Properties

Label 324.2.p
Level $324$
Weight $2$
Character orbit 324.p
Rep. character $\chi_{324}(11,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $936$
Newform subspaces $1$
Sturm bound $108$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 324.p (of order \(54\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 324 \)
Character field: \(\Q(\zeta_{54})\)
Newform subspaces: \( 1 \)
Sturm bound: \(108\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(324, [\chi])\).

Total New Old
Modular forms 1008 1008 0
Cusp forms 936 936 0
Eisenstein series 72 72 0

Trace form

\( 936q - 18q^{2} - 18q^{4} - 36q^{5} - 18q^{6} - 18q^{8} - 36q^{9} + O(q^{10}) \) \( 936q - 18q^{2} - 18q^{4} - 36q^{5} - 18q^{6} - 18q^{8} - 36q^{9} - 18q^{10} - 18q^{12} - 36q^{13} - 18q^{14} - 18q^{16} - 36q^{17} - 18q^{18} - 18q^{20} - 36q^{21} - 18q^{22} - 18q^{24} - 36q^{25} - 27q^{26} - 9q^{28} - 36q^{29} - 18q^{30} - 18q^{32} - 36q^{33} - 18q^{34} - 18q^{36} - 36q^{37} - 18q^{38} - 18q^{40} - 36q^{41} - 63q^{42} - 90q^{44} - 36q^{45} - 18q^{46} - 117q^{48} - 36q^{49} - 135q^{50} - 18q^{52} - 54q^{53} - 144q^{54} - 144q^{56} - 36q^{57} - 18q^{58} - 135q^{60} - 36q^{61} - 117q^{62} - 18q^{64} - 36q^{65} - 90q^{66} - 63q^{68} - 36q^{69} - 18q^{70} - 18q^{72} - 36q^{73} - 18q^{74} - 18q^{76} - 36q^{77} + 9q^{78} - 36q^{81} - 36q^{82} - 45q^{84} - 36q^{85} - 18q^{86} - 18q^{88} - 54q^{89} + 45q^{90} + 72q^{92} - 144q^{93} - 18q^{94} + 99q^{96} - 36q^{97} + 153q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(324, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
324.2.p.a \(936\) \(2.587\) None \(-18\) \(0\) \(-36\) \(0\)