Space of modular forms of level 1624, weight 1, and Character 1624.cf

• Label: 1624.1.cf
• Level: $1624$
• Weight: $1$
• Character orbit: 1624.cf
• Rep. character: $\chi_{1624}(13,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $240$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1624 = 2^{3} \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1624.cf (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1624 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(240\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1624, [\chi])\).

	Total	New	Old
Modular forms	36	36	0
Cusp forms	12	12	0
Eisenstein series	24	24	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

\( 12 q - 2 q^{4} - 2 q^{7} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1624, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1624.1.cf.a	$1624$	$1$	1624.cf	1624.bf	$14$	$6$	$1$	$0.810$	\(\Q(\zeta_{14})\)	$D_{14}$	\(\Q(\sqrt{-7}) \)	None		✓	1624.1.cf.a	$4$	$0$	\(-1\)	\(0\)	\(0\)	\(-1\)	$1$		\(q+\zeta_{14}^{2}q^{2}+\zeta_{14}^{4}q^{4}+\zeta_{14}^{4}q^{7}+\cdots\)
1624.1.cf.b	$1624$	$1$	1624.cf	1624.bf	$14$	$6$	$1$	$0.810$	\(\Q(\zeta_{14})\)	$D_{14}$	\(\Q(\sqrt{-7}) \)	None		✓	1624.1.cf.a	$4$	$0$	\(1\)	\(0\)	\(0\)	\(-1\)	$1$		\(q+\zeta_{14}q^{2}+\zeta_{14}^{2}q^{4}+\zeta_{14}^{4}q^{7}+\zeta_{14}^{3}q^{8}+\cdots\)