Properties

Label 935.2
Level 935
Weight 2
Dimension 30131
Nonzero newspaces 36
Newform subspaces 57
Sturm bound 138240
Trace bound 10

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 935 = 5 \cdot 11 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Newform subspaces: \( 57 \)
Sturm bound: \(138240\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(935))\).

Total New Old
Modular forms 35840 31747 4093
Cusp forms 33281 30131 3150
Eisenstein series 2559 1616 943

Trace form

\( 30131 q - 99 q^{2} - 96 q^{3} - 87 q^{4} - 159 q^{5} - 308 q^{6} - 104 q^{7} - 103 q^{8} - 109 q^{9} + O(q^{10}) \) \( 30131 q - 99 q^{2} - 96 q^{3} - 87 q^{4} - 159 q^{5} - 308 q^{6} - 104 q^{7} - 103 q^{8} - 109 q^{9} - 191 q^{10} - 385 q^{11} - 340 q^{12} - 118 q^{13} - 160 q^{14} - 238 q^{15} - 495 q^{16} - 145 q^{17} - 367 q^{18} - 140 q^{19} - 267 q^{20} - 424 q^{21} - 207 q^{22} - 268 q^{23} - 308 q^{24} - 275 q^{25} - 522 q^{26} - 204 q^{27} - 352 q^{28} - 198 q^{29} - 384 q^{30} - 436 q^{31} - 343 q^{32} - 272 q^{33} - 499 q^{34} - 484 q^{35} - 731 q^{36} - 242 q^{37} - 340 q^{38} - 352 q^{39} - 319 q^{40} - 554 q^{41} - 504 q^{42} - 236 q^{43} - 275 q^{44} - 457 q^{45} - 400 q^{46} - 144 q^{47} - 292 q^{48} - 85 q^{49} - 151 q^{50} - 392 q^{51} - 218 q^{52} - 222 q^{53} - 368 q^{54} - 187 q^{55} - 984 q^{56} - 392 q^{57} - 210 q^{58} - 264 q^{59} - 424 q^{60} - 414 q^{61} - 496 q^{62} - 456 q^{63} - 119 q^{64} - 302 q^{65} - 692 q^{66} - 344 q^{67} - 347 q^{68} - 548 q^{69} - 296 q^{70} - 452 q^{71} - 347 q^{72} - 226 q^{73} - 274 q^{74} - 330 q^{75} - 412 q^{76} - 312 q^{77} - 504 q^{78} - 208 q^{79} - 151 q^{80} - 453 q^{81} - 38 q^{82} - 260 q^{83} - 40 q^{84} - 47 q^{85} - 964 q^{86} - 208 q^{87} - 355 q^{88} - 334 q^{89} - 47 q^{90} - 432 q^{91} - 192 q^{92} - 132 q^{93} - 144 q^{94} - 140 q^{95} - 572 q^{96} + 26 q^{97} - 195 q^{98} - 129 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(935))\)

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
935.2.a \(\chi_{935}(1, \cdot)\) 935.2.a.a 1 1
935.2.a.b 1
935.2.a.c 3
935.2.a.d 3
935.2.a.e 3
935.2.a.f 3
935.2.a.g 4
935.2.a.h 6
935.2.a.i 9
935.2.a.j 11
935.2.a.k 11
935.2.b \(\chi_{935}(749, \cdot)\) 935.2.b.a 36 1
935.2.b.b 44
935.2.e \(\chi_{935}(254, \cdot)\) 935.2.e.a 88 1
935.2.f \(\chi_{935}(441, \cdot)\) 935.2.f.a 26 1
935.2.f.b 34
935.2.i \(\chi_{935}(166, \cdot)\) 935.2.i.a 52 2
935.2.i.b 68
935.2.l \(\chi_{935}(98, \cdot)\) 935.2.l.a 208 2
935.2.m \(\chi_{935}(307, \cdot)\) 935.2.m.a 192 2
935.2.p \(\chi_{935}(373, \cdot)\) 935.2.p.a 208 2
935.2.q \(\chi_{935}(208, \cdot)\) 935.2.q.a 208 2
935.2.s \(\chi_{935}(89, \cdot)\) 935.2.s.a 176 2
935.2.u \(\chi_{935}(86, \cdot)\) 935.2.u.a 4 4
935.2.u.b 4
935.2.u.c 8
935.2.u.d 52
935.2.u.e 60
935.2.u.f 60
935.2.u.g 68
935.2.w \(\chi_{935}(417, \cdot)\) 935.2.w.a 416 4
935.2.x \(\chi_{935}(111, \cdot)\) 935.2.x.a 104 4
935.2.x.b 136
935.2.z \(\chi_{935}(144, \cdot)\) 935.2.z.a 368 4
935.2.bc \(\chi_{935}(32, \cdot)\) 935.2.bc.a 416 4
935.2.bf \(\chi_{935}(16, \cdot)\) 935.2.bf.a 288 4
935.2.bg \(\chi_{935}(169, \cdot)\) 935.2.bg.a 416 4
935.2.bj \(\chi_{935}(69, \cdot)\) 935.2.bj.a 384 4
935.2.bl \(\chi_{935}(133, \cdot)\) 935.2.bl.a 720 8
935.2.bm \(\chi_{935}(131, \cdot)\) 935.2.bm.a 576 8
935.2.bp \(\chi_{935}(54, \cdot)\) 935.2.bp.a 64 8
935.2.bp.b 768
935.2.bq \(\chi_{935}(12, \cdot)\) 935.2.bq.a 720 8
935.2.bt \(\chi_{935}(4, \cdot)\) 935.2.bt.a 832 8
935.2.bv \(\chi_{935}(123, \cdot)\) 935.2.bv.a 832 8
935.2.bw \(\chi_{935}(118, \cdot)\) 935.2.bw.a 832 8
935.2.bz \(\chi_{935}(18, \cdot)\) 935.2.bz.a 768 8
935.2.ca \(\chi_{935}(13, \cdot)\) 935.2.ca.a 832 8
935.2.cd \(\chi_{935}(81, \cdot)\) 935.2.cd.a 576 8
935.2.cf \(\chi_{935}(2, \cdot)\) 935.2.cf.a 1664 16
935.2.cg \(\chi_{935}(9, \cdot)\) 935.2.cg.a 1664 16
935.2.ci \(\chi_{935}(26, \cdot)\) 935.2.ci.a 1152 16
935.2.cl \(\chi_{935}(83, \cdot)\) 935.2.cl.a 1664 16
935.2.cn \(\chi_{935}(37, \cdot)\) 935.2.cn.a 3328 32
935.2.cp \(\chi_{935}(24, \cdot)\) 935.2.cp.a 3328 32
935.2.cq \(\chi_{935}(6, \cdot)\) 935.2.cq.a 2304 32
935.2.cs \(\chi_{935}(3, \cdot)\) 935.2.cs.a 3328 32

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(935))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(935)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(187))\)\(^{\oplus 2}\)