Space of modular forms of level 2120, weight 1, and Character 2120.z

• Label: 2120.1.z
• Level: $2120$
• Weight: $1$
• Character orbit: 2120.z
• Rep. character: $\chi_{2120}(317,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $324$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2120 = 2^{3} \cdot 5 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2120.z (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2120 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(324\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2120, [\chi])\).

	Total	New	Old
Modular forms	12	12	0
Cusp forms	4	4	0
Eisenstein series	8	8	0

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

\( 4 q - 8 q^{6} - 4 q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2120, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2120.1.z.a	$2120$	$1$	2120.z	2120.z	$4$	$4$	$2$	$1.058$	\(\Q(\zeta_{8})\)	$D_{4}$	None	\(\Q(\sqrt{106}) \)		✓	2120.1.z.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$		\(q-\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}+\cdots\)