Space of modular forms of level 363, weight 3, and Character 363.k

• Label: 363.3.k
• Level: $363$
• Weight: $3$
• Character orbit: 363.k
• Rep. character: $\chi_{363}(10,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $440$
• Newform subspaces: $1$
• Sturm bound: $132$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.k (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 121 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(132\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(363, [\chi])\).

	Total	New	Old
Modular forms	900	440	460
Cusp forms	860	440	420
Eisenstein series	40	0	40

Trace form

\( 440 q + 100 q^{4} - 4 q^{5} + 1320 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(363, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
363.3.k.a	$363$	$3$	363.k	121.f	$22$	$440$	$44$	$9.891$		None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$

Decomposition of \(S_{3}^{\mathrm{old}}(363, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(363, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 2}\)