Space of modular forms of level 70, weight 6, and Character 70.c

• Label: 70.6.c
• Level: $70$
• Weight: $6$
• Character orbit: 70.c
• Rep. character: $\chi_{70}(29,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $72$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	70.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(72\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(70, [\chi])\).

	Total	New	Old
Modular forms	64	16	48
Cusp forms	56	16	40
Eisenstein series	8	0	8

Trace form

16 * q - 256 * q^4 - 176 * q^5 - 1648 * q^9 - 336 * q^10 + 864 * q^11 - 784 * q^14 + 2092 * q^15 + 4096 * q^16 + 7024 * q^19 + 2816 * q^20 + 2744 * q^21 - 10020 * q^25 + 1952 * q^26 - 10232 * q^29 + 7792 * q^30 - 22576 * q^31 - 23520 * q^34 - 6076 * q^35 + 26368 * q^36 + 20392 * q^39 + 5376 * q^40 + 9232 * q^41 - 13824 * q^44 + 21528 * q^45 + 24416 * q^46 - 38416 * q^49 - 5904 * q^50 - 20192 * q^51 + 92736 * q^54 + 38696 * q^55 + 12544 * q^56 - 187152 * q^59 - 33472 * q^60 - 51408 * q^61 - 65536 * q^64 - 24284 * q^65 + 71360 * q^66 + 25696 * q^69 - 8624 * q^70 - 196168 * q^71 - 103072 * q^74 + 431760 * q^75 - 112384 * q^76 - 55880 * q^79 - 45056 * q^80 + 366664 * q^81 - 43904 * q^84 + 329072 * q^85 + 333440 * q^86 - 308816 * q^89 - 48912 * q^90 + 65464 * q^91 + 17280 * q^94 + 103516 * q^95 - 480864 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(70, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
70.6.c.a	$70$	$6$	70.c	5.b	$2$	$2$	$2$	$11.227$	\(\Q(\sqrt{-1}) \)	None		✓			70.6.c.a	$2$	$0$	\(0\)	\(0\)	\(-110\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+4 i q^{2}-16 q^{4}+(-10 i-55)q^{5}+\cdots\)
70.6.c.b	$70$	$6$	70.c	5.b	$2$	$2$	$2$	$11.227$	\(\Q(\sqrt{-1}) \)	None		✓			70.6.c.b	$2$	$1$	\(0\)	\(0\)	\(-20\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+4 i q^{2}+27 i q^{3}-16 q^{4}+(-55 i-10)q^{5}+\cdots\)
70.6.c.c	$70$	$6$	70.c	5.b	$2$	$2$	$2$	$11.227$	\(\Q(\sqrt{-1}) \)	None		✓			70.6.c.c	$2$	$0$	\(0\)	\(0\)	\(20\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+4 i q^{2}-13 i q^{3}-16 q^{4}+(55 i+10)q^{5}+\cdots\)
70.6.c.d	$70$	$6$	70.c	5.b	$2$	$10$	$10$	$11.227$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓	✓		70.6.c.d	$2$	$0$	\(0\)	\(0\)	\(-66\)	\(0\)	$2^{3}\cdot 3^{2}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+4\beta _{3}q^{2}+(\beta _{1}-3\beta _{3})q^{3}-2^{4}q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(70, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(70, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)