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

• Label: 1225.1.g
• Level: $1225$
• Weight: $1$
• Character orbit: 1225.g
• Rep. character: $\chi_{1225}(393,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $140$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1225 = 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1225.g (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(140\)
Trace bound:			\(1\)

Dimensions

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

	Total	New	Old
Modular forms	54	16	38
Cusp forms	6	6	0
Eisenstein series	48	10	38

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

\( 6 q + O(q^{10}) \)

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.g.a	$1225$	$1$	1225.g	5.c	$4$	$2$	$1$	$0.611$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-35}) \)	\(\Q(\sqrt{5}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{4}+iq^{9}+q^{11}-q^{16}-iq^{29}+\cdots\)
1225.1.g.b	$1225$	$1$	1225.g	5.c	$4$	$4$	$2$	$0.611$	\(\Q(i, \sqrt{6})\)	$D_{6}$	\(\Q(\sqrt{-7}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{2}+2\beta _{2}q^{4}-\beta _{3}q^{8}+\beta _{2}q^{9}+\cdots\)