Space of modular forms of level 80, weight 6, and Character 80.c

• Label: 80.6.c
• Level: $80$
• Weight: $6$
• Character orbit: 80.c
• Rep. character: $\chi_{80}(49,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $4$
• Sturm bound: $72$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	80.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 \(M_{6}(80, [\chi])\).

	Total	New	Old
Modular forms	66	16	50
Cusp forms	54	14	40
Eisenstein series	12	2	10

Trace form

\( 14 q + 18 q^{5} - 974 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(80, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
80.6.c.a	$80$	$6$	80.c	5.b	$2$	$2$	$2$	$12.831$	\(\Q(\sqrt{-11}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-90\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\beta q^{3}+(-45-5\beta )q^{5}-9\beta q^{7}+\cdots\)
80.6.c.b	$80$	$6$	80.c	5.b	$2$	$2$	$2$	$12.831$	\(\Q(\sqrt{-31}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-10\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}+(-5+5\beta )q^{5}-11\beta q^{7}+119q^{9}+\cdots\)
80.6.c.c	$80$	$6$	80.c	5.b	$2$	$2$	$2$	$12.831$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(110\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+7iq^{3}+(55-5i)q^{5}-79iq^{7}+47q^{9}+\cdots\)
80.6.c.d	$80$	$6$	80.c	5.b	$2$	$8$	$8$	$12.831$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{31}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(1-\beta _{2})q^{5}+(-\beta _{2}-\beta _{6}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(80, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(80, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)