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

• Label: 2312.1.f
• Level: $2312$
• Weight: $1$
• Character orbit: 2312.f
• Rep. character: $\chi_{2312}(579,\cdot)$
• Character field: $\Q$
• Dimension: $7$
• Newform subspaces: $3$
• Sturm bound: $306$
• Trace bound: $1$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	25	22	3
Cusp forms	7	7	0
Eisenstein series	18	15	3

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	7	0	0	0

Trace form

\( 7 q - q^{2} + 7 q^{4} - q^{8} + 5 q^{9} + O(q^{10}) \)

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.f.a	$2312$	$1$	2312.f	8.d	$2$	$1$	$1$	$1.154$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \)	\(\Q(\sqrt{17}) \)	✓	$4$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{2}+q^{4}+q^{8}-q^{9}+q^{16}-q^{18}+\cdots\)
2312.1.f.b	$2312$	$1$	2312.f	8.d	$2$	$2$	$2$	$1.154$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-2}) \)	None	✓	$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{2}-\beta q^{3}+q^{4}-\beta q^{6}+q^{8}+q^{9}+\cdots\)
2312.1.f.c	$2312$	$1$	2312.f	8.d	$2$	$4$	$4$	$1.154$	\(\Q(\zeta_{16})^+\)	$D_{8}$	\(\Q(\sqrt{-2}) \)	None	✓	$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-q^{8}+\cdots\)