↑

Properties

Label 723.2
Level 723
Weight 2
Dimension 14279
Nonzero newspaces 20
Newform subspaces 51
Sturm bound 77440
Trace bound 2

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 723 = 3 \cdot 241 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Newform subspaces: \( 51 \)
Sturm bound: \(77440\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(723))\).

Total New Old
Modular forms 19840 14759 5081
Cusp forms 18881 14279 4602
Eisenstein series 959 480 479

Trace form

\( 14279 q - 3 q^{2} - 121 q^{3} - 247 q^{4} - 6 q^{5} - 123 q^{6} - 248 q^{7} - 15 q^{8} - 121 q^{9} + O(q^{10}) \) \( 14279 q - 3 q^{2} - 121 q^{3} - 247 q^{4} - 6 q^{5} - 123 q^{6} - 248 q^{7} - 15 q^{8} - 121 q^{9} - 258 q^{10} - 12 q^{11} - 127 q^{12} - 254 q^{13} - 24 q^{14} - 126 q^{15} - 271 q^{16} - 18 q^{17} - 123 q^{18} - 260 q^{19} - 42 q^{20} - 128 q^{21} - 276 q^{22} - 24 q^{23} - 135 q^{24} - 271 q^{25} - 42 q^{26} - 121 q^{27} - 296 q^{28} - 30 q^{29} - 138 q^{30} - 272 q^{31} - 63 q^{32} - 132 q^{33} - 294 q^{34} - 48 q^{35} - 127 q^{36} - 278 q^{37} - 60 q^{38} - 134 q^{39} - 330 q^{40} - 42 q^{41} - 144 q^{42} - 284 q^{43} - 84 q^{44} - 126 q^{45} - 312 q^{46} - 48 q^{47} - 151 q^{48} - 297 q^{49} - 93 q^{50} - 138 q^{51} - 338 q^{52} - 54 q^{53} - 123 q^{54} - 312 q^{55} - 120 q^{56} - 140 q^{57} - 330 q^{58} - 60 q^{59} - 162 q^{60} - 302 q^{61} - 96 q^{62} - 128 q^{63} - 367 q^{64} - 84 q^{65} - 156 q^{66} - 308 q^{67} - 126 q^{68} - 144 q^{69} - 384 q^{70} - 72 q^{71} - 135 q^{72} - 314 q^{73} - 114 q^{74} - 151 q^{75} - 380 q^{76} - 96 q^{77} - 162 q^{78} - 320 q^{79} - 186 q^{80} - 121 q^{81} - 366 q^{82} - 84 q^{83} - 176 q^{84} - 348 q^{85} - 132 q^{86} - 150 q^{87} - 420 q^{88} - 90 q^{89} - 138 q^{90} - 352 q^{91} - 168 q^{92} - 152 q^{93} - 384 q^{94} - 120 q^{95} - 183 q^{96} - 338 q^{97} - 171 q^{98} - 132 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(723))\)

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
723.2.a \(\chi_{723}(1, \cdot)\) 723.2.a.a 1 1
723.2.a.b 1
723.2.a.c 2
723.2.a.d 5
723.2.a.e 9
723.2.a.f 10
723.2.a.g 13
723.2.d \(\chi_{723}(481, \cdot)\) 723.2.d.a 4 1
723.2.d.b 16
723.2.d.c 22
723.2.e \(\chi_{723}(256, \cdot)\) 723.2.e.a 12 2
723.2.e.b 30
723.2.e.c 40
723.2.f \(\chi_{723}(64, \cdot)\) 723.2.f.a 2 2
723.2.f.b 2
723.2.f.c 4
723.2.f.d 4
723.2.f.e 34
723.2.f.f 38
723.2.h \(\chi_{723}(91, \cdot)\) 723.2.h.a 80 4
723.2.h.b 88
723.2.i \(\chi_{723}(16, \cdot)\) 723.2.i.a 8 2
723.2.i.b 32
723.2.i.c 42
723.2.l \(\chi_{723}(211, \cdot)\) 723.2.l.a 76 4
723.2.l.b 84
723.2.p \(\chi_{723}(154, \cdot)\) 723.2.p.a 80 4
723.2.p.b 88
723.2.r \(\chi_{723}(4, \cdot)\) 723.2.r.a 4 4
723.2.r.b 76
723.2.r.c 84
723.2.s \(\chi_{723}(94, \cdot)\) 723.2.s.a 160 8
723.2.s.b 168
723.2.t \(\chi_{723}(44, \cdot)\) 723.2.t.a 624 8
723.2.v \(\chi_{723}(25, \cdot)\) 723.2.v.a 160 8
723.2.v.b 176
723.2.y \(\chi_{723}(121, \cdot)\) 723.2.y.a 152 8
723.2.y.b 160
723.2.z \(\chi_{723}(10, \cdot)\) 723.2.z.a 160 8
723.2.z.b 168
723.2.bd \(\chi_{723}(61, \cdot)\) 723.2.bd.a 304 16
723.2.bd.b 336
723.2.be \(\chi_{723}(11, \cdot)\) 723.2.be.a 16 16
723.2.be.b 1248
723.2.bh \(\chi_{723}(82, \cdot)\) 723.2.bh.a 320 16
723.2.bh.b 336
723.2.bj \(\chi_{723}(17, \cdot)\) 723.2.bj.a 2496 32
723.2.bk \(\chi_{723}(49, \cdot)\) 723.2.bk.a 608 32
723.2.bk.b 640
723.2.bn \(\chi_{723}(14, \cdot)\) 723.2.bn.a 64 64
723.2.bn.b 4992

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(723))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(723)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(241))\)\(^{\oplus 2}\)