Space of modular forms of level 80, weight 5, and Character 80.p

• Label: 80.5.p
• Level: $80$
• Weight: $5$
• Character orbit: 80.p
• Rep. character: $\chi_{80}(17,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $22$
• Newform subspaces: $7$
• Sturm bound: $60$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	80.p (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(60\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(80, [\chi])\).

	Total	New	Old
Modular forms	108	26	82
Cusp forms	84	22	62
Eisenstein series	24	4	20

Trace form

22 * q + 2 * q^3 - 2 * q^5 + 2 * q^7 + 4 * q^11 - 122 * q^13 - 670 * q^15 - 122 * q^17 - 612 * q^21 + 1442 * q^23 + 166 * q^25 - 1120 * q^27 - 124 * q^31 + 1276 * q^33 + 2594 * q^35 + 1398 * q^37 - 1252 * q^41 - 4478 * q^43 - 1992 * q^45 + 4322 * q^47 - 3260 * q^51 + 2518 * q^53 - 7772 * q^55 + 3680 * q^57 + 3772 * q^61 + 11202 * q^63 - 7178 * q^65 + 12002 * q^67 + 9412 * q^71 - 1002 * q^73 - 5342 * q^75 - 4804 * q^77 - 1850 * q^81 + 5282 * q^83 - 3642 * q^85 - 33440 * q^87 - 52604 * q^91 + 14236 * q^93 - 5280 * q^95 - 7722 * q^97

Decomposition of \(S_{5}^{\mathrm{new}}(80, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
80.5.p.a	$80$	$5$	80.p	5.c	$4$	$2$	$1$	$8.270$	\(\Q(\sqrt{-1}) \)	None					40.5.l.a	$2$	$0$	\(0\)	\(-20\)	\(40\)	\(84\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(10 i-10)q^{3}+(15 i+20)q^{5}+\cdots\)
80.5.p.b	$80$	$5$	80.p	5.c	$4$	$2$	$1$	$8.270$	\(\Q(\sqrt{-1}) \)	None					10.5.c.a	$2$	$0$	\(0\)	\(-18\)	\(-30\)	\(-58\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(9 i-9)q^{3}+(20 i-15)q^{5}+(-29 i-29)q^{7}+\cdots\)
80.5.p.c	$80$	$5$	80.p	5.c	$4$	$2$	$1$	$8.270$	\(\Q(\sqrt{-1}) \)	None					10.5.c.b	$2$	$0$	\(0\)	\(-2\)	\(-30\)	\(38\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i-1)q^{3}+(-20 i-15)q^{5}+(19 i+19)q^{7}+\cdots\)
80.5.p.d	$80$	$5$	80.p	5.c	$4$	$2$	$1$	$8.270$	\(\Q(\sqrt{-1}) \)	None					5.5.c.a	$2$	$0$	\(0\)	\(12\)	\(40\)	\(52\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-6 i+6)q^{3}+(15 i+20)q^{5}+\cdots\)
80.5.p.e	$80$	$5$	80.p	5.c	$4$	$4$	$2$	$8.270$	\(\Q(i, \sqrt{241})\)	None					20.5.f.a	$2$	$0$	\(0\)	\(10\)	\(-6\)	\(-110\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(3-3\beta _{1}+\beta _{3})q^{3}+(-3-3\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
80.5.p.f	$80$	$5$	80.p	5.c	$4$	$4$	$2$	$8.270$	\(\Q(i, \sqrt{29})\)	None					40.5.l.b	$2$	$0$	\(0\)	\(12\)	\(-12\)	\(-44\)	$2^{4}\cdot 5$	$\mathrm{SU}(2)[C_{4}]$	\(q+(3-3\beta _{1})q^{3}+(-3-6\beta _{1}-\beta _{3})q^{5}+\cdots\)
80.5.p.g	$80$	$5$	80.p	5.c	$4$	$6$	$3$	$8.270$	6.0.313431616.3	None			✓		40.5.l.c	$2$	$0$	\(0\)	\(8\)	\(-4\)	\(40\)	$2^{5}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{1}+\beta _{3})q^{3}+(-1+7\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(80, [\chi])\) into lower level spaces

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