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Properties

Label 1935.2
Level 1935
Weight 2
Dimension 95346
Nonzero newspaces 60
Sturm bound 532224
Trace bound 6

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Defining parameters

Level: \( N \) = \( 1935 = 3^{2} \cdot 5 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(532224\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1935))\).

Total New Old
Modular forms 135744 97562 38182
Cusp forms 130369 95346 35023
Eisenstein series 5375 2216 3159

Trace form

\( 95346 q - 112 q^{2} - 152 q^{3} - 104 q^{4} - 171 q^{5} - 472 q^{6} - 102 q^{7} - 120 q^{8} - 160 q^{9} + O(q^{10}) \) \( 95346 q - 112 q^{2} - 152 q^{3} - 104 q^{4} - 171 q^{5} - 472 q^{6} - 102 q^{7} - 120 q^{8} - 160 q^{9} - 537 q^{10} - 370 q^{11} - 184 q^{12} - 122 q^{13} - 150 q^{14} - 260 q^{15} - 364 q^{16} - 130 q^{17} - 200 q^{18} - 338 q^{19} - 239 q^{20} - 504 q^{21} - 142 q^{22} - 150 q^{23} - 240 q^{24} - 195 q^{25} - 406 q^{26} - 200 q^{27} - 394 q^{28} - 170 q^{29} - 316 q^{30} - 348 q^{31} - 68 q^{32} - 184 q^{33} - 28 q^{34} - 131 q^{35} - 440 q^{36} - 298 q^{37} + 74 q^{38} - 104 q^{39} + 25 q^{40} - 236 q^{41} - 96 q^{42} + 116 q^{43} + 52 q^{44} - 196 q^{45} - 886 q^{46} - 4 q^{47} - 88 q^{48} - 34 q^{49} - 43 q^{50} - 472 q^{51} + 94 q^{52} - 46 q^{53} - 160 q^{54} - 549 q^{55} - 342 q^{56} - 200 q^{57} - 178 q^{58} - 214 q^{59} - 292 q^{60} - 430 q^{61} - 294 q^{62} - 288 q^{63} - 476 q^{64} - 313 q^{65} - 680 q^{66} - 174 q^{67} - 266 q^{68} - 288 q^{69} - 225 q^{70} - 422 q^{71} - 216 q^{72} - 290 q^{73} + 172 q^{74} - 236 q^{75} - 156 q^{76} + 150 q^{77} - 88 q^{78} + 66 q^{79} + 49 q^{80} - 424 q^{81} + 102 q^{82} + 186 q^{83} - 192 q^{84} - 72 q^{85} + 58 q^{86} - 248 q^{87} + 294 q^{88} + 174 q^{89} - 44 q^{90} - 870 q^{91} + 486 q^{92} - 48 q^{93} + 218 q^{94} - 25 q^{95} - 392 q^{96} + 122 q^{97} + 334 q^{98} - 128 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1935))\)

