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

• Label: 925.2.ba
• Level: $925$
• Weight: $2$
• Character orbit: 925.ba
• Rep. character: $\chi_{925}(99,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $336$
• Newform subspaces: $4$
• Sturm bound: $190$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.ba (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 185 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(190\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	600	360	240
Cusp forms	528	336	192
Eisenstein series	72	24	48

Trace form

\( 336 q + 12 q^{4} + 6 q^{9} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
925.2.ba.a	$925$	$2$	925.ba	185.v	$18$	$36$	$6$	$7.386$		None					37.2.h.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$
925.2.ba.b	$925$	$2$	925.ba	185.v	$18$	$72$	$12$	$7.386$		None					185.2.w.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{18}]$
925.2.ba.c	$925$	$2$	925.ba	185.v	$18$	$72$	$12$	$7.386$		None					185.2.w.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)		$\mathrm{SU}(2)[C_{18}]$
925.2.ba.d	$925$	$2$	925.ba	185.v	$18$	$156$	$26$	$7.386$		None		✓	✓		925.2.bb.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(925, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(925, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 2}\)