Space of modular forms of level 817, weight 1, and Character 817.bz

• Label: 817.1.bz
• Level: $817$
• Weight: $1$
• Character orbit: 817.bz
• Rep. character: $\chi_{817}(56,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $73$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 817 = 19 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	817.bz (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 817 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(73\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(817, [\chi])\).

	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

\( 12 q - 2 q^{4} + 2 q^{5} - q^{7} + q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(817, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
817.1.bz.a	$817$	$1$	817.bz	817.az	$42$	$12$	$1$	$0.408$	\(\Q(\zeta_{21})\)	$D_{21}$	\(\Q(\sqrt{-19}) \)	None		$4$	$0$	\(0\)	\(0\)	\(2\)	\(-1\)	$1$		\(q+\zeta_{42}^{12}q^{4}+(\zeta_{42}^{10}-\zeta_{42}^{19})q^{5}+\cdots\)