Space of modular forms of level 2312, weight 1, and Character 2312.q

• Label: 2312.1.q
• Level: $2312$
• Weight: $1$
• Character orbit: 2312.q
• Rep. character: $\chi_{2312}(653,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $306$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2312 = 2^{3} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2312.q (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 136 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(306\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2312, [\chi])\).

	Total	New	Old
Modular forms	160	128	32
Cusp forms	16	16	0
Eisenstein series	144	112	32

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

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

Decomposition of \(S_{1}^{\mathrm{new}}(2312, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2312.1.q.a	$2312$	$1$	2312.q	136.q	$16$	$16$	$2$	$1.154$	\(\Q(\zeta_{32})\)	$D_{4}$	None	\(\Q(\sqrt{34}) \)		$32$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$		\(q-\zeta_{32}^{2}q^{2}+(-\zeta_{32}^{3}-\zeta_{32}^{11})q^{3}+\cdots\)