# Properties

 Label 819.1 Level 819 Weight 1 Dimension 34 Nonzero newspaces 11 Newform subspaces 12 Sturm bound 48384 Trace bound 7

## Defining parameters

 Level: $$N$$ = $$819 = 3^{2} \cdot 7 \cdot 13$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$11$$ Newform subspaces: $$12$$ Sturm bound: $$48384$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(819))$$.

Total New Old
Modular forms 1252 528 724
Cusp forms 100 34 66
Eisenstein series 1152 494 658

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 18 8 8 0

## Trace form

 $$34 q + 2 q^{2} + 10 q^{7} - 8 q^{8} - 2 q^{9} + O(q^{10})$$ $$34 q + 2 q^{2} + 10 q^{7} - 8 q^{8} - 2 q^{9} - 2 q^{11} + 4 q^{13} - 4 q^{14} + 2 q^{15} - 2 q^{16} + 4 q^{18} + 2 q^{19} - 2 q^{22} - 6 q^{25} - 2 q^{28} - 2 q^{29} + 2 q^{30} - 4 q^{31} - 16 q^{34} - 6 q^{37} - 2 q^{39} + 8 q^{43} - 4 q^{49} + 4 q^{51} - 8 q^{52} - 2 q^{56} - 4 q^{57} - 6 q^{58} - 2 q^{61} - 2 q^{63} + 18 q^{64} + 2 q^{65} - 4 q^{67} - 4 q^{71} + 2 q^{72} - 4 q^{73} + 2 q^{74} - 12 q^{76} + 4 q^{77} + 4 q^{78} + 2 q^{81} + 2 q^{85} + 2 q^{88} - 2 q^{91} - 2 q^{93} - 4 q^{94} - 2 q^{95} - 8 q^{97} - 4 q^{98} - 4 q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(819))$$

