Space of modular forms of level 70, weight 2, and Character 70.i

• Label: 70.2.i
• Level: $70$
• Weight: $2$
• Character orbit: 70.i
• Rep. character: $\chi_{70}(9,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	70.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(70, [\chi])\).

	Total	New	Old
Modular forms	32	8	24
Cusp forms	16	8	8
Eisenstein series	16	0	16

Trace form

8 * q + 4 * q^4 + 2 * q^5 - 12 * q^6 + 6 * q^9 + 2 * q^10 - 6 * q^11 - 2 * q^14 - 24 * q^15 - 4 * q^16 - 14 * q^19 + 4 * q^20 + 6 * q^21 - 6 * q^24 + 14 * q^26 + 20 * q^29 + 6 * q^30 - 16 * q^31 + 16 * q^34 + 26 * q^35 + 12 * q^36 + 12 * q^39 - 2 * q^40 + 6 * q^44 + 24 * q^45 + 16 * q^46 - 26 * q^49 - 32 * q^50 - 12 * q^51 - 18 * q^54 - 24 * q^55 + 2 * q^56 - 4 * q^59 - 12 * q^60 + 6 * q^61 - 8 * q^64 - 2 * q^65 - 12 * q^69 - 2 * q^70 - 14 * q^74 + 24 * q^75 - 28 * q^76 + 8 * q^79 + 2 * q^80 - 36 * q^81 - 24 * q^84 + 8 * q^85 - 14 * q^86 - 10 * q^89 + 60 * q^90 + 20 * q^91 + 2 * q^94 + 16 * q^95 + 6 * q^96 + 36 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(70, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
70.2.i.a	$70$	$2$	70.i	35.j	$6$	$4$	$2$	$0.559$	\(\Q(\zeta_{12})\)	None		✓			70.2.i.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(-3\zeta_{12}+3\zeta_{12}^{3})q^{3}+\cdots\)
70.2.i.b	$70$	$2$	70.i	35.j	$6$	$4$	$2$	$0.559$	\(\Q(\zeta_{12})\)	None		✓			70.2.i.b	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(2-\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(70, [\chi])\) into lower level spaces

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