Space of modular forms of level 69, weight 4, and Character 69.c

• Label: 69.4.c
• Level: $69$
• Weight: $4$
• Character orbit: 69.c
• Rep. character: $\chi_{69}(68,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $3$
• Sturm bound: $32$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	69.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 69 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(32\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(69, [\chi])\).

	Total	New	Old
Modular forms	26	26	0
Cusp forms	22	22	0
Eisenstein series	4	4	0

Trace form

\( 22 q - 6 q^{3} - 72 q^{4} + 21 q^{6} - 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(69, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
69.4.c.a	$69$	$4$	69.c	69.c	$2$	$2$	$2$	$4.071$	\(\Q(\sqrt{-23}) \)	\(\Q(\sqrt{-23}) \)		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{2}+(2-\beta )q^{3}-15q^{4}+(-23+\cdots)q^{6}+\cdots\)
69.4.c.b	$69$	$4$	69.c	69.c	$2$	$4$	$4$	$4.071$	\(\Q(\sqrt{-3}, \sqrt{-23})\)	\(\Q(\sqrt{-23}) \)		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+(-1-\beta _{2}-\beta _{3})q^{2}+(-1+2\beta _{1}+\cdots)q^{3}+\cdots\)
69.4.c.c	$69$	$4$	69.c	69.c	$2$	$16$	$16$	$4.071$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$2^{9}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{11}q^{2}-\beta _{10}q^{3}+(-2+\beta _{1})q^{4}+\cdots\)