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

• Label: 70.2.e
• Level: $70$
• Weight: $2$
• Character orbit: 70.e
• Rep. character: $\chi_{70}(11,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $8$
• Newform subspaces: $4$
• Sturm bound: $24$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	70.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(24\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\), \(13\)

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 + 4 * q^6 - 8 * q^7 - 6 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^14 - 8 * q^15 - 4 * q^16 + 4 * q^17 - 8 * q^18 + 6 * q^19 - 4 * q^20 - 18 * q^21 + 8 * q^22 - 12 * q^23 - 2 * q^24 - 4 * q^25 - 10 * q^26 + 24 * q^27 + 4 * q^28 + 12 * q^29 - 2 * q^30 - 8 * q^31 + 24 * q^33 + 16 * q^34 + 6 * q^35 + 12 * q^36 + 4 * q^37 + 8 * q^38 + 12 * q^39 + 2 * q^40 + 16 * q^41 + 4 * q^42 - 40 * q^43 + 2 * q^44 + 4 * q^45 - 20 * q^47 - 22 * q^49 + 12 * q^51 - 4 * q^53 - 14 * q^54 + 16 * q^55 + 2 * q^56 - 24 * q^57 - 4 * q^59 + 4 * q^60 - 10 * q^61 - 48 * q^62 + 36 * q^63 + 8 * q^64 + 2 * q^65 + 4 * q^68 - 36 * q^69 + 6 * q^70 + 16 * q^71 - 8 * q^72 + 28 * q^73 - 18 * q^74 - 12 * q^76 - 8 * q^77 - 16 * q^78 + 8 * q^79 + 2 * q^80 + 12 * q^81 + 16 * q^82 - 32 * q^83 - 16 * q^85 + 10 * q^86 - 24 * q^87 - 4 * q^88 + 2 * q^89 - 20 * q^90 - 12 * q^91 + 24 * q^92 + 12 * q^93 - 2 * q^94 - 4 * q^95 - 2 * q^96 + 64 * q^97 + 24 * q^98 + 12 * 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.e.a	$70$	$2$	70.e	7.c	$3$	$2$	$1$	$0.559$	\(\Q(\sqrt{-3}) \)	None		✓			70.2.e.a	$2$	$0$	\(-1\)	\(-3\)	\(1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
70.2.e.b	$70$	$2$	70.e	7.c	$3$	$2$	$1$	$0.559$	\(\Q(\sqrt{-3}) \)	None		✓			70.2.e.b	$2$	$0$	\(-1\)	\(2\)	\(1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
70.2.e.c	$70$	$2$	70.e	7.c	$3$	$2$	$1$	$0.559$	\(\Q(\sqrt{-3}) \)	None		✓			70.2.e.c	$2$	$0$	\(1\)	\(-1\)	\(1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
70.2.e.d	$70$	$2$	70.e	7.c	$3$	$2$	$1$	$0.559$	\(\Q(\sqrt{-3}) \)	None		✓			70.2.e.d	$2$	$0$	\(1\)	\(2\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)

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

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