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Properties

Label 324.6.i
Level $324$
Weight $6$
Character orbit 324.i
Rep. character $\chi_{324}(37,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $90$
Newform subspaces $1$
Sturm bound $324$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 6 \)
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: \(324\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(324, [\chi])\).

Total New Old
Modular forms 1674 90 1584
Cusp forms 1566 90 1476
Eisenstein series 108 0 108

Trace form

\( 90 q + 87 q^{5} + 1257 q^{11} + 3468 q^{17} - 8106 q^{23} + 4959 q^{25} - 3468 q^{29} - 6651 q^{31} + 8229 q^{35} - 68673 q^{41} + 9459 q^{43} + 57087 q^{47} - 5490 q^{49} + 4146 q^{53} - 5388 q^{59} + 70110 q^{61}+ \cdots - 71739 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(324, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
324.6.i.a 324.i 27.e $90$ $51.964$ None 108.6.i.a \(0\) \(0\) \(87\) \(0\) $\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{6}^{\mathrm{old}}(324, [\chi])\) into lower level spaces

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