Space of modular forms of level 1800, weight 1, and Character 1800.g

• Label: 1800.1.g
• Level: $1800$
• Weight: $1$
• Character orbit: 1800.g
• Rep. character: $\chi_{1800}(451,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $3$
• Sturm bound: $360$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1800.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(360\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1800, [\chi])\).

	Total	New	Old
Modular forms	34	7	27
Cusp forms	10	4	6
Eisenstein series	24	3	21

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

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

Decomposition of \(S_{1}^{\mathrm{new}}(1800, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1800.1.g.a	$1800$	$1$	1800.g	8.d	$2$	$1$	$1$	$0.898$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-2}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{2}+q^{4}-q^{8}+q^{11}+q^{16}+q^{17}+\cdots\)
1800.1.g.b	$1800$	$1$	1800.g	8.d	$2$	$1$	$1$	$0.898$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-2}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{2}+q^{4}+q^{8}+q^{11}+q^{16}-q^{17}+\cdots\)
1800.1.g.c	$1800$	$1$	1800.g	8.d	$2$	$2$	$2$	$0.898$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-10}) \)	\(\Q(\sqrt{6}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{2}-q^{4}+iq^{8}+q^{16}+q^{19}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1800, [\chi]) \cong \)