Space of modular forms of level 3, weight 25, and Character 3.b

• Label: 3.25.b
• Level: $3$
• Weight: $25$
• Character orbit: 3.b
• Rep. character: $\chi_{3}(2,\cdot)$
• Character field: $\Q$
• Dimension: $7$
• Newform subspaces: $2$
• Sturm bound: $8$
• Trace bound: $1$

Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{25}(3, [\chi])\).

	Total	New	Old
Modular forms	9	9	0
Cusp forms	7	7	0
Eisenstein series	2	2	0

Trace form

\( 7 q - 85401 q^{3} - 46569584 q^{4} - 2673890352 q^{6} - 2131645522 q^{7} - 508757413401 q^{9} + O(q^{10}) \)

Decomposition of \(S_{25}^{\mathrm{new}}(3, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3.25.b.a	$3$	$25$	3.b	3.b	$2$	$1$	$1$	$10.949$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(531441\)	\(0\)	\(-4119710398\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{12}q^{3}+2^{24}q^{4}-4119710398q^{7}+\cdots\)
3.25.b.b	$3$	$25$	3.b	3.b	$2$	$6$	$6$	$10.949$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(-616842\)	\(0\)	\(1988064876\)	$2^{13}\cdot 3^{24}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-102807+2^{4}\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)