Space of modular forms of level 70, weight 4, and Character 70.i

• Label: 70.4.i
• Level: $70$
• Weight: $4$
• Character orbit: 70.i
• Rep. character: $\chi_{70}(9,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	70.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(70, [\chi])\).

	Total	New	Old
Modular forms	80	24	56
Cusp forms	64	24	40
Eisenstein series	16	0	16

Trace form

\( 24 q + 48 q^{4} - 8 q^{5} + 56 q^{6} + 62 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(70, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
70.4.i.a	$70$	$4$	70.i	35.j	$6$	$24$	$12$	$4.130$		None		$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(70, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(70, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)