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Properties

Label 3135.2
Level 3135
Weight 2
Dimension 230497
Nonzero newspaces 72
Sturm bound 1382400
Trace bound 14

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Defining parameters

Level: \( N \) = \( 3135 = 3 \cdot 5 \cdot 11 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(1382400\)
Trace bound: \(14\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3135))\).

Total New Old
Modular forms 351360 234177 117183
Cusp forms 339841 230497 109344
Eisenstein series 11519 3680 7839

Trace form

\( 230497 q - 13 q^{2} - 131 q^{3} - 273 q^{4} + q^{5} - 357 q^{6} - 232 q^{7} + 47 q^{8} - 83 q^{9} + O(q^{10}) \) \( 230497 q - 13 q^{2} - 131 q^{3} - 273 q^{4} + q^{5} - 357 q^{6} - 232 q^{7} + 47 q^{8} - 83 q^{9} - 325 q^{10} + 9 q^{11} - 173 q^{12} - 162 q^{13} + 192 q^{14} - 117 q^{15} - 313 q^{16} + 146 q^{17} - 41 q^{18} - 71 q^{19} + 219 q^{20} - 212 q^{21} + 3 q^{22} + 80 q^{23} + 63 q^{24} - 219 q^{25} + 226 q^{26} - 143 q^{27} + 96 q^{28} + 126 q^{29} - 55 q^{30} - 616 q^{31} + 231 q^{32} - 89 q^{33} - 218 q^{34} + 200 q^{35} - 89 q^{36} - 26 q^{37} + 479 q^{38} + 14 q^{39} - 181 q^{40} + 298 q^{41} + 224 q^{42} + 44 q^{43} + 147 q^{44} - 281 q^{45} - 400 q^{46} + 72 q^{47} - 233 q^{48} - 263 q^{49} - 5 q^{50} - 518 q^{51} - 654 q^{52} - 162 q^{53} - 405 q^{54} - 617 q^{55} - 520 q^{56} - 451 q^{57} - 1078 q^{58} - 316 q^{59} - 599 q^{60} - 818 q^{61} - 8 q^{62} - 384 q^{63} - 265 q^{64} + 46 q^{65} - 683 q^{66} - 188 q^{67} + 198 q^{68} - 56 q^{69} + 128 q^{70} + 280 q^{71} - 213 q^{72} + 578 q^{73} + 634 q^{74} + 13 q^{75} + 15 q^{76} + 500 q^{77} + 70 q^{78} + 560 q^{79} - 37 q^{80} - 475 q^{81} + 566 q^{82} + 388 q^{83} - 192 q^{84} - 302 q^{85} + 364 q^{86} + 54 q^{87} - 85 q^{88} + 242 q^{89} - 1023 q^{90} - 704 q^{91} - 440 q^{92} - 308 q^{93} - 1176 q^{94} - 365 q^{95} - 2137 q^{96} - 750 q^{97} - 1061 q^{98} - 723 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3135))\)

