Space of modular forms of level 25, weight 10, and Character 25.b

• Label: 25.10.b
• Level: $25$
• Weight: $10$
• Character orbit: 25.b
• Rep. character: $\chi_{25}(24,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $3$
• Sturm bound: $25$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
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:			\(25\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(25, [\chi])\).

	Total	New	Old
Modular forms	26	14	12
Cusp forms	20	12	8
Eisenstein series	6	2	4

Trace form

\( 12 q - 1874 q^{4} - 2006 q^{6} - 108106 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(25, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
25.10.b.a	$25$	$10$	25.b	5.b	$2$	$2$	$2$	$12.876$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+4iq^{2}-57iq^{3}+448q^{4}+912q^{6}+\cdots\)
25.10.b.b	$25$	$10$	25.b	5.b	$2$	$4$	$4$	$12.876$	\(\Q(i, \sqrt{1009})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{2}+(-2\beta _{1}+14\beta _{2}+\cdots)q^{3}+\cdots\)
25.10.b.c	$25$	$10$	25.b	5.b	$2$	$6$	$6$	$12.876$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 5^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(-2\beta _{2}-\beta _{4})q^{3}+(-114+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(25, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(25, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)