Space of modular forms of level 363, weight 2, and Character 363.j

• Label: 363.2.j
• Level: $363$
• Weight: $2$
• Character orbit: 363.j
• Rep. character: $\chi_{363}(32,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $420$
• Newform subspaces: $1$
• Sturm bound: $88$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.j (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 363 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(88\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(363, [\chi])\).

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

Trace form

\( 420 q - 22 q^{3} - 58 q^{4} + 11 q^{6} - 22 q^{7} - 18 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(363, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
363.2.j.a	$363$	$2$	363.j	363.j	$22$	$420$	$42$	$2.899$		None		$4$	$0$	\(0\)	\(-22\)	\(0\)	\(-22\)		$\mathrm{SU}(2)[C_{22}]$