 3 \cdot 13$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$12$$ Newform subspaces: $$30$$ Sturm bound: $$344064$$ Trace bound: $$25$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(2496))$$.

Total New Old
Modular forms 3900 610 3290
Cusp forms 444 126 318
Eisenstein series 3456 484 2972

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 118 0 8 0

## Trace form

 $$126 q + 2 q^{9} + O(q^{10})$$ $$126 q + 2 q^{9} + 2 q^{13} - 4 q^{21} - 10 q^{25} - 4 q^{33} + 8 q^{37} + 8 q^{43} - 4 q^{45} - 18 q^{49} - 32 q^{55} - 12 q^{57} + 8 q^{61} - 8 q^{69} - 4 q^{73} - 40 q^{75} - 10 q^{81} + 4 q^{85} + 8 q^{93} + 4 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(2496))$$

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
2496.1.b $$\chi_{2496}(545, \cdot)$$ 2496.1.b.a 2 1
2496.1.b.b 2
2496.1.b.c 4
2496.1.b.d 4
2496.1.e $$\chi_{2496}(1951, \cdot)$$ None 0 1
2496.1.f $$\chi_{2496}(833, \cdot)$$ None 0 1
2496.1.i $$\chi_{2496}(1663, \cdot)$$ None 0 1
2496.1.k $$\chi_{2496}(703, \cdot)$$ None 0 1
2496.1.l $$\chi_{2496}(1793, \cdot)$$ 2496.1.l.a 1 1
2496.1.l.b 1
2496.1.l.c 4
2496.1.o $$\chi_{2496}(415, \cdot)$$ None 0 1
2496.1.p $$\chi_{2496}(2081, \cdot)$$ None 0 1
2496.1.s $$\chi_{2496}(47, \cdot)$$ None 0 2
2496.1.t $$\chi_{2496}(1009, \cdot)$$ None 0 2
2496.1.w $$\chi_{2496}(209, \cdot)$$ None 0 2
2496.1.y $$\chi_{2496}(1039, \cdot)$$ None 0 2
2496.1.z $$\chi_{2496}(1633, \cdot)$$ None 0 2
2496.1.ba $$\chi_{2496}(385, \cdot)$$ None 0 2
2496.1.bd $$\chi_{2496}(1919, \cdot)$$ 2496.1.bd.a 2 2
2496.1.bd.b 2
2496.1.be $$\chi_{2496}(671, \cdot)$$ 2496.1.be.a 2 2
2496.1.be.b 2
2496.1.be.c 2
2496.1.be.d 2
2496.1.bi $$\chi_{2496}(1169, \cdot)$$ 2496.1.bi.a 8 2
2496.1.bk $$\chi_{2496}(79, \cdot)$$ None 0 2
2496.1.bl $$\chi_{2496}(1201, \cdot)$$ None 0 2
2496.1.bo $$\chi_{2496}(239, \cdot)$$ None 0 2
2496.1.bp $$\chi_{2496}(127, \cdot)$$ None 0 2
2496.1.bs $$\chi_{2496}(1985, \cdot)$$ 2496.1.bs.a 2 2
2496.1.bs.b 2
2496.1.bs.c 8
2496.1.bt $$\chi_{2496}(607, \cdot)$$ None 0 2
2496.1.bw $$\chi_{2496}(1505, \cdot)$$ 2496.1.bw.a 4 2
2496.1.bw.b 4
2496.1.bx $$\chi_{2496}(737, \cdot)$$ 2496.1.bx.a 4 2
2496.1.bx.b 4
2496.1.by $$\chi_{2496}(1375, \cdot)$$ None 0 2
2496.1.cb $$\chi_{2496}(257, \cdot)$$ 2496.1.cb.a 2 2
2496.1.cb.b 2
2496.1.cc $$\chi_{2496}(1855, \cdot)$$ None 0 2
2496.1.ce $$\chi_{2496}(359, \cdot)$$ None 0 4
2496.1.cg $$\chi_{2496}(73, \cdot)$$ None 0 4
2496.1.cj $$\chi_{2496}(391, \cdot)$$ None 0 4
2496.1.cl $$\chi_{2496}(103, \cdot)$$ None 0 4
2496.1.cm $$\chi_{2496}(233, \cdot)$$ None 0 4