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
819.1.b $$\chi_{819}(638, \cdot)$$ None 0 1
819.1.d $$\chi_{819}(181, \cdot)$$ 819.1.d.a 1 1
819.1.d.b 1
819.1.f $$\chi_{819}(118, \cdot)$$ None 0 1
819.1.h $$\chi_{819}(701, \cdot)$$ None 0 1
819.1.v $$\chi_{819}(190, \cdot)$$ None 0 2
819.1.x $$\chi_{819}(125, \cdot)$$ None 0 2
819.1.ba $$\chi_{819}(191, \cdot)$$ None 0 2
819.1.bc $$\chi_{819}(706, \cdot)$$ None 0 2
819.1.bd $$\chi_{819}(199, \cdot)$$ 819.1.bd.a 2 2
819.1.bf $$\chi_{819}(103, \cdot)$$ None 0 2
819.1.bi $$\chi_{819}(29, \cdot)$$ None 0 2
819.1.bj $$\chi_{819}(107, \cdot)$$ 819.1.bj.a 4 2
819.1.bl $$\chi_{819}(326, \cdot)$$ None 0 2
819.1.bo $$\chi_{819}(283, \cdot)$$ None 0 2
819.1.bp $$\chi_{819}(250, \cdot)$$ None 0 2
819.1.br $$\chi_{819}(55, \cdot)$$ None 0 2
819.1.bu $$\chi_{819}(157, \cdot)$$ None 0 2
819.1.bv $$\chi_{819}(407, \cdot)$$ None 0 2
819.1.bw $$\chi_{819}(116, \cdot)$$ None 0 2
819.1.bx $$\chi_{819}(23, \cdot)$$ None 0 2
819.1.by $$\chi_{819}(155, \cdot)$$ None 0 2
819.1.bz $$\chi_{819}(212, \cdot)$$ None 0 2
819.1.ca $$\chi_{819}(179, \cdot)$$ None 0 2
819.1.cb $$\chi_{819}(391, \cdot)$$ None 0 2
819.1.cd $$\chi_{819}(367, \cdot)$$ None 0 2
819.1.cg $$\chi_{819}(334, \cdot)$$ 819.1.cg.a 2 2
819.1.cj $$\chi_{819}(328, \cdot)$$ 819.1.cj.a 4 2
819.1.ck $$\chi_{819}(586, \cdot)$$ None 0 2
819.1.cl $$\chi_{819}(178, \cdot)$$ None 0 2
819.1.cn $$\chi_{819}(95, \cdot)$$ None 0 2
819.1.co $$\chi_{819}(134, \cdot)$$ None 0 2
819.1.cp $$\chi_{819}(506, \cdot)$$ None 0 2
819.1.cr $$\chi_{819}(443, \cdot)$$ None 0 2
819.1.cs $$\chi_{819}(347, \cdot)$$ None 0 2
819.1.cu $$\chi_{819}(386, \cdot)$$ None 0 2
819.1.cx $$\chi_{819}(10, \cdot)$$ 819.1.cx.a 2 2
819.1.cy $$\chi_{819}(454, \cdot)$$ None 0 2
819.1.da $$\chi_{819}(355, \cdot)$$ None 0 2
819.1.dc $$\chi_{819}(166, \cdot)$$ None 0 2
819.1.dg $$\chi_{819}(160, \cdot)$$ None 0 2
819.1.dh $$\chi_{819}(649, \cdot)$$ None 0 2
819.1.di $$\chi_{819}(74, \cdot)$$ None 0 2
819.1.dm $$\chi_{819}(302, \cdot)$$ None 0 2
819.1.dn $$\chi_{819}(53, \cdot)$$ None 0 2
819.1.dp $$\chi_{819}(737, \cdot)$$ 819.1.dp.a 4 2
819.1.dq $$\chi_{819}(92, \cdot)$$ None 0 2
819.1.ds $$\chi_{819}(263, \cdot)$$ None 0 2
819.1.dv $$\chi_{819}(220, \cdot)$$ None 0 2
819.1.dw $$\chi_{819}(439, \cdot)$$ None 0 2
819.1.dy $$\chi_{819}(244, \cdot)$$ None 0 2
819.1.eb $$\chi_{819}(61, \cdot)$$ None 0 2
819.1.ec $$\chi_{819}(296, \cdot)$$ None 0 2
819.1.ed $$\chi_{819}(389, \cdot)$$ None 0 2
819.1.ee $$\chi_{819}(218, \cdot)$$ None 0 2
819.1.ef $$\chi_{819}(451, \cdot)$$ 819.1.ef.a 2 2
819.1.eh $$\chi_{819}(40, \cdot)$$ None 0 2
819.1.ek $$\chi_{819}(139, \cdot)$$ 819.1.ek.a 4 2
819.1.el $$\chi_{819}(725, \cdot)$$ None 0 2
819.1.en $$\chi_{819}(67, \cdot)$$ None 0 4
819.1.eo $$\chi_{819}(89, \cdot)$$ None 0 4
819.1.er $$\chi_{819}(5, \cdot)$$ None 0 4
819.1.es $$\chi_{819}(293, \cdot)$$ None 0 4
819.1.eu $$\chi_{819}(37, \cdot)$$ 819.1.eu.a 4 4
819.1.ex $$\chi_{819}(151, \cdot)$$ None 0 4
819.1.ey $$\chi_{819}(85, \cdot)$$ None 0 4
819.1.fb $$\chi_{819}(110, \cdot)$$ None 0 4
819.1.fc $$\chi_{819}(148, \cdot)$$ None 0 4
819.1.ff $$\chi_{819}(163, \cdot)$$ 819.1.ff.a 4 4
819.1.fg $$\chi_{819}(58, \cdot)$$ None 0 4
819.1.fi $$\chi_{819}(227, \cdot)$$ None 0 4
819.1.fj $$\chi_{819}(59, \cdot)$$ None 0 4
819.1.fo $$\chi_{819}(188, \cdot)$$ None 0 4
819.1.fp $$\chi_{819}(47, \cdot)$$ None 0 4
819.1.fq $$\chi_{819}(20, \cdot)$$ None 0 4
819.1.fr $$\chi_{819}(278, \cdot)$$ None 0 4
819.1.fu $$\chi_{819}(184, \cdot)$$ None 0 4
819.1.fv $$\chi_{819}(319, \cdot)$$ None 0 4
819.1.ga $$\chi_{819}(268, \cdot)$$ None 0 4
819.1.gb $$\chi_{819}(358, \cdot)$$ None 0 4
819.1.gc $$\chi_{819}(253, \cdot)$$ None 0 4
819.1.gd $$\chi_{819}(109, \cdot)$$ None 0 4
819.1.gg $$\chi_{819}(83, \cdot)$$ None 0 4
819.1.gj $$\chi_{819}(80, \cdot)$$ None 0 4
819.1.gk $$\chi_{819}(353, \cdot)$$ None 0 4

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(819))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(819)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(117))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(273))$$$$^{\oplus 2}$$