Properties

Label 324.3.n
Level $324$
Weight $3$
Character orbit 324.n
Rep. character $\chi_{324}(7,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $1908$
Newform subspaces $1$
Sturm bound $162$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.n (of order \(54\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 324 \)
Character field: \(\Q(\zeta_{54})\)
Newform subspaces: \( 1 \)
Sturm bound: \(162\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(324, [\chi])\).

Total New Old
Modular forms 1980 1980 0
Cusp forms 1908 1908 0
Eisenstein series 72 72 0

Trace form

\( 1908 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} + O(q^{10}) \) \( 1908 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 9 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} + 477 q^{42} + 630 q^{44} - 36 q^{45} - 18 q^{46} + 477 q^{48} - 36 q^{49} + 333 q^{50} - 18 q^{52} - 18 q^{53} - 144 q^{54} - 396 q^{56} - 36 q^{57} - 18 q^{58} - 837 q^{60} - 36 q^{61} - 909 q^{62} - 18 q^{64} - 36 q^{65} - 954 q^{66} - 693 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} - 99 q^{78} - 36 q^{80} - 36 q^{81} - 36 q^{82} - 99 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} + 288 q^{89} - 1089 q^{90} - 1368 q^{92} + 1476 q^{93} - 18 q^{94} - 1305 q^{96} - 36 q^{97} - 1557 q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(324, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
324.3.n.a \(1908\) \(8.828\) None \(-18\) \(0\) \(-36\) \(0\)