2496.1.co $$\chi_{2496}(521, \cdot)$$ None 0 4
2496.1.cr $$\chi_{2496}(551, \cdot)$$ None 0 4
2496.1.ct $$\chi_{2496}(265, \cdot)$$ None 0 4
2496.1.cv $$\chi_{2496}(145, \cdot)$$ None 0 4
2496.1.cw $$\chi_{2496}(1679, \cdot)$$ None 0 4
2496.1.cy $$\chi_{2496}(367, \cdot)$$ None 0 4
2496.1.da $$\chi_{2496}(17, \cdot)$$ None 0 4
2496.1.de $$\chi_{2496}(479, \cdot)$$ 2496.1.de.a 4 4
2496.1.de.b 4
2496.1.de.c 4
2496.1.de.d 4
2496.1.df $$\chi_{2496}(383, \cdot)$$ 2496.1.df.a 4 4
2496.1.df.b 4
2496.1.di $$\chi_{2496}(193, \cdot)$$ None 0 4
2496.1.dj $$\chi_{2496}(97, \cdot)$$ None 0 4
2496.1.dk $$\chi_{2496}(751, \cdot)$$ None 0 4
2496.1.dm $$\chi_{2496}(113, \cdot)$$ None 0 4
2496.1.do $$\chi_{2496}(431, \cdot)$$ None 0 4
2496.1.dr $$\chi_{2496}(1393, \cdot)$$ None 0 4
2496.1.du $$\chi_{2496}(53, \cdot)$$ None 0 8
2496.1.dv $$\chi_{2496}(259, \cdot)$$ None 0 8
2496.1.dy $$\chi_{2496}(109, \cdot)$$ None 0 8
2496.1.dz $$\chi_{2496}(83, \cdot)$$ None 0 8
2496.1.ec $$\chi_{2496}(421, \cdot)$$ None 0 8
2496.1.ed $$\chi_{2496}(395, \cdot)$$ None 0 8
2496.1.eg $$\chi_{2496}(235, \cdot)$$ None 0 8
2496.1.eh $$\chi_{2496}(77, \cdot)$$ 2496.1.eh.a 32 8
2496.1.ei $$\chi_{2496}(457, \cdot)$$ None 0 8
2496.1.ek $$\chi_{2496}(71, \cdot)$$ None 0 8
2496.1.em $$\chi_{2496}(329, \cdot)$$ None 0 8
2496.1.eo $$\chi_{2496}(185, \cdot)$$ None 0 8
2496.1.er $$\chi_{2496}(55, \cdot)$$ None 0 8
2496.1.et $$\chi_{2496}(199, \cdot)$$ None 0 8
2496.1.ev $$\chi_{2496}(409, \cdot)$$ None 0 8
2496.1.ex $$\chi_{2496}(119, \cdot)$$ None 0 8
2496.1.ey $$\chi_{2496}(43, \cdot)$$ None 0 16
2496.1.ez $$\chi_{2496}(29, \cdot)$$ None 0 16
2496.1.fc $$\chi_{2496}(11, \cdot)$$ None 0 16
2496.1.fd $$\chi_{2496}(37, \cdot)$$ None 0 16
2496.1.fg $$\chi_{2496}(323, \cdot)$$ None 0 16
2496.1.fh $$\chi_{2496}(349, \cdot)$$ None 0 16
2496.1.fk $$\chi_{2496}(101, \cdot)$$ None 0 16
2496.1.fl $$\chi_{2496}(139, \cdot)$$ None 0 16

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(2496))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(2496)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 7}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 10}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(156))$$$$^{\oplus 5}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(208))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(312))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(416))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(624))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(832))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(1248))$$$$^{\oplus 2}$$