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

• Label: 25.3.c
• Level: $25$
• Weight: $3$
• Character orbit: 25.c
• Rep. character: $\chi_{25}(7,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $7$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	25.c (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
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	16	8	8
Cusp forms	4	4	0
Eisenstein series	12	4	8

Trace form

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

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.c.a	$25$	$3$	25.c	5.c	$4$	$4$	$2$	$0.681$	\(\Q(i, \sqrt{6})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}-\beta _{2}q^{4}-3q^{6}-4\beta _{1}q^{7}+\cdots\)