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Properties

Label 547.6
Level 547
Weight 6
Dimension 62062
Nonzero newspaces 8
Sturm bound 149604
Trace bound 1

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Defining parameters

Level: \( N \) = \( 547 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(149604\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(547))\).

Total New Old
Modular forms 62608 62606 2
Cusp forms 62062 62062 0
Eisenstein series 546 544 2

Trace form

\( 62062 q - 273 q^{2} - 273 q^{3} - 273 q^{4} - 273 q^{5} - 273 q^{6} - 273 q^{7} - 273 q^{8} - 273 q^{9} + O(q^{10}) \) \( 62062 q - 273 q^{2} - 273 q^{3} - 273 q^{4} - 273 q^{5} - 273 q^{6} - 273 q^{7} - 273 q^{8} - 273 q^{9} - 273 q^{10} - 273 q^{11} - 273 q^{12} - 273 q^{13} - 273 q^{14} - 273 q^{15} - 273 q^{16} - 273 q^{17} - 273 q^{18} - 273 q^{19} - 273 q^{20} - 273 q^{21} - 273 q^{22} - 273 q^{23} - 273 q^{24} - 273 q^{25} - 273 q^{26} - 273 q^{27} - 273 q^{28} - 273 q^{29} - 273 q^{30} - 273 q^{31} - 273 q^{32} - 273 q^{33} - 273 q^{34} - 273 q^{35} - 273 q^{36} - 273 q^{37} - 273 q^{38} - 273 q^{39} - 273 q^{40} - 273 q^{41} - 273 q^{42} - 273 q^{43} - 273 q^{44} - 273 q^{45} - 273 q^{46} - 273 q^{47} - 273 q^{48} - 273 q^{49} - 273 q^{50} - 273 q^{51} - 273 q^{52} - 273 q^{53} - 273 q^{54} - 273 q^{55} - 273 q^{56} - 273 q^{57} - 273 q^{58} - 273 q^{59} - 273 q^{60} - 273 q^{61} - 273 q^{62} - 273 q^{63} - 273 q^{64} - 273 q^{65} - 273 q^{66} - 273 q^{67} - 273 q^{68} - 273 q^{69} - 273 q^{70} - 273 q^{71} - 273 q^{72} - 273 q^{73} - 273 q^{74} - 273 q^{75} - 273 q^{76} - 273 q^{77} - 273 q^{78} - 273 q^{79} - 273 q^{80} - 273 q^{81} - 273 q^{82} - 273 q^{83} - 273 q^{84} - 273 q^{85} - 273 q^{86} - 273 q^{87} - 273 q^{88} - 273 q^{89} - 273 q^{90} - 273 q^{91} - 273 q^{92} - 273 q^{93} - 273 q^{94} - 273 q^{95} - 273 q^{96} - 273 q^{97} - 273 q^{98} - 273 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(547))\)

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
547.6.a \(\chi_{547}(1, \cdot)\) 547.6.a.a 111 1
547.6.a.b 117
547.6.c \(\chi_{547}(40, \cdot)\) n/a 454 2
547.6.e \(\chi_{547}(9, \cdot)\) n/a 1368 6
547.6.f \(\chi_{547}(46, \cdot)\) n/a 2736 12
547.6.h \(\chi_{547}(13, \cdot)\) n/a 2724 12
547.6.j \(\chi_{547}(11, \cdot)\) n/a 5448 24
547.6.m \(\chi_{547}(10, \cdot)\) n/a 16416 72
547.6.o \(\chi_{547}(4, \cdot)\) n/a 32688 144

"n/a" means that newforms for that character have not been added to the database yet