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Properties

Label 529.2
Level 529
Weight 2
Dimension 11241
Nonzero newspaces 4
Newform subspaces 30
Sturm bound 46552
Trace bound 1

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Defining parameters

Level: \( N \) = \( 529 = 23^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 30 \)
Sturm bound: \(46552\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(529))\).

Total New Old
Modular forms 12012 11946 66
Cusp forms 11265 11241 24
Eisenstein series 747 705 42

Trace form

\( 11241 q - 234 q^{2} - 235 q^{3} - 238 q^{4} - 237 q^{5} - 243 q^{6} - 239 q^{7} - 246 q^{8} - 244 q^{9} + O(q^{10}) \) \( 11241 q - 234 q^{2} - 235 q^{3} - 238 q^{4} - 237 q^{5} - 243 q^{6} - 239 q^{7} - 246 q^{8} - 244 q^{9} - 249 q^{10} - 243 q^{11} - 259 q^{12} - 245 q^{13} - 255 q^{14} - 233 q^{15} - 218 q^{16} - 227 q^{17} - 182 q^{18} - 229 q^{19} - 185 q^{20} - 197 q^{21} - 201 q^{22} - 220 q^{23} - 379 q^{24} - 218 q^{25} - 229 q^{26} - 205 q^{27} - 199 q^{28} - 239 q^{29} - 215 q^{30} - 241 q^{31} - 250 q^{32} - 257 q^{33} - 241 q^{34} - 235 q^{35} - 212 q^{36} - 181 q^{37} - 181 q^{38} - 199 q^{39} - 145 q^{40} - 229 q^{41} - 107 q^{42} - 187 q^{43} - 117 q^{44} - 155 q^{45} - 154 q^{46} - 411 q^{47} - 135 q^{48} - 156 q^{49} - 170 q^{50} - 215 q^{51} - 109 q^{52} - 241 q^{53} - 131 q^{54} - 171 q^{55} - 109 q^{56} - 157 q^{57} - 123 q^{58} - 159 q^{59} - 135 q^{60} - 205 q^{61} - 195 q^{62} - 225 q^{63} - 182 q^{64} - 161 q^{65} - 133 q^{66} - 255 q^{67} - 71 q^{68} - 187 q^{69} - 419 q^{70} - 193 q^{71} - 96 q^{72} - 261 q^{73} - 147 q^{74} - 113 q^{75} - 85 q^{76} - 129 q^{77} - 47 q^{78} - 135 q^{79} + q^{80} - 137 q^{82} - 161 q^{83} - 15 q^{84} - 75 q^{85} - 99 q^{86} - 87 q^{87} - 147 q^{88} - 189 q^{89} - 3 q^{90} - 145 q^{91} - 143 q^{92} - 315 q^{93} - 133 q^{94} - 153 q^{95} + 111 q^{96} - 131 q^{97} - 138 q^{98} - 13 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(529))\)

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
529.2.a \(\chi_{529}(1, \cdot)\) 529.2.a.a 2 1
529.2.a.b 2
529.2.a.c 2
529.2.a.d 2
529.2.a.e 2
529.2.a.f 3
529.2.a.g 4
529.2.a.h 4
529.2.a.i 5
529.2.a.j 5
529.2.c \(\chi_{529}(118, \cdot)\) 529.2.c.a 10 10
529.2.c.b 10
529.2.c.c 10
529.2.c.d 10
529.2.c.e 10
529.2.c.f 10
529.2.c.g 10
529.2.c.h 10
529.2.c.i 10
529.2.c.j 20
529.2.c.k 20
529.2.c.l 20
529.2.c.m 20
529.2.c.n 20
529.2.c.o 20
529.2.c.p 30
529.2.c.q 40
529.2.c.r 40
529.2.e \(\chi_{529}(24, \cdot)\) 529.2.e.a 990 22
529.2.g \(\chi_{529}(2, \cdot)\) 529.2.g.a 9900 220

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(529))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(529)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 2}\)