↑

Properties

Label 357.2
Level 357
Weight 2
Dimension 3143
Nonzero newspaces 20
Newform subspaces 47
Sturm bound 18432
Trace bound 7

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 357 = 3 \cdot 7 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Newform subspaces: \( 47 \)
Sturm bound: \(18432\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(357))\).

Total New Old
Modular forms 4992 3439 1553
Cusp forms 4225 3143 1082
Eisenstein series 767 296 471

Trace form

\( 3143 q + 9 q^{2} - 25 q^{3} - 47 q^{4} + 6 q^{5} - 35 q^{6} - 69 q^{7} + 9 q^{8} - 37 q^{9} + O(q^{10}) \) \( 3143 q + 9 q^{2} - 25 q^{3} - 47 q^{4} + 6 q^{5} - 35 q^{6} - 69 q^{7} + 9 q^{8} - 37 q^{9} - 74 q^{10} - 32 q^{11} - 79 q^{12} - 82 q^{13} - 35 q^{14} - 110 q^{15} - 175 q^{16} - 9 q^{17} - 119 q^{18} - 64 q^{19} - 58 q^{20} - 57 q^{21} - 164 q^{22} - 8 q^{23} - 103 q^{24} - 155 q^{25} - 102 q^{26} - 37 q^{27} - 203 q^{28} - 62 q^{29} - 154 q^{30} - 172 q^{31} - 103 q^{32} - 112 q^{33} - 275 q^{34} - 58 q^{35} - 119 q^{36} - 158 q^{37} - 88 q^{38} - 50 q^{39} - 218 q^{40} - 2 q^{41} - 19 q^{42} - 204 q^{43} - 44 q^{44} + 22 q^{45} - 56 q^{46} + 36 q^{47} + 129 q^{48} - 77 q^{49} + 99 q^{50} + 55 q^{51} - 18 q^{52} + 18 q^{53} + 9 q^{54} - 120 q^{55} - 59 q^{56} - 140 q^{57} - 186 q^{58} - 116 q^{59} - 82 q^{60} - 194 q^{61} - 200 q^{62} - 141 q^{63} - 367 q^{64} - 168 q^{65} - 156 q^{66} - 152 q^{67} - 287 q^{68} - 264 q^{69} - 298 q^{70} - 96 q^{71} - 215 q^{72} - 330 q^{73} - 198 q^{74} - 227 q^{75} - 404 q^{76} - 124 q^{77} - 386 q^{78} - 236 q^{79} - 346 q^{80} - 125 q^{81} - 406 q^{82} - 140 q^{83} - 131 q^{84} - 310 q^{85} + 16 q^{86} + 10 q^{87} - 292 q^{88} + 54 q^{89} + 142 q^{90} - 174 q^{91} - 152 q^{92} + 112 q^{93} - 200 q^{94} + 4 q^{95} + 393 q^{96} - 106 q^{97} - 19 q^{98} + 108 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(357))\)

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
357.2.a \(\chi_{357}(1, \cdot)\) 357.2.a.a 1 1
357.2.a.b 1
357.2.a.c 1
357.2.a.d 1
357.2.a.e 2
357.2.a.f 2
357.2.a.g 3
357.2.a.h 4
357.2.c \(\chi_{357}(356, \cdot)\) 357.2.c.a 20 1
357.2.c.b 24
357.2.d \(\chi_{357}(188, \cdot)\) 357.2.d.a 22 1
357.2.d.b 22
357.2.f \(\chi_{357}(169, \cdot)\) 357.2.f.a 6 1
357.2.f.b 10
357.2.i \(\chi_{357}(205, \cdot)\) 357.2.i.a 2 2
357.2.i.b 2
357.2.i.c 2
357.2.i.d 8
357.2.i.e 8
357.2.i.f 10
357.2.i.g 12
357.2.k \(\chi_{357}(64, \cdot)\) 357.2.k.a 12 2
357.2.k.b 20
357.2.l \(\chi_{357}(251, \cdot)\) 357.2.l.a 4 2
357.2.l.b 4
357.2.l.c 80
357.2.p \(\chi_{357}(16, \cdot)\) 357.2.p.a 48 2
357.2.r \(\chi_{357}(290, \cdot)\) 357.2.r.a 2 2
357.2.r.b 2
357.2.r.c 2
357.2.r.d 2
357.2.r.e 4
357.2.r.f 4
357.2.r.g 34
357.2.r.h 34
357.2.s \(\chi_{357}(101, \cdot)\) 357.2.s.a 88 2
357.2.u \(\chi_{357}(43, \cdot)\) 357.2.u.a 32 4
357.2.u.b 48
357.2.w \(\chi_{357}(83, \cdot)\) 357.2.w.a 176 4
357.2.y \(\chi_{357}(38, \cdot)\) 357.2.y.a 176 4
357.2.bb \(\chi_{357}(4, \cdot)\) 357.2.bb.a 96 4
357.2.bc \(\chi_{357}(97, \cdot)\) 357.2.bc.a 192 8
357.2.bf \(\chi_{357}(29, \cdot)\) 357.2.bf.a 288 8
357.2.bh \(\chi_{357}(25, \cdot)\) 357.2.bh.a 192 8
357.2.bj \(\chi_{357}(26, \cdot)\) 357.2.bj.a 352 8
357.2.bl \(\chi_{357}(10, \cdot)\) 357.2.bl.a 384 16
357.2.bm \(\chi_{357}(11, \cdot)\) 357.2.bm.a 704 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(357))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(357)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(357))\)\(^{\oplus 1}\)