Space of modular forms of level 799, weight 1, and Character 799.h

• Label: 799.1.h
• Level: $799$
• Weight: $1$
• Character orbit: 799.h
• Rep. character: $\chi_{799}(93,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $20$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 799 = 17 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	799.h (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 799 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(72\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(799, [\chi])\).

	Total	New	Old
Modular forms	28	28	0
Cusp forms	20	20	0
Eisenstein series	8	8	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	20	0	0	0

Trace form

\( 20 q - 20 q^{16} - 20 q^{24} - 20 q^{42} + 20 q^{48} - 20 q^{51} + 20 q^{54} + 20 q^{56} - 20 q^{83} + 40 q^{84}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(799, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
799.1.h.a	$799$	$1$	799.h	799.h	$8$	$4$	$1$	$0.399$	\(\Q(\zeta_{8})\)	$D_{8}$	\(\Q(\sqrt{-47}) \)	None		✓			799.1.h.a	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$		\(q+(1-\zeta_{8})q^{3}+\zeta_{8}^{2}q^{4}+(\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
799.1.h.b	$799$	$1$	799.h	799.h	$8$	$16$	$4$	$0.399$	\(\Q(\zeta_{40})\)	$D_{40}$	\(\Q(\sqrt{-47}) \)	None		✓	✓		799.1.h.b	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{40}^{11}-\zeta_{40}^{19})q^{2}+(-\zeta_{40}^{7}+\zeta_{40}^{8}+\cdots)q^{3}+\cdots\)