Space of modular forms of level 25, weight 4, and Character 25.d

• Label: 25.4.d
• Level: $25$
• Weight: $4$
• Character orbit: 25.d
• Rep. character: $\chi_{25}(6,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $28$
• Newform subspaces: $1$
• Sturm bound: $10$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	25.d (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(10\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(25, [\chi])\).

	Total	New	Old
Modular forms	36	36	0
Cusp forms	28	28	0
Eisenstein series	8	8	0

Trace form

\( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(25, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
25.4.d.a	$25$	$4$	25.d	25.d	$5$	$28$	$7$	$1.475$		None		$2$	$0$	\(-1\)	\(-7\)	\(-20\)	\(-16\)		$\mathrm{SU}(2)[C_{5}]$