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

• Label: 69.4.e
• Level: $69$
• Weight: $4$
• Character orbit: 69.e
• Rep. character: $\chi_{69}(4,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $120$
• Newform subspaces: $2$
• Sturm bound: $32$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(32\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	260	120	140
Cusp forms	220	120	100
Eisenstein series	40	0	40

Trace form

\( 120 q + 4 q^{2} - 56 q^{4} + 16 q^{5} - 12 q^{6} + 20 q^{7} - 36 q^{8} - 108 q^{9} + O(q^{10}) \)

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.e.a	$69$	$4$	69.e	23.c	$11$	$60$	$6$	$4.071$		None		$2$	$0$	\(0\)	\(-18\)	\(22\)	\(24\)		$\mathrm{SU}(2)[C_{11}]$
69.4.e.b	$69$	$4$	69.e	23.c	$11$	$60$	$6$	$4.071$		None		$2$	$0$	\(4\)	\(18\)	\(-6\)	\(-4\)		$\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{4}^{\mathrm{old}}(69, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(69, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)