Properties

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

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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

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