Properties

Label 324.4.i
Level $324$
Weight $4$
Character orbit 324.i
Rep. character $\chi_{324}(37,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $54$
Newform subspaces $1$
Sturm bound $216$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 324.i (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 1 \)
Sturm bound: \(216\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 1026 54 972
Cusp forms 918 54 864
Eisenstein series 108 0 108

Trace form

\( 54q - 12q^{5} + O(q^{10}) \) \( 54q - 12q^{5} + 87q^{11} - 204q^{17} - 96q^{23} - 216q^{25} - 318q^{29} - 54q^{31} - 6q^{35} - 867q^{41} - 513q^{43} + 1548q^{47} + 594q^{49} + 1068q^{53} + 1218q^{59} - 54q^{61} - 96q^{65} - 2997q^{67} + 120q^{71} - 216q^{73} - 3480q^{77} + 2808q^{79} - 4464q^{83} + 2160q^{85} - 4029q^{89} + 270q^{91} + 1650q^{95} - 3483q^{97} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
324.4.i.a \(54\) \(19.117\) None \(0\) \(0\) \(-12\) \(0\)

Decomposition of \(S_{4}^{\mathrm{old}}(324, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(324, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database