Space of modular forms of level 416, weight 1, and Character 416.bl

• Label: 416.1.bl
• Level: $416$
• Weight: $1$
• Character orbit: 416.bl
• Rep. character: $\chi_{416}(33,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	416.bl (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(56\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(416, [\chi])\).

	Total	New	Old
Modular forms	36	4	32
Cusp forms	4	4	0
Eisenstein series	32	0	32

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

\( 4 q - 2 q^{5} + 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(416, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
416.1.bl.a	$416$	$1$	416.bl	13.f	$12$	$4$	$1$	$0.208$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q+(\zeta_{12}^{4}+\zeta_{12}^{5})q^{5}+\zeta_{12}^{2}q^{9}+\zeta_{12}q^{13}+\cdots\)