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

• Label: 70.4.e
• Level: $70$
• Weight: $4$
• Character orbit: 70.e
• Rep. character: $\chi_{70}(11,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $16$
• Newform subspaces: $5$
• Sturm bound: $48$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	70.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(48\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	80	16	64
Cusp forms	64	16	48
Eisenstein series	16	0	16

Trace form

16 * q - 12 * q^3 - 32 * q^4 - 10 * q^5 - 8 * q^6 + 100 * q^7 - 118 * q^9 - 20 * q^10 + 6 * q^11 - 48 * q^12 + 16 * q^13 - 124 * q^14 - 80 * q^15 - 128 * q^16 - 132 * q^17 + 112 * q^18 + 250 * q^19 + 80 * q^20 + 258 * q^21 + 112 * q^22 + 168 * q^23 + 16 * q^24 - 200 * q^25 - 156 * q^26 + 816 * q^27 - 128 * q^28 - 332 * q^29 - 140 * q^30 + 96 * q^31 - 128 * q^33 - 480 * q^34 + 90 * q^35 + 944 * q^36 - 1036 * q^37 - 704 * q^38 - 100 * q^39 - 80 * q^40 + 1096 * q^41 + 248 * q^42 + 1856 * q^43 + 24 * q^44 - 380 * q^45 - 184 * q^46 + 500 * q^47 + 384 * q^48 - 674 * q^49 - 900 * q^51 - 32 * q^52 - 1012 * q^53 + 556 * q^54 - 480 * q^55 - 16 * q^56 - 1720 * q^57 - 288 * q^58 + 1140 * q^59 + 160 * q^60 + 1146 * q^61 - 160 * q^62 - 6036 * q^63 + 1024 * q^64 + 570 * q^65 + 2880 * q^66 + 1636 * q^67 - 528 * q^68 + 1684 * q^69 + 180 * q^70 - 2384 * q^71 + 448 * q^72 - 972 * q^73 - 876 * q^74 - 300 * q^75 - 2000 * q^76 - 944 * q^77 + 864 * q^78 + 40 * q^79 - 160 * q^80 - 2704 * q^81 + 1536 * q^82 + 968 * q^83 + 96 * q^84 + 2560 * q^85 - 804 * q^86 + 2580 * q^87 - 224 * q^88 - 162 * q^89 + 1800 * q^90 + 3668 * q^91 - 1344 * q^92 + 1956 * q^93 + 1084 * q^94 + 580 * q^95 + 64 * q^96 + 3504 * q^97 + 2352 * q^98 + 724 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
70.4.e.a	$70$	$4$	70.e	7.c	$3$	$2$	$1$	$4.130$	\(\Q(\sqrt{-3}) \)	None		✓			70.4.e.a	$2$	$0$	\(-2\)	\(-1\)	\(5\)	\(35\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
70.4.e.b	$70$	$4$	70.e	7.c	$3$	$2$	$1$	$4.130$	\(\Q(\sqrt{-3}) \)	None		✓			70.4.e.b	$2$	$0$	\(2\)	\(-10\)	\(5\)	\(28\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{2}+(-10+10\zeta_{6})q^{3}+(-4+\cdots)q^{4}+\cdots\)
70.4.e.c	$70$	$4$	70.e	7.c	$3$	$2$	$1$	$4.130$	\(\Q(\sqrt{-3}) \)	None		✓			70.4.e.c	$2$	$0$	\(2\)	\(1\)	\(5\)	\(17\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
70.4.e.d	$70$	$4$	70.e	7.c	$3$	$4$	$2$	$4.130$	\(\Q(\sqrt{-3}, \sqrt{46})\)	None		✓			70.4.e.d	$2$	$0$	\(4\)	\(2\)	\(-10\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-4+\cdots)q^{4}+\cdots\)
70.4.e.e	$70$	$4$	70.e	7.c	$3$	$6$	$3$	$4.130$	6.0.\(\cdots\).2	None		✓	✓		70.4.e.e	$2$	$0$	\(-6\)	\(-4\)	\(-15\)	\(14\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\beta _{3})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(70, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)