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

• Label: 1800.1.cj
• Level: $1800$
• Weight: $1$
• Character orbit: 1800.cj
• Rep. character: $\chi_{1800}(443,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $24$
• Newform subspaces: $3$
• Sturm bound: $360$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1800.cj (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 360 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(360\)
Trace bound:			\(11\)

Dimensions

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

	Total	New	Old
Modular forms	72	40	32
Cusp forms	24	24	0
Eisenstein series	48	16	32

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	24	0	0	0

Trace form

\( 24 q + O(q^{10}) \)

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.cj.a	$1800$	$1$	1800.cj	360.at	$12$	$8$	$2$	$0.898$	\(\Q(\zeta_{24})\)	$D_{6}$	\(\Q(\sqrt{-2}) \)	None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{24}^{11}q^{2}-\zeta_{24}^{9}q^{3}-\zeta_{24}^{10}q^{4}+\cdots\)
1800.1.cj.b	$1800$	$1$	1800.cj	360.at	$12$	$8$	$2$	$0.898$	\(\Q(\zeta_{24})\)	$D_{6}$	\(\Q(\sqrt{-2}) \)	None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{5}q^{3}-\zeta_{24}^{10}q^{4}+\cdots\)
1800.1.cj.c	$1800$	$1$	1800.cj	360.at	$12$	$8$	$2$	$0.898$	\(\Q(\zeta_{24})\)	$D_{6}$	\(\Q(\sqrt{-2}) \)	None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{24}^{11}q^{2}-\zeta_{24}q^{3}-\zeta_{24}^{10}q^{4}+\cdots\)