Space of modular forms of level 361, weight 2, and Character 361.i

• Label: 361.2.i
• Level: $361$
• Weight: $2$
• Character orbit: 361.i
• Rep. character: $\chi_{361}(7,\cdot)$
• Character field: $\Q(\zeta_{57})$
• Dimension: $1080$
• Newform subspaces: $1$
• Sturm bound: $63$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.i (of order \(57\) and degree \(36\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 361 \)
Character field:			\(\Q(\zeta_{57})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(63\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(361, [\chi])\).

	Total	New	Old
Modular forms	1152	1152	0
Cusp forms	1080	1080	0
Eisenstein series	72	72	0

Trace form

\( 1080 q - 38 q^{2} - 19 q^{3} - 8 q^{4} - 37 q^{5} - 38 q^{6} - 40 q^{7} - 38 q^{8} + 49 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(361, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
361.2.i.a	$361$	$2$	361.i	361.i	$57$	$1080$	$30$	$2.883$		None		$2$	$0$	\(-38\)	\(-19\)	\(-37\)	\(-40\)		$\mathrm{SU}(2)[C_{57}]$