Space of modular forms of level 775, weight 2, and Character 775.cz

• Label: 775.2.cz
• Level: $775$
• Weight: $2$
• Character orbit: 775.cz
• Rep. character: $\chi_{775}(3,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $1248$
• Newform subspaces: $1$
• Sturm bound: $160$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.cz (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 775 \)
Character field:			\(\Q(\zeta_{60})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(160\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(775, [\chi])\).

	Total	New	Old
Modular forms	1312	1312	0
Cusp forms	1248	1248	0
Eisenstein series	64	64	0

Trace form

\( 1248 q - 12 q^{2} - 14 q^{3} - 20 q^{4} - 8 q^{5} - 18 q^{6} - 14 q^{7} + 60 q^{8} - 20 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(775, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
775.2.cz.a	$775$	$2$	775.cz	775.bz	$60$	$1248$	$78$	$6.188$		None		$2$	$0$	\(-12\)	\(-14\)	\(-8\)	\(-14\)		$\mathrm{SU}(2)[C_{60}]$