Space of modular forms of level 777, weight 1, and Character 777.w

• Label: 777.1.w
• Level: $777$
• Weight: $1$
• Character orbit: 777.w
• Rep. character: $\chi_{777}(221,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $101$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 777 = 3 \cdot 7 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	777.w (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 777 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(101\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(777, [\chi])\).

	Total	New	Old
Modular forms	24	24	0
Cusp forms	16	16	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	16	0	0	0

Trace form

\( 16 q - 8 q^{4} - 8 q^{9} - 8 q^{16} - 8 q^{25} + 16 q^{28} + 8 q^{30} - 16 q^{34} + 16 q^{36} - 16 q^{40} - 16 q^{48} + 8 q^{58} + 16 q^{64} + 16 q^{70} - 8 q^{81} + 16 q^{84}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(777, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
777.1.w.a	$777$	$1$	777.w	777.w	$6$	$2$	$1$	$0.388$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-111}) \)	None		✓			777.1.w.a	$4$	$0$	\(-1\)	\(-1\)	\(2\)	\(2\)	$1$		\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{5}+q^{6}+q^{7}+\cdots\)
777.1.w.b	$777$	$1$	777.w	777.w	$6$	$2$	$1$	$0.388$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-111}) \)	None		✓			777.1.w.a	$4$	$0$	\(1\)	\(-1\)	\(-2\)	\(2\)	$1$		\(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{5}-q^{6}+q^{7}+\cdots\)
777.1.w.c	$777$	$1$	777.w	777.w	$6$	$4$	$2$	$0.388$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-111}) \)	None		✓			777.1.w.c	$8$	$0$	\(0\)	\(-2\)	\(0\)	\(-4\)	$3$		\(q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{2}-\zeta_{12}^{2}q^{3}+\cdots\)
777.1.w.d	$777$	$1$	777.w	777.w	$6$	$8$	$4$	$0.388$	\(\Q(\zeta_{24})\)	$D_{12}$	\(\Q(\sqrt{-111}) \)	None		✓	✓		777.1.w.d	$8$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{24}^{7}+\zeta_{24}^{9})q^{2}+\zeta_{24}^{4}q^{3}+(-\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)