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Properties

Label 819.6
Level 819
Weight 6
Dimension 90180
Nonzero newspaces 84
Sturm bound 290304
Trace bound 9

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Defining parameters

Level: \( N \) = \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 84 \)
Sturm bound: \(290304\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(819))\).

Total New Old
Modular forms 122112 91172 30940
Cusp forms 119808 90180 29628
Eisenstein series 2304 992 1312

Trace form

\( 90180 q - 18 q^{2} - 120 q^{3} - 362 q^{4} + 300 q^{5} + 612 q^{6} + 434 q^{7} - 4626 q^{8} - 1728 q^{9} + O(q^{10}) \) \( 90180 q - 18 q^{2} - 120 q^{3} - 362 q^{4} + 300 q^{5} + 612 q^{6} + 434 q^{7} - 4626 q^{8} - 1728 q^{9} - 3276 q^{10} + 4632 q^{11} + 10440 q^{12} + 3692 q^{13} + 7110 q^{14} - 1800 q^{15} - 2722 q^{16} - 17058 q^{17} - 38424 q^{18} - 19632 q^{19} - 32628 q^{20} + 3600 q^{21} - 7332 q^{22} + 38076 q^{23} + 24396 q^{24} + 44928 q^{25} + 31230 q^{26} - 10572 q^{27} - 16746 q^{28} - 14106 q^{29} + 78588 q^{30} + 4168 q^{31} + 197478 q^{32} + 74688 q^{33} + 156300 q^{34} + 66744 q^{35} - 134028 q^{36} - 94534 q^{37} - 420948 q^{38} - 157008 q^{39} - 646692 q^{40} - 376662 q^{41} - 196536 q^{42} - 165272 q^{43} + 339336 q^{44} + 423144 q^{45} + 641268 q^{46} + 508992 q^{47} + 540876 q^{48} + 333166 q^{49} + 523290 q^{50} - 189480 q^{51} - 47062 q^{52} - 226872 q^{53} - 696936 q^{54} - 337812 q^{55} - 793938 q^{56} - 455880 q^{57} - 654024 q^{58} - 31092 q^{59} + 1097004 q^{60} - 341198 q^{61} + 75840 q^{62} + 645792 q^{63} + 80710 q^{64} + 1038438 q^{65} + 967500 q^{66} + 646160 q^{67} + 1084800 q^{68} - 416976 q^{69} + 1800600 q^{70} + 640572 q^{71} - 692664 q^{72} + 508644 q^{73} - 2343132 q^{74} - 999744 q^{75} - 1811796 q^{76} - 160092 q^{77} - 1815216 q^{78} - 1261080 q^{79} - 1695504 q^{80} - 725832 q^{81} - 2037756 q^{82} - 1129836 q^{83} - 860892 q^{84} + 199758 q^{85} + 944940 q^{86} - 23196 q^{87} + 1028988 q^{88} - 286812 q^{89} + 1875684 q^{90} - 67854 q^{91} + 4467192 q^{92} + 2269476 q^{93} + 1893720 q^{94} + 1449348 q^{95} + 1873032 q^{96} + 1083184 q^{97} + 3373026 q^{98} + 991632 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(819))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
819.6.a \(\chi_{819}(1, \cdot)\) 819.6.a.a 1 1
819.6.a.b 6
819.6.a.c 6
819.6.a.d 6
819.6.a.e 6
819.6.a.f 6
819.6.a.g 7
819.6.a.h 7
819.6.a.i 8
819.6.a.j 8
819.6.a.k 9
819.6.a.l 9
819.6.a.m 11
819.6.a.n 12
819.6.a.o 14
819.6.a.p 16
819.6.a.q 18
819.6.c \(\chi_{819}(64, \cdot)\) n/a 174 1
819.6.e \(\chi_{819}(755, \cdot)\) n/a 160 1
819.6.g \(\chi_{819}(818, \cdot)\) n/a 184 1
819.6.i \(\chi_{819}(211, \cdot)\) n/a 840 2
819.6.j \(\chi_{819}(235, \cdot)\) n/a 400 2
819.6.k \(\chi_{819}(529, \cdot)\) n/a 1112 2
819.6.l \(\chi_{819}(373, \cdot)\) n/a 1112 2
819.6.m \(\chi_{819}(274, \cdot)\) n/a 720 2
819.6.n \(\chi_{819}(100, \cdot)\) n/a 462 2
819.6.o \(\chi_{819}(568, \cdot)\) n/a 352 2
819.6.p \(\chi_{819}(16, \cdot)\) n/a 1112 2
819.6.q \(\chi_{819}(79, \cdot)\) n/a 960 2
819.6.r \(\chi_{819}(625, \cdot)\) n/a 960 2
819.6.s \(\chi_{819}(289, \cdot)\) n/a 462 2
819.6.t \(\chi_{819}(22, \cdot)\) n/a 840 2
819.6.u \(\chi_{819}(445, \cdot)\) n/a 1112 2
