Properties

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

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Defining parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Newforms: \( 37 \)
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

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

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

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