Space of modular forms of level 847, weight 1, and Character 847.j

• Label: 847.1.j
• Level: $847$
• Weight: $1$
• Character orbit: 847.j
• Rep. character: $\chi_{847}(27,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $12$
• Newform subspaces: $3$
• Sturm bound: $88$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	847.j (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(88\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(847, [\chi])\).

	Total	New	Old
Modular forms	68	44	24
Cusp forms	20	12	8
Eisenstein series	48	32	16

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 + 2 * q^2 + q^4 + q^7 - q^8 - 3 * q^9 - q^14 - 3 * q^18 - 6 * q^23 - 3 * q^25 - 2 * q^28 + 2 * q^29 - 4 * q^32 + q^36 - q^37 + 2 * q^43 - q^46 - 3 * q^49 + 2 * q^50 - q^53 - 12 * q^56 + 3 * q^58 + q^63 + 4 * q^64 - 6 * q^67 - q^71 - q^72 + 4 * q^74 - 3 * q^79 - 3 * q^81 + 3 * q^86 + 2 * q^92 + 2 * q^98

Decomposition of \(S_{1}^{\mathrm{new}}(847, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
847.1.j.a	$847$	$1$	847.j	77.j	$10$	$4$	$1$	$0.423$	\(\Q(\zeta_{10})\)	$D_{5}$	\(\Q(\sqrt{-7}) \)	None					77.1.j.a	$4$	$0$	\(-3\)	\(0\)	\(0\)	\(1\)	$1$		\(q+(-1-\zeta_{10}^{4})q^{2}+(1-\zeta_{10}^{3}+\zeta_{10}^{4}+\cdots)q^{4}+\cdots\)
847.1.j.b	$847$	$1$	847.j	77.j	$10$	$4$	$1$	$0.423$	\(\Q(\zeta_{10})\)	$D_{5}$	\(\Q(\sqrt{-7}) \)	None					77.1.j.a	$4$	$0$	\(2\)	\(0\)	\(0\)	\(1\)	$1$		\(q+(\zeta_{10}+\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{4}+\cdots\)
847.1.j.c	$847$	$1$	847.j	77.j	$10$	$4$	$1$	$0.423$	\(\Q(\zeta_{10})\)	$D_{5}$	\(\Q(\sqrt{-7}) \)	None					77.1.j.a	$4$	$0$	\(3\)	\(0\)	\(0\)	\(-1\)	$1$		\(q+(1+\zeta_{10}^{4})q^{2}+(1-\zeta_{10}^{3}+\zeta_{10}^{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(847, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(847, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)