Space of modular forms of level 25, weight 3, and Character 25.f

• Label: 25.3.f
• Level: $25$
• Weight: $3$
• Character orbit: 25.f
• Rep. character: $\chi_{25}(2,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $7$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	25.f (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(7\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(25, [\chi])\).

	Total	New	Old
Modular forms	48	48	0
Cusp forms	32	32	0
Eisenstein series	16	16	0

Trace form

\( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(25, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
25.3.f.a	$25$	$3$	25.f	25.f	$20$	$32$	$4$	$0.681$		None		$2$	$0$	\(-10\)	\(-10\)	\(-10\)	\(-10\)		$\mathrm{SU}(2)[C_{20}]$