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

• Label: 775.2.ck
• Level: $775$
• Weight: $2$
• Character orbit: 775.ck
• Rep. character: $\chi_{775}(49,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $368$
• Newform subspaces: $4$
• Sturm bound: $160$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.ck (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 155 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(160\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	688	400	288
Cusp forms	592	368	224
Eisenstein series	96	32	64

Trace form

\( 368 q + 92 q^{4} + 8 q^{6} - 20 q^{9} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
775.2.ck.a	$775$	$2$	775.ck	155.u	$30$	$32$	$4$	$6.188$		None					31.2.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{30}]$
775.2.ck.b	$775$	$2$	775.ck	155.u	$30$	$80$	$10$	$6.188$		None					155.2.q.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{30}]$
775.2.ck.c	$775$	$2$	775.ck	155.u	$30$	$80$	$10$	$6.188$		None					155.2.q.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{30}]$
775.2.ck.d	$775$	$2$	775.ck	155.u	$30$	$176$	$22$	$6.188$		None		✓	✓		775.2.bl.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{30}]$

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

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