Space of modular forms of level 324, weight 2, and Character 324.l

• Label: 324.2.l
• Level: $324$
• Weight: $2$
• Character orbit: 324.l
• Rep. character: $\chi_{324}(35,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $96$
• Newform subspaces: $1$
• Sturm bound: $108$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.l (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 108 \)
Character field:			\(\Q(\zeta_{18})\)
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	360	120	240
Cusp forms	288	96	192
Eisenstein series	72	24	48

Trace form

96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

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

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
324.2.l.a	$324$	$2$	324.l	108.l	$18$	$96$	$16$	$2.587$		None			✓	✓	108.2.l.a	$4$	$0$	\(6\)	\(0\)	\(12\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

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

\( S_{2}^{\mathrm{old}}(324, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)