Space of modular forms of level 511, weight 1, and Character 511.c

• Label: 511.1.c
• Level: $511$
• Weight: $1$
• Character orbit: 511.c
• Rep. character: $\chi_{511}(510,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $49$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 511 = 7 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	511.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 511 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(49\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(511, [\chi])\).

	Total	New	Old
Modular forms	8	8	0
Cusp forms	6	6	0
Eisenstein series	2	2	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

6 * q - 2 * q^2 + 4 * q^4 - 4 * q^8 + 6 * q^9 + 2 * q^16 - 2 * q^18 - 2 * q^23 + 4 * q^25 - 6 * q^32 - 2 * q^35 + 4 * q^36 - 2 * q^37 - 4 * q^46 + 6 * q^49 - 6 * q^50 - 4 * q^65 - 2 * q^67 - 4 * q^70 - 2 * q^71 - 4 * q^72 - 4 * q^74 - 2 * q^79 + 6 * q^81 - 4 * q^85 - 2 * q^91 - 6 * q^92 - 2 * q^98

Decomposition of \(S_{1}^{\mathrm{new}}(511, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
511.1.c.a	$511$	$1$	511.c	511.c	$2$	$3$	$3$	$0.255$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-511}) \)	None	✓	✓			511.1.c.a	$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(3\)	$1$		\(q+(-1+\beta _{1}-\beta _{2})q^{2}+(1-\beta _{1})q^{4}+\cdots\)
511.1.c.b	$511$	$1$	511.c	511.c	$2$	$3$	$3$	$0.255$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-511}) \)	None	✓	✓			511.1.c.a	$2$	$0$	\(-1\)	\(0\)	\(1\)	\(-3\)	$1$		\(q+(-1+\beta _{1}-\beta _{2})q^{2}+(1-\beta _{1})q^{4}+\cdots\)