Properties

Label 2805.2
Level 2805
Weight 2
Dimension 183985
Nonzero newspaces 72
Sturm bound 1105920
Trace bound 14

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Defining parameters

Level: \( N \) = \( 2805 = 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(1105920\)
Trace bound: \(14\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2805))\).

Total New Old
Modular forms 281600 187233 94367
Cusp forms 271361 183985 87376
Eisenstein series 10239 3248 6991

Trace form

\( 183985q - 13q^{2} - 115q^{3} - 241q^{4} + q^{5} - 309q^{6} - 200q^{7} + 47q^{8} - 67q^{9} + O(q^{10}) \) \( 183985q - 13q^{2} - 115q^{3} - 241q^{4} + q^{5} - 309q^{6} - 200q^{7} + 47q^{8} - 67q^{9} - 261q^{10} + 41q^{11} - 89q^{12} - 162q^{13} + 176q^{14} - 81q^{15} - 217q^{16} + 93q^{17} - 61q^{18} - 76q^{19} + 187q^{20} - 152q^{21} - 5q^{22} + 72q^{23} + 95q^{24} - 131q^{25} + 370q^{26} - 175q^{27} + 200q^{28} + 142q^{29} - 29q^{30} - 408q^{31} + 191q^{32} - 99q^{33} - 53q^{34} + 184q^{35} - 201q^{36} + 46q^{37} + 324q^{38} + 22q^{39} - 201q^{40} + 314q^{41} - 120q^{42} - 20q^{43} + 95q^{44} - 329q^{45} - 536q^{46} - 72q^{47} - 441q^{48} - 375q^{49} - 113q^{50} - 491q^{51} - 878q^{52} - 66q^{53} - 237q^{54} - 499q^{55} - 200q^{56} - 300q^{57} - 310q^{58} - 60q^{59} - 369q^{60} - 578q^{61} + 80q^{62} + 16q^{63} - 681q^{64} + 70q^{65} - 469q^{66} - 372q^{67} + 399q^{68} - 28q^{69} - 224q^{70} + 120q^{71} + 31q^{72} + 122q^{73} + 154q^{74} - 29q^{75} - 388q^{76} + 240q^{77} - 22q^{78} + 64q^{79} - 413q^{80} - 59q^{81} - 418q^{82} + 380q^{83} - 592q^{84} - 783q^{85} - 108q^{86} - 314q^{87} - 361q^{88} - 166q^{89} - 613q^{90} - 1088q^{91} - 864q^{92} - 508q^{93} - 1152q^{94} - 448q^{95} - 1465q^{96} - 758q^{97} - 773q^{98} - 579q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2805))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2805.2.a \(\chi_{2805}(1, \cdot)\) 2805.2.a.a 1 1
2805.2.a.b 1
2805.2.a.c 1
2805.2.a.d 1
2805.2.a.e 1
2805.2.a.f 2
2805.2.a.g 4
2805.2.a.h 4
2805.2.a.i 4
2805.2.a.j 4
2805.2.a.k 5
2805.2.a.l 5
2805.2.a.m 6
2805.2.a.n 6
2805.2.a.o 7
2805.2.a.p 7
2805.2.a.q 7
2805.2.a.r 7
2805.2.a.s 7
2805.2.a.t 8
2805.2.a.u 8
2805.2.a.v 9
2805.2.c \(\chi_{2805}(1684, \cdot)\) n/a 160 1
2805.2.d \(\chi_{2805}(2804, \cdot)\) n/a 424 1
2805.2.g \(\chi_{2805}(1189, \cdot)\) n/a 184 1
2805.2.h \(\chi_{2805}(494, \cdot)\) n/a 384 1
2805.2.j \(\chi_{2805}(1616, \cdot)\) n/a 256 1
2805.2.m \(\chi_{2805}(2311, \cdot)\) n/a 120 1
2805.2.n \(\chi_{2805}(1121, \cdot)\) n/a 288 1
2805.2.r \(\chi_{2805}(956, \cdot)\) n/a 576 2
2805.2.s \(\chi_{2805}(166, \cdot)\) n/a 240 2
2805.2.u \(\chi_{2805}(208, \cdot)\) n/a 432 2
2805.2.w \(\chi_{2805}(353, \cdot)\) n/a 720 2
2805.2.y \(\chi_{2805}(1937, \cdot)\) n/a 720 2
2805.2.bb \(\chi_{2805}(307, \cdot)\) n/a 384 2
2805.2.bc \(\chi_{2805}(188, \cdot)\) n/a 640 2
2805.2.bf \(\chi_{2805}(373, \cdot)\) n/a 432 2
2805.2.bh \(\chi_{2805}(1033, \cdot)\) n/a 432 2
2805.2.bj \(\chi_{2805}(2333, \cdot)\) n/a 720 2
