Space of modular forms of level 810, weight 2, and Character 810.w

• Label: 810.2.w
• Level: $810$
• Weight: $2$
• Character orbit: 810.w
• Rep. character: $\chi_{810}(23,\cdot)$
• Character field: $\Q(\zeta_{108})$
• Dimension: $1944$
• Newform subspaces: $1$
• Sturm bound: $324$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.w (of order \(108\) and degree \(36\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 405 \)
Character field:			\(\Q(\zeta_{108})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(324\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(810, [\chi])\).

	Total	New	Old
Modular forms	5976	1944	4032
Cusp forms	5688	1944	3744
Eisenstein series	288	0	288

Trace form

\( 1944 q + 36 q^{20} + 108 q^{30} + 108 q^{35} + 36 q^{41} + 216 q^{51} + 108 q^{67} - 144 q^{72} - 576 q^{77} - 576 q^{87} - 144 q^{92} + 36 q^{93} + 108 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(810, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
810.2.w.a	$810$	$2$	810.w	405.x	$108$	$1944$	$54$	$6.468$		None		✓	✓	✓	810.2.w.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{108}]$

Decomposition of \(S_{2}^{\mathrm{old}}(810, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(810, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 2}\)