Space of modular forms of level 80, weight 8, and Character 80.c

• Label: 80.8.c
• Level: $80$
• Weight: $8$
• Character orbit: 80.c
• Rep. character: $\chi_{80}(49,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $5$
• Sturm bound: $96$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	80.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(96\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(80, [\chi])\).

	Total	New	Old
Modular forms	90	22	68
Cusp forms	78	20	58
Eisenstein series	12	2	10

Trace form

20 * q - 140 * q^5 - 13124 * q^9 - 7984 * q^11 - 20912 * q^15 + 10864 * q^19 + 3200 * q^21 + 6212 * q^25 - 3592 * q^29 + 44736 * q^31 - 36784 * q^35 + 11552 * q^39 - 347816 * q^41 + 430716 * q^45 - 3183892 * q^49 - 3350080 * q^51 - 3277424 * q^55 + 3237840 * q^59 + 1583752 * q^61 + 1555456 * q^65 + 4213824 * q^69 + 12631328 * q^71 + 9020832 * q^75 - 4647168 * q^79 + 2220692 * q^81 - 3744832 * q^85 - 250872 * q^89 - 30866528 * q^91 - 14573008 * q^95 + 10510576 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(80, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
80.8.c.a	$80$	$8$	80.c	5.b	$2$	$2$	$2$	$24.991$	\(\Q(\sqrt{-29}) \)	None					5.8.b.a	$2$	$0$	\(0\)	\(0\)	\(150\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\beta q^{3}+(75+5^{2}\beta )q^{5}-39\beta q^{7}+\cdots\)
80.8.c.b	$80$	$8$	80.c	5.b	$2$	$2$	$2$	$24.991$	\(\Q(\sqrt{-1}) \)	None					40.8.c.a	$2$	$0$	\(0\)	\(0\)	\(550\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+17\beta q^{3}+(-25\beta+275)q^{5}-53\beta q^{7}+\cdots\)
80.8.c.c	$80$	$8$	80.c	5.b	$2$	$4$	$4$	$24.991$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None					20.8.c.a	$2$	$0$	\(0\)	\(0\)	\(-156\)	\(0\)	$2^{7}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-39+\beta _{1}+\beta _{2})q^{5}+(-5\beta _{1}+\cdots)q^{7}+\cdots\)
80.8.c.d	$80$	$8$	80.c	5.b	$2$	$4$	$4$	$24.991$	\(\Q(i, \sqrt{31})\)	None					10.8.b.a	$2$	$0$	\(0\)	\(0\)	\(60\)	\(0\)	$2^{10}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2\beta _{1}-\beta _{3})q^{3}+(15+\beta _{2}+3\beta _{3})q^{5}+\cdots\)
80.8.c.e	$80$	$8$	80.c	5.b	$2$	$8$	$8$	$24.991$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None			✓		40.8.c.b	$2$	$0$	\(0\)	\(0\)	\(-744\)	\(0\)	$2^{38}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-93+\beta _{1}+\beta _{3})q^{5}+(3\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(80, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(80, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)