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

• Label: 775.2.by
• Level: $775$
• Weight: $2$
• Character orbit: 775.by
• Rep. character: $\chi_{775}(27,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $624$
• 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.by (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 775 \)
Character field:			\(\Q(\zeta_{20})\)
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	656	656	0
Cusp forms	624	624	0
Eisenstein series	32	32	0

Trace form

\( 624 q - 6 q^{2} - 10 q^{3} - 10 q^{4} - 16 q^{5} + 2 q^{7} + 30 q^{8} - 10 q^{9} + O(q^{10}) \)

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.by.a	$775$	$2$	775.by	775.ay	$20$	$624$	$78$	$6.188$		None		$2$	$0$	\(-6\)	\(-10\)	\(-16\)	\(2\)		$\mathrm{SU}(2)[C_{20}]$