Space of modular forms of level 25, weight 6, and Character 25.b

• Label: 25.6.b
• Level: $25$
• Weight: $6$
• Character orbit: 25.b
• Rep. character: $\chi_{25}(24,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $15$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(15\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(25, [\chi])\).

	Total	New	Old
Modular forms	16	8	8
Cusp forms	10	6	4
Eisenstein series	6	2	4

Trace form

\( 6 q - 82 q^{4} - 398 q^{6} + 62 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(25, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
25.6.b.a	$25$	$6$	25.b	5.b	$2$	$2$	$2$	$4.010$	\(\Q(\sqrt{-1}) \)	None					5.6.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+2iq^{3}+28q^{4}-8q^{6}+96iq^{7}+\cdots\)
25.6.b.b	$25$	$6$	25.b	5.b	$2$	$4$	$4$	$4.010$	\(\Q(i, \sqrt{241})\)	None		✓	✓		25.6.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{2}+(-2\beta _{1}-\beta _{2})q^{3}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(25, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(25, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)