Space of modular forms of level 368, weight 3, and Character 368.v

• Label: 368.3.v
• Level: $368$
• Weight: $3$
• Character orbit: 368.v
• Rep. character: $\chi_{368}(5,\cdot)$
• Character field: $\Q(\zeta_{44})$
• Dimension: $1880$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	368.v (of order \(44\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 368 \)
Character field:			\(\Q(\zeta_{44})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(368, [\chi])\).

	Total	New	Old
Modular forms	1960	1960	0
Cusp forms	1880	1880	0
Eisenstein series	80	80	0

Trace form

\( 1880 q - 18 q^{2} - 18 q^{3} - 6 q^{4} - 22 q^{5} - 24 q^{6} - 18 q^{8} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(368, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
368.3.v.a	$368$	$3$	368.v	368.v	$44$	$1880$	$94$	$10.027$		None		✓	✓	✓	368.3.v.a	$4$	$0$	\(-18\)	\(-18\)	\(-22\)	\(0\)		$\mathrm{SU}(2)[C_{44}]$