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Properties

Label 3185.2
Level 3185
Weight 2
Dimension 340236
Nonzero newspaces 100
Sturm bound 1580544
Trace bound 11

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Defining parameters

Level: \( N \) = \( 3185 = 5 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 100 \)
Sturm bound: \(1580544\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3185))\).

Total New Old
Modular forms 400896 346640 54256
Cusp forms 389377 340236 49141
Eisenstein series 11519 6404 5115

Trace form

\( 340236 q - 318 q^{2} - 312 q^{3} - 294 q^{4} - 458 q^{5} - 888 q^{6} - 344 q^{7} - 492 q^{8} - 242 q^{9} + O(q^{10}) \) \( 340236 q - 318 q^{2} - 312 q^{3} - 294 q^{4} - 458 q^{5} - 888 q^{6} - 344 q^{7} - 492 q^{8} - 242 q^{9} - 399 q^{10} - 876 q^{11} - 116 q^{12} - 288 q^{13} - 720 q^{14} - 752 q^{15} - 734 q^{16} - 210 q^{17} - 36 q^{18} - 176 q^{19} - 293 q^{20} - 980 q^{21} - 324 q^{22} - 168 q^{23} - 48 q^{24} - 420 q^{25} - 900 q^{26} - 540 q^{27} - 272 q^{28} - 462 q^{29} - 432 q^{30} - 812 q^{31} - 114 q^{32} - 204 q^{33} - 156 q^{34} - 534 q^{35} - 1590 q^{36} - 330 q^{37} - 252 q^{38} - 340 q^{39} - 1176 q^{40} - 882 q^{41} - 516 q^{42} - 508 q^{43} - 372 q^{44} - 473 q^{45} - 960 q^{46} - 180 q^{47} - 460 q^{48} - 512 q^{49} - 1263 q^{50} - 756 q^{51} - 382 q^{52} - 504 q^{53} - 348 q^{54} - 528 q^{55} - 1272 q^{56} - 452 q^{57} - 474 q^{58} - 324 q^{59} - 722 q^{60} - 1006 q^{61} - 336 q^{62} - 312 q^{63} - 660 q^{64} - 524 q^{65} - 1716 q^{66} - 296 q^{67} - 138 q^{68} - 204 q^{69} - 654 q^{70} - 1392 q^{71} - 762 q^{72} - 260 q^{73} - 330 q^{74} - 512 q^{75} - 1328 q^{76} - 396 q^{77} - 1002 q^{78} - 1116 q^{79} - 1013 q^{80} - 1322 q^{81} - 1422 q^{82} - 636 q^{83} - 1520 q^{84} - 1155 q^{85} - 1368 q^{86} - 1152 q^{87} - 2232 q^{88} - 756 q^{89} - 1662 q^{90} - 1526 q^{91} - 2280 q^{92} - 1268 q^{93} - 1764 q^{94} - 940 q^{95} - 2952 q^{96} - 1160 q^{97} - 1536 q^{98} - 1704 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3185))\)

