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Properties

Label 324.3.o
Level $324$
Weight $3$
Character orbit 324.o
Rep. character $\chi_{324}(5,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $324$
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.o (of order \(54\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
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 1998 324 1674
Cusp forms 1890 324 1566
Eisenstein series 108 0 108

Trace form

\( 324 q + O(q^{10}) \) \( 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
324.3.o.a 324.o 81.h $324$ $8.828$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{54}]$

Decomposition of \(S_{3}^{\mathrm{old}}(324, [\chi])\) into lower level spaces

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