Space of modular forms of level 925, weight 2, and Character 925.bk

• Label: 925.2.bk
• Level: $925$
• Weight: $2$
• Character orbit: 925.bk
• Rep. character: $\chi_{925}(11,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $752$
• Newform subspaces: $1$
• Sturm bound: $190$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.bk (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 925 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(190\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(925, [\chi])\).

	Total	New	Old
Modular forms	784	784	0
Cusp forms	752	752	0
Eisenstein series	32	32	0

Trace form

\( 752 q - 9 q^{2} - 5 q^{3} - 97 q^{4} - 9 q^{5} - 8 q^{7} + 93 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(925, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
925.2.bk.a	$925$	$2$	925.bk	925.ak	$30$	$752$	$94$	$7.386$		None		$4$	$0$	\(-9\)	\(-5\)	\(-9\)	\(-8\)		$\mathrm{SU}(2)[C_{30}]$