Space of modular forms of level 69, weight 8, and Character 69.c

• Label: 69.8.c
• Level: $69$
• Weight: $8$
• Character orbit: 69.c
• Rep. character: $\chi_{69}(68,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $2$
• Sturm bound: $64$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	69.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 69 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(64\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(69, [\chi])\).

	Total	New	Old
Modular forms	58	58	0
Cusp forms	54	54	0
Eisenstein series	4	4	0

Trace form

\( 54 q + 24 q^{3} - 3384 q^{4} + 1269 q^{6} + 648 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(69, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
69.8.c.a	$69$	$8$	69.c	69.c	$2$	$6$	$6$	$21.555$	6.0.8869743.1	\(\Q(\sqrt{-23}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q+(-2\beta _{1}-6\beta _{2}+3\beta _{3}+2\beta _{4}+2\beta _{5})q^{2}+\cdots\)
69.8.c.b	$69$	$8$	69.c	69.c	$2$	$48$	$48$	$21.555$		None		$4$	$0$	\(0\)	\(24\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$