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Properties

Label 324.2.i
Level $324$
Weight $2$
Character orbit 324.i
Rep. character $\chi_{324}(37,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $18$
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.i (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{9})\)
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 378 18 360
Cusp forms 270 18 252
Eisenstein series 108 0 108

Trace form

\( 18 q - 3 q^{5} - 3 q^{11} + 12 q^{17} + 30 q^{23} + 9 q^{25} + 24 q^{29} + 9 q^{31} + 21 q^{35} - 21 q^{41} - 9 q^{43} - 45 q^{47} - 18 q^{49} - 66 q^{53} - 60 q^{59} - 18 q^{61} - 33 q^{65} - 27 q^{67}+ \cdots - 27 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
324.2.i.a 324.i 27.e $18$ $2.587$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None 108.2.i.a \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\beta _{1}-\beta _{3})q^{5}+(-\beta _{8}-\beta _{9}-\beta _{10}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(324, [\chi])\) into lower level spaces

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