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
3135.2.a \(\chi_{3135}(1, \cdot)\) 3135.2.a.a 1 1
3135.2.a.b 1
3135.2.a.c 1
3135.2.a.d 1
3135.2.a.e 1
3135.2.a.f 1
3135.2.a.g 1
3135.2.a.h 1
3135.2.a.i 3
3135.2.a.j 3
3135.2.a.k 3
3135.2.a.l 3
3135.2.a.m 4
3135.2.a.n 6
3135.2.a.o 6
3135.2.a.p 6
3135.2.a.q 7
3135.2.a.r 7
3135.2.a.s 7
3135.2.a.t 9
3135.2.a.u 9
3135.2.a.v 9
3135.2.a.w 9
3135.2.a.x 10
3135.2.a.y 12
3135.2.b \(\chi_{3135}(2509, \cdot)\) n/a 176 1
3135.2.e \(\chi_{3135}(2564, \cdot)\) n/a 400 1
3135.2.f \(\chi_{3135}(2089, \cdot)\) n/a 240 1
3135.2.i \(\chi_{3135}(989, \cdot)\) n/a 432 1
3135.2.j \(\chi_{3135}(1616, \cdot)\) n/a 288 1
3135.2.m \(\chi_{3135}(2716, \cdot)\) n/a 160 1
3135.2.n \(\chi_{3135}(56, \cdot)\) n/a 264 1
3135.2.q \(\chi_{3135}(1816, \cdot)\) n/a 272 2
3135.2.s \(\chi_{3135}(1253, \cdot)\) n/a 944 2
3135.2.u \(\chi_{3135}(1198, \cdot)\) n/a 432 2
3135.2.w \(\chi_{3135}(1673, \cdot)\) n/a 720 2
3135.2.y \(\chi_{3135}(892, \cdot)\) n/a 400 2
3135.2.z \(\chi_{3135}(856, \cdot)\) n/a 576 4
3135.2.ba \(\chi_{3135}(901, \cdot)\) n/a 320 2
3135.2.bd \(\chi_{3135}(296, \cdot)\) n/a 640 2
3135.2.bg \(\chi_{3135}(221, \cdot)\) n/a 528 2
3135.2.bh \(\chi_{3135}(749, \cdot)\) n/a 800 2
3135.2.bk \(\chi_{3135}(1189, \cdot)\) n/a 400 2
3135.2.bl \(\chi_{3135}(824, \cdot)\) n/a 944 2
3135.2.bo \(\chi_{3135}(274, \cdot)\) n/a 480 2
3135.2.bp \(\chi_{3135}(826, \cdot)\) n/a 792 6
3135.2.br \(\chi_{3135}(911, \cdot)\) n/a 1280 4
3135.2.bu \(\chi_{3135}(151, \cdot)\) n/a 640 4
3135.2.bv \(\chi_{3135}(761, \cdot)\) n/a 1152 4
3135.2.by \(\chi_{3135}(134, \cdot)\) n/a 1728 4
3135.2.bz \(\chi_{3135}(94, \cdot)\) n/a 960 4
3135.2.cc \(\chi_{3135}(284, \cdot)\) n/a 1888 4
3135.2.cd \(\chi_{3135}(229, \cdot)\) n/a 864 4
3135.2.cf \(\chi_{3135}(353, \cdot)\) n/a 1600 4
3135.2.ch \(\chi_{3135}(958, \cdot)\) n/a 800 4
3135.2.cj \(\chi_{3135}(692, \cdot)\) n/a 1888 4
3135.2.cl \(\chi_{3135}(1033, \cdot)\) n/a 960 4
3135.2.cn \(\chi_{3135}(676, \cdot)\) n/a 1280 8
3135.2.cp \(\chi_{3135}(716, \cdot)\) n/a 1608 6
3135.2.cs \(\chi_{3135}(109, \cdot)\) n/a 1440 6
3135.2.ct \(\chi_{3135}(329, \cdot)\) n/a 2832 6
3135.2.cv \(\chi_{3135}(241, \cdot)\) n/a 960 6
3135.2.cy \(\chi_{3135}(131, \cdot)\) n/a 1920 6
3135.2.cz \(\chi_{3135}(199, \cdot)\) n/a 1200 6
3135.2.dc \(\chi_{3135}(89, \cdot)\) n/a 2400 6
3135.2.dd \(\chi_{3135}(37, \cdot)\) n/a 1920 8
3135.2.df \(\chi_{3135}(533, \cdot)\) n/a 3456 8
3135.2.dh \(\chi_{3135}(172, \cdot)\) n/a 1728 8
3135.2.dj \(\chi_{3135}(227, \cdot)\) n/a 3776 8
3135.2.dm \(\chi_{3135}(259, \cdot)\) n/a 1920 8
3135.2.dn \(\chi_{3135}(239, \cdot)\) n/a 3776 8
3135.2.dq \(\chi_{3135}(49, \cdot)\) n/a 1920 8
3135.2.dr \(\chi_{3135}(179, \cdot)\) n/a 3776 8
3135.2.du \(\chi_{3135}(236, \cdot)\) n/a 2560 8
3135.2.dx \(\chi_{3135}(596, \cdot)\) n/a 2560 8
3135.2.dy \(\chi_{3135}(46, \cdot)\) n/a 1280 8
3135.2.eb \(\chi_{3135}(43, \cdot)\) n/a 2880 12
3135.2.ed \(\chi_{3135}(67, \cdot)\) n/a 2400 12
3135.2.ee \(\chi_{3135}(23, \cdot)\) n/a 4800 12
3135.2.eg \(\chi_{3135}(32, \cdot)\) n/a 5664 12
3135.2.ei \(\chi_{3135}(16, \cdot)\) n/a 3840 24
3135.2.ek \(\chi_{3135}(7, \cdot)\) n/a 3840 16
3135.2.em \(\chi_{3135}(8, \cdot)\) n/a 7552 16
3135.2.eo \(\chi_{3135}(103, \cdot)\) n/a 3840 16
3135.2.eq \(\chi_{3135}(368, \cdot)\) n/a 7552 16
3135.2.er \(\chi_{3135}(14, \cdot)\) n/a 11328 24
3135.2.eu \(\chi_{3135}(4, \cdot)\) n/a 5760 24
3135.2.ev \(\chi_{3135}(101, \cdot)\) n/a 7680 24
3135.2.ey \(\chi_{3135}(211, \cdot)\) n/a 3840 24
3135.2.fa \(\chi_{3135}(74, \cdot)\) n/a 11328 24
3135.2.fb \(\chi_{3135}(79, \cdot)\) n/a 5760 24
3135.2.fe \(\chi_{3135}(71, \cdot)\) n/a 7680 24
3135.2.fh \(\chi_{3135}(2, \cdot)\) n/a 22656 48
3135.2.fj \(\chi_{3135}(47, \cdot)\) n/a 22656 48
3135.2.fk \(\chi_{3135}(97, \cdot)\) n/a 11520 48
3135.2.fm \(\chi_{3135}(28, \cdot)\) n/a 11520 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3135))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3135)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(209))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(285))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(627))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1045))\)\(^{\oplus 2}\)