Space of modular forms of level 848, weight 1, and Character 848.x

• Label: 848.1.x
• Level: $848$
• Weight: $1$
• Character orbit: 848.x
• Rep. character: $\chi_{848}(143,\cdot)$
• Character field: $\Q(\zeta_{26})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $108$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 848 = 2^{4} \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	848.x (of order \(26\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 212 \)
Character field:			\(\Q(\zeta_{26})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(108\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(848, [\chi])\).

	Total	New	Old
Modular forms	84	12	72
Cusp forms	12	12	0
Eisenstein series	72	0	72

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

\( 12 q + q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(848, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
848.1.x.a	$848$	$1$	848.x	212.h	$26$	$12$	$1$	$0.423$	\(\Q(\zeta_{26})\)	$D_{26}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{26}+\zeta_{26}^{11})q^{5}-\zeta_{26}^{6}q^{9}+\cdots\)