Space of modular forms of level 1225, weight 1, and Character 1225.j

• Label: 1225.1.j
• Level: $1225$
• Weight: $1$
• Character orbit: 1225.j
• Rep. character: $\chi_{1225}(374,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $140$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1225 = 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1225.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(140\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1225, [\chi])\).

	Total	New	Old
Modular forms	52	12	40
Cusp forms	4	4	0
Eisenstein series	48	8	40

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q + 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1225, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1225.1.j.a	$1225$	$1$	1225.j	35.i	$6$	$4$	$2$	$0.611$	\(\Q(\zeta_{12})\)	$D_{3}$	\(\Q(\sqrt{-7}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{3}q^{8}+\zeta_{12}^{2}q^{9}+\cdots\)