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

• Label: 324.2.m
• Level: $324$
• Weight: $2$
• Character orbit: 324.m
• Rep. character: $\chi_{324}(13,\cdot)$
• Character field: $\Q(\zeta_{27})$
• Dimension: $162$
• 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.m (of order \(27\) and degree \(18\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 81 \)
Character field:			\(\Q(\zeta_{27})\)
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	1026	162	864
Cusp forms	918	162	756
Eisenstein series	108	0	108

Trace form

162 * q + 27 * q^21 + 27 * q^23 + 27 * q^27 + 27 * q^29 + 27 * q^33 + 27 * q^35 - 18 * q^41 - 54 * q^45 - 54 * q^47 - 63 * q^51 - 54 * q^53 - 54 * q^57 - 63 * q^59 - 54 * q^63 - 90 * q^65 + 27 * q^67 - 90 * q^69 - 72 * q^71 - 90 * q^75 - 144 * q^77 + 54 * q^79 - 72 * q^81 - 72 * q^83 + 54 * q^85 - 144 * q^87 - 99 * q^89 - 90 * q^93 - 126 * q^95 + 27 * q^97 - 90 * q^99

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.m.a	$324$	$2$	324.m	81.g	$27$	$162$	$9$	$2.587$		None		✓	✓	✓	324.2.m.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{27}]$

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

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