Space of modular forms of level 80, weight 3, and Character 80.p

• Label: 80.3.p
• Level: $80$
• Weight: $3$
• Character orbit: 80.p
• Rep. character: $\chi_{80}(17,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $10$
• Newform subspaces: $4$
• Sturm bound: $36$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	80.p (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(36\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(80, [\chi])\).

	Total	New	Old
Modular forms	60	14	46
Cusp forms	36	10	26
Eisenstein series	24	4	20

Trace form

10 * q + 2 * q^3 - 2 * q^5 + 2 * q^7 + 4 * q^11 - 14 * q^13 + 50 * q^15 + 2 * q^17 + 12 * q^21 - 46 * q^23 - 14 * q^25 - 112 * q^27 - 60 * q^31 - 68 * q^33 - 46 * q^35 - 22 * q^37 + 12 * q^41 + 66 * q^43 + 108 * q^45 + 242 * q^47 + 292 * q^51 + 26 * q^53 + 148 * q^55 - 16 * q^57 - 36 * q^61 - 222 * q^63 + 122 * q^65 - 334 * q^67 - 412 * q^71 + 170 * q^73 - 302 * q^75 - 100 * q^77 + 34 * q^81 + 274 * q^83 - 142 * q^85 + 496 * q^87 + 580 * q^91 - 116 * q^93 + 240 * q^95 - 22 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(80, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
80.3.p.a	$80$	$3$	80.p	5.c	$4$	$2$	$1$	$2.180$	\(\Q(\sqrt{-1}) \)	None					20.3.f.a	$2$	$0$	\(0\)	\(-2\)	\(-6\)	\(14\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i-1)q^{3}+(4 i-3)q^{5}+(7 i+7)q^{7}+\cdots\)
80.3.p.b	$80$	$3$	80.p	5.c	$4$	$2$	$1$	$2.180$	\(\Q(\sqrt{-1}) \)	None					40.3.l.a	$2$	$0$	\(0\)	\(-2\)	\(10\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i-1)q^{3}+5 q^{5}+(3 i+3)q^{7}+\cdots\)
80.3.p.c	$80$	$3$	80.p	5.c	$4$	$2$	$1$	$2.180$	\(\Q(\sqrt{-1}) \)	None					10.3.c.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2 i+2)q^{3}-5 i q^{5}+(-2 i-2)q^{7}+\cdots\)
80.3.p.d	$80$	$3$	80.p	5.c	$4$	$4$	$2$	$2.180$	\(\Q(i, \sqrt{41})\)	None			✓		40.3.l.b	$2$	$0$	\(0\)	\(2\)	\(-6\)	\(-14\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(80, [\chi])\) into lower level spaces

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