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
3185.2.a \(\chi_{3185}(1, \cdot)\) 3185.2.a.a 1 1
3185.2.a.b 1
3185.2.a.c 1
3185.2.a.d 1
3185.2.a.e 1
3185.2.a.f 1
3185.2.a.g 1
3185.2.a.h 1
3185.2.a.i 1
3185.2.a.j 2
3185.2.a.k 2
3185.2.a.l 4
3185.2.a.m 4
3185.2.a.n 4
3185.2.a.o 4
3185.2.a.p 4
3185.2.a.q 4
3185.2.a.r 6
3185.2.a.s 7
3185.2.a.t 7
3185.2.a.u 7
3185.2.a.v 8
3185.2.a.w 8
3185.2.a.x 8
3185.2.a.y 8
3185.2.a.z 8
3185.2.a.ba 8
3185.2.a.bb 10
3185.2.a.bc 10
3185.2.a.bd 16
3185.2.a.be 16
3185.2.c \(\chi_{3185}(2549, \cdot)\) n/a 246 1
3185.2.d \(\chi_{3185}(246, \cdot)\) n/a 190 1
3185.2.f \(\chi_{3185}(2794, \cdot)\) n/a 276 1
3185.2.i \(\chi_{3185}(2206, \cdot)\) n/a 384 2
3185.2.j \(\chi_{3185}(716, \cdot)\) n/a 320 2
3185.2.k \(\chi_{3185}(2811, \cdot)\) n/a 372 2
3185.2.l \(\chi_{3185}(471, \cdot)\) n/a 372 2
3185.2.m \(\chi_{3185}(148, \cdot)\) n/a 554 2
3185.2.p \(\chi_{3185}(1126, \cdot)\) n/a 368 2
3185.2.r \(\chi_{3185}(1028, \cdot)\) n/a 480 2
3185.2.s \(\chi_{3185}(1273, \cdot)\) n/a 544 2
3185.2.u \(\chi_{3185}(489, \cdot)\) n/a 544 2
3185.2.x \(\chi_{3185}(1373, \cdot)\) n/a 554 2
3185.2.z \(\chi_{3185}(1096, \cdot)\) n/a 372 2
3185.2.ba \(\chi_{3185}(1439, \cdot)\) n/a 544 2
3185.2.bc \(\chi_{3185}(1304, \cdot)\) n/a 544 2
3185.2.bh \(\chi_{3185}(324, \cdot)\) n/a 544 2
3185.2.bj \(\chi_{3185}(589, \cdot)\) n/a 552 2
3185.2.bm \(\chi_{3185}(2174, \cdot)\) n/a 544 2
3185.2.bo \(\chi_{3185}(116, \cdot)\) n/a 376 2
3185.2.bq \(\chi_{3185}(491, \cdot)\) n/a 384 2
3185.2.br \(\chi_{3185}(1569, \cdot)\) n/a 556 2
3185.2.bt \(\chi_{3185}(79, \cdot)\) n/a 480 2
3185.2.bv \(\chi_{3185}(361, \cdot)\) n/a 372 2
3185.2.bz \(\chi_{3185}(459, \cdot)\) n/a 544 2
3185.2.ca \(\chi_{3185}(456, \cdot)\) n/a 1344 6
3185.2.cc \(\chi_{3185}(1047, \cdot)\) n/a 1088 4
3185.2.ce \(\chi_{3185}(67, \cdot)\) n/a 1088 4
3185.2.cf \(\chi_{3185}(197, \cdot)\) n/a 1108 4
3185.2.ch \(\chi_{3185}(1243, \cdot)\) n/a 1088 4
3185.2.cj \(\chi_{3185}(656, \cdot)\) n/a 744 4
3185.2.cm \(\chi_{3185}(509, \cdot)\) n/a 1088 4
3185.2.co \(\chi_{3185}(734, \cdot)\) n/a 1088 4
3185.2.cp \(\chi_{3185}(619, \cdot)\) n/a 1088 4
3185.2.cs \(\chi_{3185}(472, \cdot)\) n/a 1088 4
3185.2.ct \(\chi_{3185}(68, \cdot)\) n/a 1088 4
3185.2.cv \(\chi_{3185}(313, \cdot)\) n/a 960 4
3185.2.cx \(\chi_{3185}(1538, \cdot)\) n/a 1088 4
3185.2.da \(\chi_{3185}(342, \cdot)\) n/a 1088 4
3185.2.dc \(\chi_{3185}(607, \cdot)\) n/a 1088 4
3185.2.dd \(\chi_{3185}(48, \cdot)\) n/a 1088 4
3185.2.dg \(\chi_{3185}(558, \cdot)\) n/a 1088 4
3185.2.dh \(\chi_{3185}(1146, \cdot)\) n/a 744 4
3185.2.dk \(\chi_{3185}(31, \cdot)\) n/a 752 4
3185.2.dl \(\chi_{3185}(1371, \cdot)\) n/a 752 4
3185.2.do \(\chi_{3185}(19, \cdot)\) n/a 1088 4
3185.2.dp \(\chi_{3185}(557, \cdot)\) n/a 1088 4
