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

• Label: 925.2.e
• Level: $925$
• Weight: $2$
• Character orbit: 925.e
• Rep. character: $\chi_{925}(26,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $114$
• Newform subspaces: $6$
• Sturm bound: $190$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(190\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	200	126	74
Cusp forms	176	114	62
Eisenstein series	24	12	12

Trace form

\( 114 q - q^{2} + 4 q^{3} - 53 q^{4} - 16 q^{6} + 6 q^{8} - 49 q^{9} + O(q^{10}) \)

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.e.a	$925$	$2$	925.e	37.c	$3$	$2$	$1$	$7.386$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{7}+3q^{8}+\cdots\)
925.2.e.b	$925$	$2$	925.e	37.c	$3$	$14$	$7$	$7.386$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(-2\)	\(2\)	\(0\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{8}q^{2}-\beta _{6}q^{3}+(-1+\beta _{5}-\beta _{7}+\cdots)q^{4}+\cdots\)
925.2.e.c	$925$	$2$	925.e	37.c	$3$	$14$	$7$	$7.386$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{4})q^{2}+\beta _{6}q^{3}+(\beta _{2}+\beta _{9}-\beta _{11}+\cdots)q^{4}+\cdots\)
925.2.e.d	$925$	$2$	925.e	37.c	$3$	$24$	$12$	$7.386$		None		$2$	$0$	\(-1\)	\(-2\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{3}]$
925.2.e.e	$925$	$2$	925.e	37.c	$3$	$24$	$12$	$7.386$		None		$2$	$0$	\(1\)	\(2\)	\(0\)	\(6\)		$\mathrm{SU}(2)[C_{3}]$
925.2.e.f	$925$	$2$	925.e	37.c	$3$	$36$	$18$	$7.386$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{3}]$

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

\( S_{2}^{\mathrm{old}}(925, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 3}\)