Properties

Label 731.2
Level 731
Weight 2
Dimension 21381
Nonzero newspaces 20
Newform subspaces 37
Sturm bound 88704
Trace bound 2

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Defining parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Newform subspaces: \( 37 \)
Sturm bound: \(88704\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(731))\).

Total New Old
Modular forms 22848 22613 235
Cusp forms 21505 21381 124
Eisenstein series 1343 1232 111

Trace form

\( 21381 q - 287 q^{2} - 290 q^{3} - 299 q^{4} - 296 q^{5} - 314 q^{6} - 302 q^{7} - 323 q^{8} - 317 q^{9} + O(q^{10}) \) \( 21381 q - 287 q^{2} - 290 q^{3} - 299 q^{4} - 296 q^{5} - 314 q^{6} - 302 q^{7} - 323 q^{8} - 317 q^{9} - 324 q^{10} - 298 q^{11} - 314 q^{12} - 304 q^{13} - 318 q^{14} - 302 q^{15} - 299 q^{16} - 318 q^{17} - 651 q^{18} - 322 q^{19} - 348 q^{20} - 326 q^{21} - 354 q^{22} - 334 q^{23} - 378 q^{24} - 315 q^{25} - 332 q^{26} - 350 q^{27} - 350 q^{28} - 328 q^{29} - 366 q^{30} - 296 q^{31} - 271 q^{32} - 258 q^{33} - 213 q^{34} - 594 q^{35} - 167 q^{36} - 244 q^{37} - 194 q^{38} - 252 q^{39} - 20 q^{40} - 274 q^{41} - 164 q^{42} - 123 q^{43} - 464 q^{44} - 198 q^{45} - 230 q^{46} - 300 q^{47} - 106 q^{48} - 287 q^{49} - 261 q^{50} - 333 q^{51} - 540 q^{52} - 268 q^{53} - 272 q^{54} - 282 q^{55} - 314 q^{56} - 312 q^{57} - 372 q^{58} - 330 q^{59} - 446 q^{60} - 336 q^{61} - 358 q^{62} - 350 q^{63} - 435 q^{64} - 378 q^{65} - 454 q^{66} - 402 q^{67} - 344 q^{68} - 578 q^{69} - 270 q^{70} - 314 q^{71} - 51 q^{72} - 216 q^{73} - 158 q^{74} - 100 q^{75} - 164 q^{76} - 154 q^{77} + 100 q^{78} - 222 q^{79} - 148 q^{80} - 97 q^{81} - 20 q^{82} - 234 q^{83} + 258 q^{84} - 220 q^{85} - 427 q^{86} - 320 q^{87} - 78 q^{88} - 236 q^{89} + 232 q^{90} - 222 q^{91} + 22 q^{92} - 134 q^{93} - 54 q^{94} - 246 q^{95} + 40 q^{96} - 192 q^{97} - 153 q^{98} - 148 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(731))\)

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
731.2.a \(\chi_{731}(1, \cdot)\) 731.2.a.a 1 1
731.2.a.b 2
731.2.a.c 6
731.2.a.d 8
731.2.a.e 19
731.2.a.f 21
731.2.d \(\chi_{731}(560, \cdot)\) 731.2.d.a 2 1
731.2.d.b 8
731.2.d.c 20
731.2.d.d 34
731.2.e \(\chi_{731}(307, \cdot)\) 731.2.e.a 58 2
731.2.e.b 58
731.2.f \(\chi_{731}(259, \cdot)\) 731.2.f.a 2 2
731.2.f.b 2
731.2.f.c 56
731.2.f.d 68
731.2.j \(\chi_{731}(135, \cdot)\) 731.2.j.a 128 2
731.2.k \(\chi_{731}(35, \cdot)\) 731.2.k.a 180 6
731.2.k.b 180
731.2.m \(\chi_{731}(87, \cdot)\) 731.2.m.a 4 4
731.2.m.b 116
731.2.m.c 128
731.2.n \(\chi_{731}(208, \cdot)\) 731.2.n.a 256 4
731.2.p \(\chi_{731}(16, \cdot)\) 731.2.p.a 384 6
731.2.s \(\chi_{731}(214, \cdot)\) 731.2.s.a 16 8
731.2.s.b 496
731.2.u \(\chi_{731}(52, \cdot)\) 731.2.u.a 348 12
731.2.u.b 348
731.2.v \(\chi_{731}(36, \cdot)\) 731.2.v.a 512 8
731.2.y \(\chi_{731}(4, \cdot)\) 731.2.y.a 768 12
731.2.z \(\chi_{731}(67, \cdot)\) 731.2.z.a 768 12
731.2.bd \(\chi_{731}(7, \cdot)\) 731.2.bd.a 1024 16
731.2.be \(\chi_{731}(59, \cdot)\) 731.2.be.a 1536 24
731.2.bh \(\chi_{731}(13, \cdot)\) 731.2.bh.a 1536 24
731.2.bj \(\chi_{731}(22, \cdot)\) 731.2.bj.a 3072 48
731.2.bl \(\chi_{731}(9, \cdot)\) 731.2.bl.a 3072 48
731.2.bm \(\chi_{731}(3, \cdot)\) 731.2.bm.a 6144 96

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(731))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(731)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 2}\)