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Properties

Label 504.3.cm
Level $504$
Weight $3$
Character orbit 504.cm
Rep. character $\chi_{504}(131,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $376$
Sturm bound $288$

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Defining parameters

Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 504.cm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 504 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(504, [\chi])\).

Total New Old
Modular forms 392 392 0
Cusp forms 376 376 0
Eisenstein series 16 16 0

Trace form

\( 376 q - 6 q^{3} - 2 q^{4} + 12 q^{6} - 2 q^{9} + O(q^{10}) \) \( 376 q - 6 q^{3} - 2 q^{4} + 12 q^{6} - 2 q^{9} - 6 q^{10} - 6 q^{11} + 12 q^{12} - 48 q^{14} - 2 q^{16} - 10 q^{18} - 12 q^{19} + 6 q^{22} + 24 q^{24} + 862 q^{25} - 12 q^{26} + 12 q^{28} - 83 q^{30} - 6 q^{33} + 12 q^{34} - 150 q^{35} + 50 q^{36} - 93 q^{38} - 78 q^{40} + 64 q^{42} - 4 q^{43} + 3 q^{44} - 10 q^{46} - 27 q^{48} - 2 q^{49} + 69 q^{50} + 114 q^{51} + 93 q^{52} - 33 q^{54} - 150 q^{56} - 44 q^{57} - 7 q^{58} - 12 q^{59} - 47 q^{60} - 24 q^{62} - 8 q^{64} - 306 q^{66} - 4 q^{67} + 222 q^{68} + 51 q^{70} - 304 q^{72} - 12 q^{73} - 153 q^{74} - 6 q^{75} - 48 q^{76} + 3 q^{78} + 171 q^{80} - 34 q^{81} + 6 q^{82} - 720 q^{83} - 107 q^{84} + 285 q^{86} - 63 q^{88} + 144 q^{89} + 183 q^{90} + 188 q^{91} + 444 q^{92} - 549 q^{96} - 141 q^{98} + 154 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(504, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.