819.6.w \(\chi_{819}(8, \cdot)\) n/a 280 2
819.6.y \(\chi_{819}(307, \cdot)\) n/a 460 2
819.6.z \(\chi_{819}(394, \cdot)\) n/a 1112 2
819.6.bb \(\chi_{819}(146, \cdot)\) n/a 1112 2
819.6.be \(\chi_{819}(131, \cdot)\) n/a 960 2
819.6.bg \(\chi_{819}(269, \cdot)\) n/a 372 2
819.6.bh \(\chi_{819}(589, \cdot)\) n/a 840 2
819.6.bk \(\chi_{819}(25, \cdot)\) n/a 1112 2
819.6.bm \(\chi_{819}(478, \cdot)\) n/a 462 2
819.6.bn \(\chi_{819}(185, \cdot)\) n/a 1112 2
819.6.bq \(\chi_{819}(62, \cdot)\) n/a 376 2
819.6.bs \(\chi_{819}(563, \cdot)\) n/a 1112 2
819.6.bt \(\chi_{819}(311, \cdot)\) n/a 1112 2
819.6.cc \(\chi_{819}(101, \cdot)\) n/a 1112 2
819.6.ce \(\chi_{819}(272, \cdot)\) n/a 1112 2
819.6.cf \(\chi_{819}(647, \cdot)\) n/a 372 2
819.6.ch \(\chi_{819}(524, \cdot)\) n/a 1112 2
819.6.ci \(\chi_{819}(467, \cdot)\) n/a 376 2
819.6.cm \(\chi_{819}(257, \cdot)\) n/a 1112 2
819.6.cq \(\chi_{819}(142, \cdot)\) n/a 1112 2
819.6.ct \(\chi_{819}(127, \cdot)\) n/a 348 2
819.6.cv \(\chi_{819}(4, \cdot)\) n/a 1112 2
819.6.cw \(\chi_{819}(152, \cdot)\) n/a 372 2
819.6.cz \(\chi_{819}(698, \cdot)\) n/a 1112 2
819.6.db \(\chi_{819}(209, \cdot)\) n/a 960 2
819.6.dd \(\chi_{819}(68, \cdot)\) n/a 1112 2
819.6.de \(\chi_{819}(419, \cdot)\) n/a 1112 2
819.6.df \(\chi_{819}(404, \cdot)\) n/a 320 2
819.6.dj \(\chi_{819}(277, \cdot)\) n/a 1112 2
819.6.dk \(\chi_{819}(43, \cdot)\) n/a 840 2
819.6.dl \(\chi_{819}(298, \cdot)\) n/a 464 2
819.6.do \(\chi_{819}(361, \cdot)\) n/a 462 2
819.6.dr \(\chi_{819}(88, \cdot)\) n/a 1112 2
819.6.dt \(\chi_{819}(337, \cdot)\) n/a 840 2
819.6.du \(\chi_{819}(248, \cdot)\) n/a 960 2
819.6.dx \(\chi_{819}(503, \cdot)\) n/a 376 2
819.6.dz \(\chi_{819}(614, \cdot)\) n/a 1112 2
819.6.ea \(\chi_{819}(173, \cdot)\) n/a 1112 2
819.6.eg \(\chi_{819}(38, \cdot)\) n/a 1112 2
819.6.ei \(\chi_{819}(17, \cdot)\) n/a 372 2
819.6.ej \(\chi_{819}(335, \cdot)\) n/a 1112 2
819.6.em \(\chi_{819}(158, \cdot)\) n/a 2224 4
819.6.ep \(\chi_{819}(229, \cdot)\) n/a 2224 4
819.6.eq \(\chi_{819}(202, \cdot)\) n/a 2224 4
819.6.et \(\chi_{819}(136, \cdot)\) n/a 924 4
819.6.ev \(\chi_{819}(86, \cdot)\) n/a 2224 4
819.6.ew \(\chi_{819}(176, \cdot)\) n/a 1680 4
819.6.ez \(\chi_{819}(305, \cdot)\) n/a 744 4
819.6.fa \(\chi_{819}(124, \cdot)\) n/a 2224 4
819.6.fd \(\chi_{819}(422, \cdot)\) n/a 744 4
819.6.fe \(\chi_{819}(11, \cdot)\) n/a 2224 4
819.6.fh \(\chi_{819}(239, \cdot)\) n/a 1680 4
819.6.fk \(\chi_{819}(31, \cdot)\) n/a 2224 4
819.6.fl \(\chi_{819}(76, \cdot)\) n/a 2224 4
819.6.fm \(\chi_{819}(370, \cdot)\) n/a 928 4
819.6.fn \(\chi_{819}(73, \cdot)\) n/a 928 4
819.6.fs \(\chi_{819}(241, \cdot)\) n/a 2224 4
819.6.ft \(\chi_{819}(409, \cdot)\) n/a 2224 4
819.6.fw \(\chi_{819}(71, \cdot)\) n/a 560 4
819.6.fx \(\chi_{819}(317, \cdot)\) n/a 2224 4
819.6.fy \(\chi_{819}(50, \cdot)\) n/a 1680 4
819.6.fz \(\chi_{819}(44, \cdot)\) n/a 752 4
819.6.ge \(\chi_{819}(137, \cdot)\) n/a 2224 4
819.6.gf \(\chi_{819}(2, \cdot)\) n/a 2224 4
819.6.gh \(\chi_{819}(19, \cdot)\) n/a 924 4
819.6.gi \(\chi_{819}(115, \cdot)\) n/a 2224 4
819.6.gl \(\chi_{819}(34, \cdot)\) n/a 2224 4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(819))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(819)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(273))\)\(^{\oplus 2}\)