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Properties

Label 324.5.k
Level $324$
Weight $5$
Character orbit 324.k
Rep. character $\chi_{324}(17,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $72$
Newform subspaces $1$
Sturm bound $270$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 324.k (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(270\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(324, [\chi])\).

Total New Old
Modular forms 1350 72 1278
Cusp forms 1242 72 1170
Eisenstein series 108 0 108

Trace form

\( 72 q - 9 q^{5} + O(q^{10}) \) \( 72 q - 9 q^{5} - 18 q^{11} + 1278 q^{23} + 441 q^{25} - 1854 q^{29} - 1665 q^{31} + 2673 q^{35} + 5472 q^{41} + 1260 q^{43} - 5103 q^{47} - 5904 q^{49} + 10944 q^{59} + 8352 q^{61} - 8757 q^{65} + 378 q^{67} + 19764 q^{71} + 6111 q^{73} + 5679 q^{77} - 5652 q^{79} + 20061 q^{83} + 26100 q^{85} - 15633 q^{89} - 6039 q^{91} - 48024 q^{95} - 37530 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(324, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
324.5.k.a 324.k 27.f $72$ $33.492$ None \(0\) \(0\) \(-9\) \(0\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{5}^{\mathrm{old}}(324, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(324, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 2}\)