Space of modular forms of level 2816, weight 1, and Character 2816.v

• Label: 2816.1.v
• Level: $2816$
• Weight: $1$
• Character orbit: 2816.v
• Rep. character: $\chi_{2816}(511,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $384$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2816 = 2^{8} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2816.v (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 44 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(384\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2816, [\chi])\).

	Total	New	Old
Modular forms	112	32	80
Cusp forms	16	16	0
Eisenstein series	96	16	80

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

\( 16 q + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2816, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2816.1.v.a	$2816$	$1$	2816.v	44.h	$10$	$4$	$1$	$1.405$	\(\Q(\zeta_{10})\)	$D_{10}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{10}+\zeta_{10}^{3})q^{3}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{9}+\cdots\)
2816.1.v.b	$2816$	$1$	2816.v	44.h	$10$	$4$	$1$	$1.405$	\(\Q(\zeta_{10})\)	$D_{10}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{10}-\zeta_{10}^{3})q^{3}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{9}+\cdots\)
2816.1.v.c	$2816$	$1$	2816.v	44.h	$10$	$8$	$2$	$1.405$	\(\Q(\zeta_{20})\)	$D_{5}$	\(\Q(\sqrt{-2}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{20}-\zeta_{20}^{7})q^{3}+(\zeta_{20}^{2}-\zeta_{20}^{4}+\cdots)q^{9}+\cdots\)