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Properties

Label 324.4.p
Level $324$
Weight $4$
Character orbit 324.p
Rep. character $\chi_{324}(11,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $2880$
Sturm bound $216$

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Defining parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 324.p (of order \(54\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 324 \)
Character field: \(\Q(\zeta_{54})\)
Sturm bound: \(216\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(324, [\chi])\).

Total New Old
Modular forms 2952 2952 0
Cusp forms 2880 2880 0
Eisenstein series 72 72 0

Trace form

\( 2880 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} + O(q^{10}) \) \( 2880 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 3573 q^{42} - 2682 q^{44} - 36 q^{45} - 18 q^{46} + 2259 q^{48} - 36 q^{49} + 4779 q^{50} - 18 q^{52} - 54 q^{53} + 6660 q^{54} + 5904 q^{56} - 36 q^{57} - 18 q^{58} + 1269 q^{60} - 36 q^{61} - 1899 q^{62} - 18 q^{64} - 36 q^{65} - 7434 q^{66} - 7083 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 225 q^{78} - 36 q^{81} - 36 q^{82} - 261 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 4266 q^{89} + 12519 q^{90} + 11952 q^{92} - 11160 q^{93} - 18 q^{94} + 2907 q^{96} - 36 q^{97} - 2925 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(324, [\chi])\) into newform subspaces

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