↑

Properties

Label 783.2
Level 783
Weight 2
Dimension 17446
Nonzero newspaces 18
Newform subspaces 41
Sturm bound 90720
Trace bound 4

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 783 = 3^{3} \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 18 \)
Newform subspaces: \( 41 \)
Sturm bound: \(90720\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(783))\).

Total New Old
Modular forms 23520 18310 5210
Cusp forms 21841 17446 4395
Eisenstein series 1679 864 815

Trace form

\( 17446 q - 100 q^{2} - 156 q^{3} - 180 q^{4} - 106 q^{5} - 168 q^{6} - 182 q^{7} - 124 q^{8} - 168 q^{9} + O(q^{10}) \) \( 17446 q - 100 q^{2} - 156 q^{3} - 180 q^{4} - 106 q^{5} - 168 q^{6} - 182 q^{7} - 124 q^{8} - 168 q^{9} - 190 q^{10} - 118 q^{11} - 192 q^{12} - 194 q^{13} - 142 q^{14} - 186 q^{15} - 204 q^{16} - 130 q^{17} - 186 q^{18} - 176 q^{19} - 106 q^{20} - 144 q^{21} - 202 q^{22} - 88 q^{23} - 132 q^{24} - 192 q^{25} - 52 q^{26} - 150 q^{27} - 428 q^{28} - 106 q^{29} - 318 q^{30} - 194 q^{31} - 112 q^{32} - 168 q^{33} - 214 q^{34} - 136 q^{35} - 204 q^{36} - 212 q^{37} - 196 q^{38} - 234 q^{39} - 238 q^{40} - 142 q^{41} - 204 q^{42} - 218 q^{43} - 118 q^{44} - 150 q^{45} - 190 q^{46} - 82 q^{47} - 138 q^{48} - 208 q^{49} - 46 q^{50} - 132 q^{51} - 194 q^{52} - 76 q^{53} - 60 q^{54} - 424 q^{55} - 102 q^{56} - 162 q^{57} - 217 q^{58} - 200 q^{59} - 168 q^{60} - 218 q^{61} - 88 q^{62} - 186 q^{63} - 204 q^{64} - 118 q^{65} - 150 q^{66} - 176 q^{67} - 130 q^{68} - 186 q^{69} - 222 q^{70} - 250 q^{71} - 204 q^{72} - 250 q^{73} - 346 q^{74} - 246 q^{75} - 352 q^{76} - 282 q^{77} - 204 q^{78} - 202 q^{79} - 588 q^{80} - 240 q^{81} - 536 q^{82} - 302 q^{83} - 180 q^{84} - 310 q^{85} - 522 q^{86} - 177 q^{87} - 668 q^{88} - 270 q^{89} - 204 q^{90} - 366 q^{91} - 370 q^{92} - 90 q^{93} - 278 q^{94} - 270 q^{95} - 168 q^{96} - 220 q^{97} - 246 q^{98} - 114 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(783))\)

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
783.2.a \(\chi_{783}(1, \cdot)\) 783.2.a.a 2 1
783.2.a.b 2
783.2.a.c 2
783.2.a.d 2
783.2.a.e 3
783.2.a.f 3
783.2.a.g 4
783.2.a.h 4
783.2.a.i 8
783.2.a.j 8
783.2.c \(\chi_{783}(28, \cdot)\) 783.2.c.a 8 1
783.2.c.b 12
783.2.c.c 20
783.2.e \(\chi_{783}(262, \cdot)\) 783.2.e.a 22 2
783.2.e.b 34
783.2.g \(\chi_{783}(215, \cdot)\) 783.2.g.a 8 2
783.2.g.b 32
783.2.g.c 40
783.2.i \(\chi_{783}(289, \cdot)\) 783.2.i.a 56 2
783.2.k \(\chi_{783}(82, \cdot)\) 783.2.k.a 6 6
783.2.k.b 6
783.2.k.c 54
783.2.k.d 54
783.2.k.e 60
783.2.k.f 60
783.2.l \(\chi_{783}(88, \cdot)\) 783.2.l.a 234 6
783.2.l.b 270
783.2.m \(\chi_{783}(17, \cdot)\) 783.2.m.a 112 4
783.2.p \(\chi_{783}(109, \cdot)\) 783.2.p.a 12 6
783.2.p.b 108
783.2.p.c 120
783.2.t \(\chi_{783}(115, \cdot)\) 783.2.t.a 528 6
783.2.u \(\chi_{783}(181, \cdot)\) 783.2.u.a 336 12
783.2.v \(\chi_{783}(26, \cdot)\) 783.2.v.a 240 12
783.2.v.b 240
783.2.x \(\chi_{783}(41, \cdot)\) 783.2.x.a 1056 12
783.2.ba \(\chi_{783}(64, \cdot)\) 783.2.ba.a 336 12
783.2.bc \(\chi_{783}(7, \cdot)\) 783.2.bc.a 3168 36
783.2.be \(\chi_{783}(8, \cdot)\) 783.2.be.a 672 24
783.2.bf \(\chi_{783}(4, \cdot)\) 783.2.bf.a 3168 36
783.2.bj \(\chi_{783}(2, \cdot)\) 783.2.bj.a 6336 72

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(783))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(783)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(261))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(783))\)\(^{\oplus 1}\)