Space of modular forms of level 69, weight 7, and Character 69.b

• Label: 69.7.b
• Level: $69$
• Weight: $7$
• Character orbit: 69.b
• Rep. character: $\chi_{69}(47,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	69.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(56\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(69, [\chi])\).

	Total	New	Old
Modular forms	50	44	6
Cusp forms	46	44	2
Eisenstein series	4	0	4

Trace form

\( 44 q + 20 q^{3} - 1408 q^{4} + 95 q^{6} + 568 q^{7} - 548 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(69, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
69.7.b.a	$69$	$7$	69.b	3.b	$2$	$44$	$44$	$15.874$		None		$2$	$0$	\(0\)	\(20\)	\(0\)	\(568\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{7}^{\mathrm{old}}(69, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(69, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)