Space of modular forms of level 225, weight 1, and Character 225.g

• Label: 225.1.g
• Level: $225$
• Weight: $1$
• Character orbit: 225.g
• Rep. character: $\chi_{225}(82,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $30$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	225.g (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(30\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(225, [\chi])\).

	Total	New	Old
Modular forms	26	4	22
Cusp forms	2	2	0
Eisenstein series	24	2	22

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q - 2 q^{16} - 4 q^{31} + 4 q^{61} + 4 q^{76}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(225, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
225.1.g.a	$225$	$1$	225.g	5.c	$4$	$2$	$1$	$0.112$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-15}) \)	\(\Q(\sqrt{5}) \)		✓	✓	✓	225.1.g.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+i q^{4}-q^{16}-2 i q^{19}-2 q^{31}+\cdots\)