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

• Label: 2312.1.p
• Level: $2312$
• Weight: $1$
• Character orbit: 2312.p
• Rep. character: $\chi_{2312}(155,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $24$
• Newform subspaces: $5$
• Sturm bound: $306$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 2312 = 2^{3} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2312.p (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 136 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(306\)
Trace bound:			\(9\)

Dimensions

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

	Total	New	Old
Modular forms	104	80	24
Cusp forms	32	24	8
Eisenstein series	72	56	16

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	24	0	0	0

Trace form

24 * q + 4 * q^9 + 4 * q^11 - 4 * q^12 - 24 * q^16 - 8 * q^18 - 4 * q^24 - 4 * q^27 + 16 * q^33 + 4 * q^36 - 4 * q^43 - 4 * q^54 + 4 * q^59 - 4 * q^66 + 8 * q^67 + 4 * q^75 + 4 * q^82 - 4 * q^83 - 8 * q^86 + 4 * q^88 + 4 * q^97

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2312.1.p.a	$2312$	$1$	2312.p	136.p	$8$	$4$	$1$	$1.154$	\(\Q(\zeta_{8})\)	$D_{8}$	\(\Q(\sqrt{-2}) \)	None					136.1.p.a	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$		\(q+\zeta_{8}^{3}q^{2}+(-1-\zeta_{8})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)
2312.1.p.b	$2312$	$1$	2312.p	136.p	$8$	$4$	$1$	$1.154$	\(\Q(\zeta_{8})\)	$D_{8}$	\(\Q(\sqrt{-2}) \)	None					136.1.p.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{8}^{3}q^{2}+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)
2312.1.p.c	$2312$	$1$	2312.p	136.p	$8$	$4$	$1$	$1.154$	\(\Q(\zeta_{8})\)	$D_{2}$	\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \)	\(\Q(\sqrt{17}) \)					136.1.e.a	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{8}-\zeta_{8}q^{9}+\cdots\)
2312.1.p.d	$2312$	$1$	2312.p	136.p	$8$	$4$	$1$	$1.154$	\(\Q(\zeta_{8})\)	$D_{8}$	\(\Q(\sqrt{-2}) \)	None					136.1.p.a	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$		\(q+\zeta_{8}^{3}q^{2}+(1+\zeta_{8})q^{3}-\zeta_{8}^{2}q^{4}+(-1+\cdots)q^{6}+\cdots\)
2312.1.p.e	$2312$	$1$	2312.p	136.p	$8$	$8$	$2$	$1.154$	\(\Q(\zeta_{16})\)	$D_{4}$	\(\Q(\sqrt{-2}) \)	None			✓		136.1.j.a	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$		\(q+\zeta_{16}^{6}q^{2}+(-\zeta_{16}^{3}-\zeta_{16}^{7})q^{3}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2312, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2312, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 2}\)