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Properties

Label 547.2
Level 547
Weight 2
Dimension 12195
Nonzero newspaces 8
Newform subspaces 10
Sturm bound 49868
Trace bound 1

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Defining parameters

Level: \( N \) = \( 547 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 10 \)
Sturm bound: \(49868\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(547))\).

Total New Old
Modular forms 12740 12740 0
Cusp forms 12195 12195 0
Eisenstein series 545 545 0

Trace form

\( 12195 q - 270 q^{2} - 269 q^{3} - 266 q^{4} - 267 q^{5} - 261 q^{6} - 265 q^{7} - 258 q^{8} - 260 q^{9} + O(q^{10}) \) \( 12195 q - 270 q^{2} - 269 q^{3} - 266 q^{4} - 267 q^{5} - 261 q^{6} - 265 q^{7} - 258 q^{8} - 260 q^{9} - 255 q^{10} - 261 q^{11} - 245 q^{12} - 259 q^{13} - 249 q^{14} - 249 q^{15} - 242 q^{16} - 255 q^{17} - 234 q^{18} - 253 q^{19} - 231 q^{20} - 241 q^{21} - 237 q^{22} - 249 q^{23} - 213 q^{24} - 242 q^{25} - 231 q^{26} - 233 q^{27} - 217 q^{28} - 243 q^{29} - 201 q^{30} - 241 q^{31} - 210 q^{32} - 225 q^{33} - 219 q^{34} - 225 q^{35} - 182 q^{36} - 235 q^{37} - 213 q^{38} - 217 q^{39} - 183 q^{40} - 231 q^{41} - 177 q^{42} - 229 q^{43} - 189 q^{44} - 195 q^{45} - 201 q^{46} - 225 q^{47} - 149 q^{48} - 216 q^{49} - 180 q^{50} - 201 q^{51} - 175 q^{52} - 219 q^{53} - 153 q^{54} - 201 q^{55} - 153 q^{56} - 193 q^{57} - 183 q^{58} - 213 q^{59} - 105 q^{60} - 211 q^{61} - 177 q^{62} - 169 q^{63} - 146 q^{64} - 189 q^{65} - 129 q^{66} - 205 q^{67} - 147 q^{68} - 177 q^{69} - 129 q^{70} - 201 q^{71} - 78 q^{72} - 199 q^{73} - 159 q^{74} - 149 q^{75} - 133 q^{76} - 177 q^{77} - 105 q^{78} - 193 q^{79} - 87 q^{80} - 152 q^{81} - 147 q^{82} - 189 q^{83} - 49 q^{84} - 165 q^{85} - 141 q^{86} - 153 q^{87} - 93 q^{88} - 183 q^{89} - 39 q^{90} - 161 q^{91} - 105 q^{92} - 145 q^{93} - 129 q^{94} - 153 q^{95} - 21 q^{96} - 175 q^{97} - 102 q^{98} - 117 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(547))\)

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
547.2.a \(\chi_{547}(1, \cdot)\) 547.2.a.a 2 1
547.2.a.b 18
547.2.a.c 25
547.2.c \(\chi_{547}(40, \cdot)\) 547.2.c.a 90 2
547.2.e \(\chi_{547}(9, \cdot)\) 547.2.e.a 264 6
547.2.f \(\chi_{547}(46, \cdot)\) 547.2.f.a 528 12
547.2.h \(\chi_{547}(13, \cdot)\) 547.2.h.a 540 12
547.2.j \(\chi_{547}(11, \cdot)\) 547.2.j.a 1080 24
547.2.m \(\chi_{547}(10, \cdot)\) 547.2.m.a 3168 72
547.2.o \(\chi_{547}(4, \cdot)\) 547.2.o.a 6480 144