3185.2.ds \(\chi_{3185}(18, \cdot)\) n/a 1088 4
3185.2.du \(\chi_{3185}(687, \cdot)\) n/a 1108 4
3185.2.dv \(\chi_{3185}(128, \cdot)\) n/a 1088 4
3185.2.dz \(\chi_{3185}(64, \cdot)\) n/a 2328 6
3185.2.eb \(\chi_{3185}(701, \cdot)\) n/a 1584 6
3185.2.ec \(\chi_{3185}(274, \cdot)\) n/a 2016 6
3185.2.ee \(\chi_{3185}(16, \cdot)\) n/a 3144 12
3185.2.ef \(\chi_{3185}(81, \cdot)\) n/a 3144 12
3185.2.eg \(\chi_{3185}(261, \cdot)\) n/a 2688 12
3185.2.eh \(\chi_{3185}(211, \cdot)\) n/a 3120 12
3185.2.ei \(\chi_{3185}(8, \cdot)\) n/a 4656 12
3185.2.el \(\chi_{3185}(34, \cdot)\) n/a 4656 12
3185.2.en \(\chi_{3185}(272, \cdot)\) n/a 4656 12
3185.2.eo \(\chi_{3185}(27, \cdot)\) n/a 4032 12
3185.2.eq \(\chi_{3185}(216, \cdot)\) n/a 3168 12
3185.2.et \(\chi_{3185}(372, \cdot)\) n/a 4656 12
3185.2.eu \(\chi_{3185}(4, \cdot)\) n/a 4656 12
3185.2.ey \(\chi_{3185}(121, \cdot)\) n/a 3144 12
3185.2.fa \(\chi_{3185}(144, \cdot)\) n/a 4032 12
3185.2.fc \(\chi_{3185}(29, \cdot)\) n/a 4656 12
3185.2.fd \(\chi_{3185}(36, \cdot)\) n/a 3120 12
3185.2.ff \(\chi_{3185}(51, \cdot)\) n/a 3120 12
3185.2.fh \(\chi_{3185}(9, \cdot)\) n/a 4656 12
3185.2.fk \(\chi_{3185}(134, \cdot)\) n/a 4656 12
3185.2.fm \(\chi_{3185}(389, \cdot)\) n/a 4656 12
3185.2.fr \(\chi_{3185}(179, \cdot)\) n/a 4656 12
3185.2.ft \(\chi_{3185}(74, \cdot)\) n/a 4656 12
3185.2.fu \(\chi_{3185}(186, \cdot)\) n/a 3144 12
3185.2.fx \(\chi_{3185}(2, \cdot)\) n/a 9312 24
3185.2.fy \(\chi_{3185}(242, \cdot)\) n/a 9312 24
3185.2.ga \(\chi_{3185}(232, \cdot)\) n/a 9312 24
3185.2.gd \(\chi_{3185}(58, \cdot)\) n/a 9312 24
3185.2.ge \(\chi_{3185}(24, \cdot)\) n/a 9312 24
3185.2.gh \(\chi_{3185}(6, \cdot)\) n/a 6240 24
3185.2.gi \(\chi_{3185}(96, \cdot)\) n/a 6240 24
3185.2.gl \(\chi_{3185}(136, \cdot)\) n/a 6288 24
3185.2.gm \(\chi_{3185}(12, \cdot)\) n/a 9312 24
3185.2.gp \(\chi_{3185}(237, \cdot)\) n/a 9312 24
3185.2.gq \(\chi_{3185}(3, \cdot)\) n/a 9312 24
3185.2.gs \(\chi_{3185}(62, \cdot)\) n/a 9312 24
3185.2.gv \(\chi_{3185}(82, \cdot)\) n/a 9312 24
3185.2.gx \(\chi_{3185}(157, \cdot)\) n/a 8064 24
3185.2.gz \(\chi_{3185}(87, \cdot)\) n/a 9312 24
3185.2.ha \(\chi_{3185}(17, \cdot)\) n/a 9312 24
3185.2.hd \(\chi_{3185}(164, \cdot)\) n/a 9312 24
3185.2.he \(\chi_{3185}(279, \cdot)\) n/a 9312 24
3185.2.hg \(\chi_{3185}(54, \cdot)\) n/a 9312 24
3185.2.hj \(\chi_{3185}(171, \cdot)\) n/a 6288 24
3185.2.hl \(\chi_{3185}(162, \cdot)\) n/a 9312 24
3185.2.hn \(\chi_{3185}(268, \cdot)\) n/a 9312 24
3185.2.ho \(\chi_{3185}(163, \cdot)\) n/a 9312 24
3185.2.hq \(\chi_{3185}(37, \cdot)\) n/a 9312 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3185))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3185)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(455))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(637))\)\(^{\oplus 2}\)