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

\( 16 q - 256 q^{4} - 176 q^{5} - 1648 q^{9} + O(q^{10}) \)

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	$2$	$0$	\(0\)	\(0\)	\(-110\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+4iq^{2}-2^{4}q^{4}+(-55-10i)q^{5}+\cdots\)
70.6.c.b	$70$	$6$	70.c	5.b	$2$	$2$	$2$	$11.227$	\(\Q(\sqrt{-1}) \)	None		✓			70.6.c.b	$2$	$1$	\(0\)	\(0\)	\(-20\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+4iq^{2}+3^{3}iq^{3}-2^{4}q^{4}+(-10+\cdots)q^{5}+\cdots\)
70.6.c.c	$70$	$6$	70.c	5.b	$2$	$2$	$2$	$11.227$	\(\Q(\sqrt{-1}) \)	None		✓			70.6.c.c	$2$	$0$	\(0\)	\(0\)	\(20\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+4iq^{2}-13iq^{3}-2^{4}q^{4}+(10+55i)q^{5}+\cdots\)
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

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