Space of modular forms of level 25, weight 8, and Character 25.b

• Label: 25.8.b
• Level: $25$
• Weight: $8$
• Character orbit: 25.b
• Rep. character: $\chi_{25}(24,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $3$
• Sturm bound: $20$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(20\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(25, [\chi])\).

	Total	New	Old
Modular forms	20	12	8
Cusp forms	14	10	4
Eisenstein series	6	2	4

Trace form

\( 10 q - 690 q^{4} + 1210 q^{6} - 6790 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(25, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
25.8.b.a	$25$	$8$	25.b	5.b	$2$	$2$	$2$	$7.810$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+7iq^{2}-24iq^{3}-68q^{4}+672q^{6}+\cdots\)
25.8.b.b	$25$	$8$	25.b	5.b	$2$	$4$	$4$	$7.810$	\(\Q(i, \sqrt{649})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+2\beta _{2})q^{2}+(2\beta _{1}-5\beta _{2})q^{3}+\cdots\)
25.8.b.c	$25$	$8$	25.b	5.b	$2$	$4$	$4$	$7.810$	\(\Q(i, \sqrt{19})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{3})q^{2}+(-\beta _{1}+8\beta _{3})q^{3}+(-48+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(25, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(25, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)