Space of modular forms of level 2400, weight 1, and Character 2400.ca

• Label: 2400.1.ca
• Level: $2400$
• Weight: $1$
• Character orbit: 2400.ca
• Rep. character: $\chi_{2400}(101,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $480$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2400.ca (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 96 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(480\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2400, [\chi])\).

	Total	New	Old
Modular forms	56	32	24
Cusp forms	8	8	0
Eisenstein series	48	24	24

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2400, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2400.1.ca.a	$2400$	$1$	2400.ca	96.p	$8$	$8$	$2$	$1.198$	\(\Q(\zeta_{16})\)	$D_{8}$	\(\Q(\sqrt{-15}) \)	None			480.1.bu.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{16}^{5}q^{2}+\zeta_{16}q^{3}-\zeta_{16}^{2}q^{4}+\zeta_{16}^{6}q^{6}+\cdots\)