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 + 728 * q^11 + 1192 * q^15 - 984 * q^19 + 1304 * q^21 - 586 * q^25 + 8260 * q^29 - 9344 * q^31 - 12712 * q^35 + 10544 * q^39 + 3580 * q^41 - 10578 * q^45 - 31222 * q^49 + 73088 * q^51 + 22952 * q^55 - 69896 * q^59 + 21748 * q^61 + 4016 * q^65 - 21096 * q^69 - 47792 * q^71 - 85584 * q^75 + 82912 * q^79 + 141254 * q^81 - 97920 * q^85 + 110188 * q^89 + 105680 * q^91 - 195752 * q^95 - 152024 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
80.6.c.a	$80$	$6$	80.c	5.b	$2$	$2$	$2$	$12.831$	\(\Q(\sqrt{-11}) \)	None					5.6.b.a	$2$	$0$	\(0\)	\(0\)	\(-90\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\beta q^{3}+(-45-5\beta )q^{5}-9\beta q^{7}+\cdots\)
80.6.c.b	$80$	$6$	80.c	5.b	$2$	$2$	$2$	$12.831$	\(\Q(\sqrt{-31}) \)	None					20.6.c.a	$2$	$0$	\(0\)	\(0\)	\(-10\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}+(-5+5\beta )q^{5}-11\beta q^{7}+119q^{9}+\cdots\)
80.6.c.c	$80$	$6$	80.c	5.b	$2$	$2$	$2$	$12.831$	\(\Q(\sqrt{-1}) \)	None					10.6.b.a	$2$	$0$	\(0\)	\(0\)	\(110\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+7\beta q^{3}+(-5\beta+55)q^{5}-79\beta q^{7}+\cdots\)
80.6.c.d	$80$	$6$	80.c	5.b	$2$	$8$	$8$	$12.831$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None			✓		40.6.c.a	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{31}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(1-\beta _{2})q^{5}+(-\beta _{2}-\beta _{6}+\cdots)q^{7}+\cdots\)

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

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