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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

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

Display 100 coefficients 10 coefficients

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 available 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

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