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Properties

Label 715.2
Level 715
Weight 2
Dimension 17367
Nonzero newspaces 40
Newform subspaces 68
Sturm bound 80640
Trace bound 5

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Defining parameters

Level: \( N \) = \( 715 = 5 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Newform subspaces: \( 68 \)
Sturm bound: \(80640\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(715))\).

Total New Old
Modular forms 21120 18551 2569
Cusp forms 19201 17367 1834
Eisenstein series 1919 1184 735

Trace form

\( 17367 q - 67 q^{2} - 64 q^{3} - 55 q^{4} - 111 q^{5} - 212 q^{6} - 80 q^{7} - 107 q^{8} - 109 q^{9} + O(q^{10}) \) \( 17367 q - 67 q^{2} - 64 q^{3} - 55 q^{4} - 111 q^{5} - 212 q^{6} - 80 q^{7} - 107 q^{8} - 109 q^{9} - 165 q^{10} - 273 q^{11} - 276 q^{12} - 117 q^{13} - 208 q^{14} - 166 q^{15} - 335 q^{16} - 118 q^{17} - 211 q^{18} - 156 q^{19} - 229 q^{20} - 336 q^{21} - 199 q^{22} - 212 q^{23} - 356 q^{24} - 183 q^{25} - 387 q^{26} - 316 q^{27} - 328 q^{28} - 194 q^{29} - 352 q^{30} - 316 q^{31} - 351 q^{32} - 240 q^{33} - 366 q^{34} - 264 q^{35} - 651 q^{36} - 150 q^{37} - 284 q^{38} - 216 q^{39} - 367 q^{40} - 462 q^{41} - 448 q^{42} - 228 q^{43} - 203 q^{44} - 395 q^{45} - 448 q^{46} - 120 q^{47} - 84 q^{48} - 157 q^{49} - 217 q^{50} - 328 q^{51} - 71 q^{52} - 206 q^{53} + 24 q^{54} - 63 q^{55} - 456 q^{56} - 32 q^{57} + 90 q^{58} + 212 q^{60} - 194 q^{61} - 96 q^{62} + 21 q^{64} - 87 q^{65} - 724 q^{66} - 144 q^{67} - 170 q^{68} - 44 q^{69} - 220 q^{70} - 436 q^{71} - 179 q^{72} - 242 q^{73} - 470 q^{74} - 266 q^{75} - 620 q^{76} - 352 q^{77} - 580 q^{78} - 416 q^{79} - 613 q^{80} - 645 q^{81} - 538 q^{82} - 476 q^{83} - 688 q^{84} - 456 q^{85} - 796 q^{86} - 656 q^{87} - 731 q^{88} - 550 q^{89} - 531 q^{90} - 624 q^{91} - 704 q^{92} - 508 q^{93} - 560 q^{94} - 340 q^{95} - 916 q^{96} - 262 q^{97} - 339 q^{98} - 249 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(715))\)

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
715.2.a \(\chi_{715}(1, \cdot)\) 715.2.a.a 1 1
715.2.a.b 1
715.2.a.c 2
715.2.a.d 3
715.2.a.e 3
715.2.a.f 6
715.2.a.g 6
715.2.a.h 8
715.2.a.i 9
715.2.b \(\chi_{715}(144, \cdot)\) 715.2.b.a 26 1
715.2.b.b 34
715.2.e \(\chi_{715}(441, \cdot)\) 715.2.e.a 2 1
715.2.e.b 18
715.2.e.c 24
715.2.f \(\chi_{715}(584, \cdot)\) 715.2.f.a 72 1
715.2.i \(\chi_{715}(276, \cdot)\) 715.2.i.a 4 2
715.2.i.b 16
715.2.i.c 20
715.2.i.d 28
715.2.i.e 28
715.2.j \(\chi_{715}(177, \cdot)\) 715.2.j.a 140 2
715.2.l \(\chi_{715}(109, \cdot)\) 715.2.l.a 4 2
715.2.l.b 4
715.2.l.c 16
715.2.l.d 136
715.2.o \(\chi_{715}(417, \cdot)\) 715.2.o.a 144 2
715.2.q \(\chi_{715}(142, \cdot)\) 715.2.q.a 160 2
715.2.s \(\chi_{715}(21, \cdot)\) 715.2.s.a 112 2
715.2.t \(\chi_{715}(122, \cdot)\) 715.2.t.a 140 2
715.2.v \(\chi_{715}(196, \cdot)\) 715.2.v.a 4 4
715.2.v.b 32
715.2.v.c 44
715.2.v.d 52
715.2.v.e 60
715.2.y \(\chi_{715}(199, \cdot)\) 715.2.y.a 144 2
715.2.z \(\chi_{715}(56, \cdot)\) 715.2.z.a 8 2
715.2.z.b 32
715.2.z.c 56
715.2.bc \(\chi_{715}(419, \cdot)\) 715.2.bc.a 8 2
715.2.bc.b 60
715.2.bc.c 68
715.2.bf \(\chi_{715}(64, \cdot)\) 715.2.bf.a 320 4
715.2.bg \(\chi_{715}(181, \cdot)\) 715.2.bg.a 224 4
715.2.bj \(\chi_{715}(14, \cdot)\) 715.2.bj.a 288 4
715.2.bl \(\chi_{715}(67, \cdot)\) 715.2.bl.a 280 4
715.2.bm \(\chi_{715}(76, \cdot)\) 715.2.bm.a 224 4
715.2.bo \(\chi_{715}(43, \cdot)\) 715.2.bo.a 320 4
715.2.bq \(\chi_{715}(87, \cdot)\) 715.2.bq.a 320 4
715.2.bt \(\chi_{715}(54, \cdot)\) 715.2.bt.a 32 4
715.2.bt.b 288
715.2.bv \(\chi_{715}(188, \cdot)\) 715.2.bv.a 280 4
715.2.bw \(\chi_{715}(16, \cdot)\) 715.2.bw.a 224 8
715.2.bw.b 224
715.2.by \(\chi_{715}(203, \cdot)\) 715.2.by.a 640 8
715.2.bz \(\chi_{715}(96, \cdot)\) 715.2.bz.a 448 8
715.2.cb \(\chi_{715}(233, \cdot)\) 715.2.cb.a 640 8
715.2.cd \(\chi_{715}(118, \cdot)\) 715.2.cd.a 576 8
715.2.cg \(\chi_{715}(239, \cdot)\) 715.2.cg.a 640 8
715.2.ci \(\chi_{715}(47, \cdot)\) 715.2.ci.a 640 8
715.2.cj \(\chi_{715}(9, \cdot)\) 715.2.cj.a 640 8
715.2.cm \(\chi_{715}(36, \cdot)\) 715.2.cm.a 448 8
715.2.cn \(\chi_{715}(4, \cdot)\) 715.2.cn.a 640 8
715.2.cq \(\chi_{715}(37, \cdot)\) 715.2.cq.a 1280 16
715.2.cs \(\chi_{715}(19, \cdot)\) 715.2.cs.a 1280 16
715.2.cv \(\chi_{715}(68, \cdot)\) 715.2.cv.a 1280 16
715.2.cx \(\chi_{715}(17, \cdot)\) 715.2.cx.a 1280 16
715.2.cz \(\chi_{715}(6, \cdot)\) 715.2.cz.a 896 16
715.2.da \(\chi_{715}(97, \cdot)\) 715.2.da.a 1280 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(715))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(715)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 2}\)