2805.2.bk \(\chi_{2805}(1024, \cdot)\) n/a 368 2
2805.2.bn \(\chi_{2805}(659, \cdot)\) n/a 848 2
2805.2.bo \(\chi_{2805}(256, \cdot)\) n/a 512 4
2805.2.bp \(\chi_{2805}(637, \cdot)\) n/a 864 4
2805.2.bs \(\chi_{2805}(848, \cdot)\) n/a 1440 4
2805.2.bt \(\chi_{2805}(824, \cdot)\) n/a 1696 4
2805.2.bu \(\chi_{2805}(331, \cdot)\) n/a 480 4
2805.2.bz \(\chi_{2805}(529, \cdot)\) n/a 704 4
2805.2.ca \(\chi_{2805}(461, \cdot)\) n/a 1152 4
2805.2.cb \(\chi_{2805}(287, \cdot)\) n/a 1440 4
2805.2.ce \(\chi_{2805}(43, \cdot)\) n/a 864 4
2805.2.ch \(\chi_{2805}(101, \cdot)\) n/a 1152 4
2805.2.ci \(\chi_{2805}(16, \cdot)\) n/a 576 4
2805.2.cl \(\chi_{2805}(596, \cdot)\) n/a 1024 4
2805.2.cn \(\chi_{2805}(239, \cdot)\) n/a 1536 4
2805.2.co \(\chi_{2805}(169, \cdot)\) n/a 864 4
2805.2.cr \(\chi_{2805}(1019, \cdot)\) n/a 1696 4
2805.2.cs \(\chi_{2805}(664, \cdot)\) n/a 768 4
2805.2.cw \(\chi_{2805}(362, \cdot)\) n/a 3392 8
2805.2.cx \(\chi_{2805}(133, \cdot)\) n/a 1440 8
2805.2.cz \(\chi_{2805}(241, \cdot)\) n/a 1152 8
2805.2.da \(\chi_{2805}(419, \cdot)\) n/a 2880 8
2805.2.dc \(\chi_{2805}(56, \cdot)\) n/a 1920 8
2805.2.df \(\chi_{2805}(109, \cdot)\) n/a 1728 8
2805.2.dg \(\chi_{2805}(197, \cdot)\) n/a 3392 8
2805.2.dh \(\chi_{2805}(793, \cdot)\) n/a 1440 8
2805.2.dk \(\chi_{2805}(149, \cdot)\) n/a 3392 8
2805.2.dn \(\chi_{2805}(4, \cdot)\) n/a 1728 8
2805.2.dp \(\chi_{2805}(38, \cdot)\) n/a 3392 8
2805.2.dr \(\chi_{2805}(13, \cdot)\) n/a 1728 8
2805.2.ds \(\chi_{2805}(118, \cdot)\) n/a 1728 8
2805.2.dv \(\chi_{2805}(137, \cdot)\) n/a 3072 8
2805.2.dw \(\chi_{2805}(52, \cdot)\) n/a 1536 8
2805.2.dz \(\chi_{2805}(152, \cdot)\) n/a 3392 8
2805.2.ea \(\chi_{2805}(608, \cdot)\) n/a 3392 8
2805.2.ec \(\chi_{2805}(217, \cdot)\) n/a 1728 8
2805.2.ef \(\chi_{2805}(361, \cdot)\) n/a 1152 8
2805.2.eg \(\chi_{2805}(446, \cdot)\) n/a 2304 8
2805.2.ej \(\chi_{2805}(257, \cdot)\) n/a 6784 16
2805.2.ek \(\chi_{2805}(172, \cdot)\) n/a 3456 16
2805.2.em \(\chi_{2805}(49, \cdot)\) n/a 3456 16
2805.2.en \(\chi_{2805}(161, \cdot)\) n/a 4608 16
2805.2.es \(\chi_{2805}(134, \cdot)\) n/a 6784 16
2805.2.et \(\chi_{2805}(196, \cdot)\) n/a 2304 16
2805.2.ev \(\chi_{2805}(127, \cdot)\) n/a 3456 16
2805.2.ew \(\chi_{2805}(53, \cdot)\) n/a 6784 16
2805.2.fa \(\chi_{2805}(37, \cdot)\) n/a 6912 32
2805.2.fb \(\chi_{2805}(62, \cdot)\) n/a 13568 32
2805.2.fd \(\chi_{2805}(71, \cdot)\) n/a 9216 32
2805.2.fe \(\chi_{2805}(79, \cdot)\) n/a 6912 32
2805.2.fg \(\chi_{2805}(46, \cdot)\) n/a 4608 32
2805.2.fj \(\chi_{2805}(14, \cdot)\) n/a 13568 32
2805.2.fk \(\chi_{2805}(148, \cdot)\) n/a 6912 32
2805.2.fl \(\chi_{2805}(107, \cdot)\) n/a 13568 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2805))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2805)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(187))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(255))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(561))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(935))\)\(^{\oplus 2}\)