Space of modular forms of level 69, weight 5, and Character 69.d

• Label: 69.5.d
• Level: $69$
• Weight: $5$
• Character orbit: 69.d
• Rep. character: $\chi_{69}(22,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $40$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	69.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(40\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(69, [\chi])\).

	Total	New	Old
Modular forms	34	16	18
Cusp forms	30	16	14
Eisenstein series	4	0	4

Trace form

\( 16 q + 12 q^{2} + 144 q^{4} - 36 q^{6} + 372 q^{8} + 432 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(69, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
69.5.d.a	$69$	$5$	69.d	23.b	$2$	$16$	$16$	$7.133$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(12\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{2})q^{2}+\beta _{3}q^{3}+(9+\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(69, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(69, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)