Space of modular forms of level 25, weight 5, and Character 25.c

• Label: 25.5.c
• Level: $25$
• Weight: $5$
• Character orbit: 25.c
• Rep. character: $\chi_{25}(7,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $10$
• Newform subspaces: $3$
• Sturm bound: $12$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	25.c (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(12\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(25, [\chi])\).

	Total	New	Old
Modular forms	26	14	12
Cusp forms	14	10	4
Eisenstein series	12	4	8

Trace form

\( 10 q + 2 q^{2} + 12 q^{3} - 60 q^{6} + 52 q^{7} + 60 q^{8} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(25, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
25.5.c.a	$25$	$5$	25.c	5.c	$4$	$2$	$1$	$2.584$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(12\)	\(0\)	\(52\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+i)q^{2}+(6-6i)q^{3}-14iq^{4}+\cdots\)
25.5.c.b	$25$	$5$	25.c	5.c	$4$	$4$	$2$	$2.584$	\(\Q(i, \sqrt{6})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+3\beta _{1}q^{2}+7\beta _{3}q^{3}+11\beta _{2}q^{4}-63q^{6}+\cdots\)
25.5.c.c	$25$	$5$	25.c	5.c	$4$	$4$	$2$	$2.584$	\(\Q(i, \sqrt{21})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{3}q^{2}+\beta _{2}q^{3}-26\beta _{1}q^{4}+42q^{6}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(25, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(25, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)