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

• Label: 775.2.df
• Level: $775$
• Weight: $2$
• Character orbit: 775.df
• Rep. character: $\chi_{775}(43,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $736$
• 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.df (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 155 \)
Character field:			\(\Q(\zeta_{60})\)
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	1376	800	576
Cusp forms	1184	736	448
Eisenstein series	192	64	128

Trace form

\( 736 q + 12 q^{2} + 14 q^{3} - 72 q^{6} - 6 q^{7} + 40 q^{8} + O(q^{10}) \)

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.df.a	$775$	$2$	775.df	155.x	$60$	$160$	$10$	$6.188$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{60}]$
775.2.df.b	$775$	$2$	775.df	155.x	$60$	$224$	$14$	$6.188$		None		$4$	$0$	\(12\)	\(14\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{60}]$
775.2.df.c	$775$	$2$	775.df	155.x	$60$	$352$	$22$	$6.188$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{60}]$

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

\( S_{2}^{\mathrm{old}}(775, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 2}\)