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Properties

Label 527.2
Level 527
Weight 2
Dimension 10979
Nonzero newspaces 20
Newform subspaces 28
Sturm bound 46080
Trace bound 3

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Defining parameters

Level: \( N \) = \( 527 = 17 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Newform subspaces: \( 28 \)
Sturm bound: \(46080\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(527))\).

Total New Old
Modular forms 12000 11851 149
Cusp forms 11041 10979 62
Eisenstein series 959 872 87

Trace form

\( 10979 q - 203 q^{2} - 206 q^{3} - 215 q^{4} - 212 q^{5} - 230 q^{6} - 218 q^{7} - 239 q^{8} - 233 q^{9} + O(q^{10}) \) \( 10979 q - 203 q^{2} - 206 q^{3} - 215 q^{4} - 212 q^{5} - 230 q^{6} - 218 q^{7} - 239 q^{8} - 233 q^{9} - 240 q^{10} - 214 q^{11} - 230 q^{12} - 220 q^{13} - 234 q^{14} - 218 q^{15} - 215 q^{16} - 228 q^{17} - 471 q^{18} - 238 q^{19} - 264 q^{20} - 232 q^{21} - 210 q^{22} - 220 q^{23} - 174 q^{24} - 161 q^{25} - 188 q^{26} - 176 q^{27} - 106 q^{28} - 184 q^{29} - 132 q^{30} - 173 q^{31} - 301 q^{32} - 198 q^{33} - 126 q^{34} - 438 q^{35} - 147 q^{36} - 154 q^{37} - 218 q^{38} - 196 q^{39} - 152 q^{40} - 202 q^{41} - 230 q^{42} - 236 q^{43} - 254 q^{44} - 324 q^{45} - 314 q^{46} - 258 q^{47} - 268 q^{48} - 241 q^{49} - 195 q^{50} - 195 q^{51} - 434 q^{52} - 208 q^{53} + 16 q^{54} - 162 q^{55} - 44 q^{56} - 62 q^{57} - 78 q^{58} - 186 q^{59} + 148 q^{60} - 42 q^{61} - 107 q^{62} - 236 q^{63} - 111 q^{64} - 114 q^{65} + 80 q^{66} - 258 q^{67} - 149 q^{68} - 302 q^{69} - 84 q^{70} - 194 q^{71} - 57 q^{72} - 156 q^{73} - 218 q^{74} - 100 q^{75} - 124 q^{76} - 172 q^{77} - 92 q^{78} - 236 q^{79} - 100 q^{80} - 229 q^{81} - 236 q^{82} - 108 q^{83} - 138 q^{84} - 175 q^{85} - 350 q^{86} - 242 q^{87} - 54 q^{88} - 170 q^{89} + 10 q^{90} - 176 q^{91} + 76 q^{92} - 118 q^{93} - 396 q^{94} - 90 q^{95} + 28 q^{96} - 230 q^{97} - 3 q^{98} - 208 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(527))\)

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
527.2.a \(\chi_{527}(1, \cdot)\) 527.2.a.a 2 1
527.2.a.b 5
527.2.a.c 7
527.2.a.d 11
527.2.a.e 16
527.2.b \(\chi_{527}(373, \cdot)\) 527.2.b.a 46 1
527.2.e \(\chi_{527}(222, \cdot)\) 527.2.e.a 38 2
527.2.e.b 46
527.2.g \(\chi_{527}(404, \cdot)\) 527.2.g.a 92 2
527.2.h \(\chi_{527}(35, \cdot)\) 527.2.h.a 4 4
527.2.h.b 76
527.2.h.c 96
527.2.k \(\chi_{527}(67, \cdot)\) 527.2.k.a 92 2
527.2.l \(\chi_{527}(32, \cdot)\) 527.2.l.a 176 4
527.2.o \(\chi_{527}(16, \cdot)\) 527.2.o.a 184 4
527.2.q \(\chi_{527}(98, \cdot)\) 527.2.q.a 184 4
527.2.s \(\chi_{527}(18, \cdot)\) 527.2.s.a 152 8
527.2.s.b 184
527.2.t \(\chi_{527}(61, \cdot)\) 527.2.t.a 368 8
527.2.v \(\chi_{527}(4, \cdot)\) 527.2.v.a 368 8
527.2.y \(\chi_{527}(25, \cdot)\) 527.2.y.a 368 8
527.2.ba \(\chi_{527}(50, \cdot)\) 527.2.ba.a 368 8
527.2.bd \(\chi_{527}(2, \cdot)\) 527.2.bd.a 736 16
527.2.bf \(\chi_{527}(6, \cdot)\) 527.2.bf.a 736 16
527.2.bh \(\chi_{527}(38, \cdot)\) 527.2.bh.a 736 16
527.2.bj \(\chi_{527}(23, \cdot)\) 527.2.bj.a 1472 32
527.2.bk \(\chi_{527}(9, \cdot)\) 527.2.bk.a 1472 32
527.2.bm \(\chi_{527}(3, \cdot)\) 527.2.bm.a 2944 64

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(527))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(527)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(527))\)\(^{\oplus 1}\)