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
1935.2.a \(\chi_{1935}(1, \cdot)\) 1935.2.a.a 1 1
1935.2.a.b 1
1935.2.a.c 1
1935.2.a.d 1
1935.2.a.e 1
1935.2.a.f 1
1935.2.a.g 1
1935.2.a.h 1
1935.2.a.i 1
1935.2.a.j 1
1935.2.a.k 1
1935.2.a.l 2
1935.2.a.m 2
1935.2.a.n 2
1935.2.a.o 3
1935.2.a.p 3
1935.2.a.q 3
1935.2.a.r 3
1935.2.a.s 5
1935.2.a.t 5
1935.2.a.u 5
1935.2.a.v 5
1935.2.a.w 5
1935.2.a.x 5
1935.2.a.y 5
1935.2.a.z 6
1935.2.b \(\chi_{1935}(1549, \cdot)\) 1935.2.b.a 4 1
1935.2.b.b 4
1935.2.b.c 6
1935.2.b.d 14
1935.2.b.e 16
1935.2.b.f 20
1935.2.b.g 40
1935.2.d \(\chi_{1935}(1934, \cdot)\) 1935.2.d.a 88 1
1935.2.g \(\chi_{1935}(386, \cdot)\) 1935.2.g.a 2 1
1935.2.g.b 2
1935.2.g.c 26
1935.2.g.d 26
1935.2.i \(\chi_{1935}(646, \cdot)\) n/a 336 2
1935.2.j \(\chi_{1935}(436, \cdot)\) n/a 352 2
1935.2.k \(\chi_{1935}(1111, \cdot)\) n/a 352 2
1935.2.l \(\chi_{1935}(1081, \cdot)\) n/a 148 2
1935.2.m \(\chi_{1935}(818, \cdot)\) n/a 168 2
1935.2.p \(\chi_{1935}(343, \cdot)\) n/a 216 2
1935.2.r \(\chi_{1935}(179, \cdot)\) n/a 176 2
1935.2.t \(\chi_{1935}(694, \cdot)\) n/a 216 2
1935.2.u \(\chi_{1935}(596, \cdot)\) n/a 352 2
1935.2.z \(\chi_{1935}(1031, \cdot)\) n/a 352 2
1935.2.bb \(\chi_{1935}(1856, \cdot)\) n/a 352 2
1935.2.be \(\chi_{1935}(724, \cdot)\) n/a 520 2
1935.2.bf \(\chi_{1935}(1469, \cdot)\) n/a 520 2
1935.2.bh \(\chi_{1935}(644, \cdot)\) n/a 520 2
1935.2.bj \(\chi_{1935}(49, \cdot)\) n/a 520 2
1935.2.bl \(\chi_{1935}(259, \cdot)\) n/a 504 2
1935.2.bo \(\chi_{1935}(209, \cdot)\) n/a 520 2
1935.2.bq \(\chi_{1935}(566, \cdot)\) n/a 120 2
1935.2.bs \(\chi_{1935}(226, \cdot)\) n/a 432 6
1935.2.bu \(\chi_{1935}(638, \cdot)\) n/a 352 4
1935.2.bv \(\chi_{1935}(37, \cdot)\) n/a 432 4
1935.2.bx \(\chi_{1935}(7, \cdot)\) n/a 1040 4
1935.2.ca \(\chi_{1935}(652, \cdot)\) n/a 1040 4
1935.2.cc \(\chi_{1935}(472, \cdot)\) n/a 1040 4
1935.2.cd \(\chi_{1935}(173, \cdot)\) n/a 1008 4
1935.2.cf \(\chi_{1935}(92, \cdot)\) n/a 1040 4
1935.2.ci \(\chi_{1935}(608, \cdot)\) n/a 1040 4
1935.2.cj \(\chi_{1935}(161, \cdot)\) n/a 336 6
1935.2.cn \(\chi_{1935}(64, \cdot)\) n/a 648 6
1935.2.cp \(\chi_{1935}(629, \cdot)\) n/a 528 6
1935.2.cq \(\chi_{1935}(181, \cdot)\) n/a 888 12
1935.2.cr \(\chi_{1935}(31, \cdot)\) n/a 2112 12
1935.2.cs \(\chi_{1935}(16, \cdot)\) n/a 2112 12
1935.2.ct \(\chi_{1935}(196, \cdot)\) n/a 2112 12
1935.2.cu \(\chi_{1935}(82, \cdot)\) n/a 1296 12
1935.2.cx \(\chi_{1935}(107, \cdot)\) n/a 1056 12
1935.2.da \(\chi_{1935}(26, \cdot)\) n/a 720 12
1935.2.db \(\chi_{1935}(124, \cdot)\) n/a 3120 12
1935.2.de \(\chi_{1935}(194, \cdot)\) n/a 3120 12
1935.2.dg \(\chi_{1935}(29, \cdot)\) n/a 3120 12
1935.2.di \(\chi_{1935}(4, \cdot)\) n/a 3120 12
1935.2.dk \(\chi_{1935}(139, \cdot)\) n/a 3120 12
1935.2.dl \(\chi_{1935}(104, \cdot)\) n/a 3120 12
1935.2.do \(\chi_{1935}(191, \cdot)\) n/a 2112 12
1935.2.dr \(\chi_{1935}(356, \cdot)\) n/a 2112 12
1935.2.dt \(\chi_{1935}(131, \cdot)\) n/a 2112 12
1935.2.dw \(\chi_{1935}(89, \cdot)\) n/a 1056 12
1935.2.dy \(\chi_{1935}(109, \cdot)\) n/a 1296 12
1935.2.ea \(\chi_{1935}(23, \cdot)\) n/a 6240 24
1935.2.ed \(\chi_{1935}(38, \cdot)\) n/a 6240 24
1935.2.ef \(\chi_{1935}(47, \cdot)\) n/a 6240 24
1935.2.eg \(\chi_{1935}(22, \cdot)\) n/a 6240 24
1935.2.ei \(\chi_{1935}(112, \cdot)\) n/a 6240 24
1935.2.el \(\chi_{1935}(148, \cdot)\) n/a 6240 24
1935.2.en \(\chi_{1935}(28, \cdot)\) n/a 2592 24
1935.2.eo \(\chi_{1935}(17, \cdot)\) n/a 2112 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1935))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1935)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(129))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(215))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(387))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(645))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1935))\)\(^{\oplus 1}\)