Properties

Label 539.2
Level 539
Weight 2
Dimension 10662
Nonzero newspaces 16
Newform subspaces 70
Sturm bound 47040
Trace bound 2

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Defining parameters

Level: \( N \) = \( 539 = 7^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 70 \)
Sturm bound: \(47040\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(539))\).

Total New Old
Modular forms 12360 11534 826
Cusp forms 11161 10662 499
Eisenstein series 1199 872 327

Trace form

\( 10662 q - 119 q^{2} - 121 q^{3} - 127 q^{4} - 125 q^{5} - 142 q^{6} - 152 q^{7} - 237 q^{8} - 149 q^{9} + O(q^{10}) \) \( 10662 q - 119 q^{2} - 121 q^{3} - 127 q^{4} - 125 q^{5} - 142 q^{6} - 152 q^{7} - 237 q^{8} - 149 q^{9} - 164 q^{10} - 151 q^{11} - 344 q^{12} - 146 q^{13} - 180 q^{14} - 265 q^{15} - 205 q^{16} - 164 q^{17} - 221 q^{18} - 168 q^{19} - 232 q^{20} - 194 q^{21} - 302 q^{22} - 331 q^{23} - 288 q^{24} - 205 q^{25} - 242 q^{26} - 223 q^{27} - 236 q^{28} - 282 q^{29} - 322 q^{30} - 197 q^{31} - 289 q^{32} - 222 q^{33} - 416 q^{34} - 222 q^{35} - 361 q^{36} - 163 q^{37} - 204 q^{38} - 182 q^{39} - 126 q^{40} - 158 q^{41} - 138 q^{42} - 246 q^{43} - 162 q^{44} - 284 q^{45} - 70 q^{46} - 160 q^{47} - 126 q^{48} - 68 q^{49} - 463 q^{50} - 154 q^{51} - 86 q^{52} - 192 q^{53} - 226 q^{54} - 161 q^{55} - 276 q^{56} - 348 q^{57} - 210 q^{58} - 199 q^{59} - 2 q^{60} - 124 q^{61} - 206 q^{62} - 174 q^{63} - 197 q^{64} - 176 q^{65} + 77 q^{66} - 349 q^{67} - 130 q^{68} - 95 q^{69} - 210 q^{70} - 171 q^{71} + 27 q^{72} - 146 q^{73} - 216 q^{74} + 4 q^{75} + 132 q^{76} - 153 q^{77} - 262 q^{78} - 178 q^{79} + 56 q^{80} + 178 q^{81} - 20 q^{82} - 18 q^{83} + 292 q^{84} - 110 q^{85} + 162 q^{86} + 168 q^{87} + 117 q^{88} - 225 q^{89} + 472 q^{90} - 76 q^{91} - 164 q^{92} + 185 q^{93} - 58 q^{94} - 72 q^{95} + 406 q^{96} - 199 q^{97} + 156 q^{98} - 553 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(539))\)

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
539.2.a \(\chi_{539}(1, \cdot)\) 539.2.a.a 1 1
539.2.a.b 1
539.2.a.c 1
539.2.a.d 1
539.2.a.e 2
539.2.a.f 2
539.2.a.g 3
539.2.a.h 3
539.2.a.i 3
539.2.a.j 3
539.2.a.k 4
539.2.a.l 10
539.2.b \(\chi_{539}(538, \cdot)\) 539.2.b.a 8 1
539.2.b.b 12
539.2.b.c 16
539.2.e \(\chi_{539}(67, \cdot)\) 539.2.e.a 2 2
539.2.e.b 2
539.2.e.c 2
539.2.e.d 2
539.2.e.e 2
539.2.e.f 2
539.2.e.g 2
539.2.e.h 2
539.2.e.i 4
539.2.e.j 4
539.2.e.k 4
539.2.e.l 6
539.2.e.m 6
539.2.e.n 8
539.2.e.o 20
539.2.f \(\chi_{539}(148, \cdot)\) 539.2.f.a 4 4
539.2.f.b 4
539.2.f.c 8
539.2.f.d 8
539.2.f.e 16
539.2.f.f 16
539.2.f.g 20
539.2.f.h 20
539.2.f.i 48
539.2.i \(\chi_{539}(362, \cdot)\) 539.2.i.a 4 2
539.2.i.b 8
539.2.i.c 12
539.2.i.d 16
539.2.i.e 32
539.2.j \(\chi_{539}(78, \cdot)\) 539.2.j.a 144 6
539.2.j.b 144
539.2.m \(\chi_{539}(195, \cdot)\) 539.2.m.a 48 4
539.2.m.b 96
539.2.p \(\chi_{539}(76, \cdot)\) 539.2.p.a 324 6
539.2.q \(\chi_{539}(214, \cdot)\) 539.2.q.a 8 8
539.2.q.b 16
539.2.q.c 16
539.2.q.d 16
539.2.q.e 32
539.2.q.f 32
539.2.q.g 32
539.2.q.h 40
539.2.q.i 96
539.2.r \(\chi_{539}(23, \cdot)\) 539.2.r.a 276 12
539.2.r.b 276
539.2.s \(\chi_{539}(19, \cdot)\) 539.2.s.a 16 8
539.2.s.b 16
539.2.s.c 16
539.2.s.d 48
539.2.s.e 192
539.2.v \(\chi_{539}(15, \cdot)\) 539.2.v.a 1296 24
539.2.w \(\chi_{539}(10, \cdot)\) 539.2.w.a 648 12
539.2.z \(\chi_{539}(6, \cdot)\) 539.2.z.a 1296 24
539.2.bc \(\chi_{539}(4, \cdot)\) 539.2.bc.a 2592 48
539.2.bf \(\chi_{539}(17, \cdot)\) 539.2.bf.a 2592 48

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(539))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(539)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 2}\)