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

• Label: 775.2.j
• Level: $775$
• Weight: $2$
• Character orbit: 775.j
• Rep. character: $\chi_{775}(156,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $304$
• Newform subspaces: $3$
• Sturm bound: $160$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.j (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(160\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	328	304	24
Cusp forms	312	304	8
Eisenstein series	16	0	16

Trace form

\( 304 q - 2 q^{2} - 78 q^{4} - 6 q^{5} - 4 q^{7} + 3 q^{8} - 80 q^{9} + O(q^{10}) \)

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.j.a	$775$	$2$	775.j	25.d	$5$	$4$	$1$	$6.188$	\(\Q(\zeta_{10})\)	None		$2$	$1$	\(-2\)	\(-6\)	\(-5\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-2+2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots\)
775.2.j.b	$775$	$2$	775.j	25.d	$5$	$140$	$35$	$6.188$		None		$2$	$0$	\(-1\)	\(0\)	\(-3\)	\(-2\)		$\mathrm{SU}(2)[C_{5}]$
775.2.j.c	$775$	$2$	775.j	25.d	$5$	$160$	$40$	$6.188$		None		$2$	$0$	\(1\)	\(6\)	\(2\)	\(-10\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{2}^{\mathrm{old}}(775, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(775, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)