Space of modular forms of level 80, weight 2, and Character 80.c

• Label: 80.2.c
• Level: $80$
• Weight: $2$
• Character orbit: 80.c
• Rep. character: $\chi_{80}(49,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(80, [\chi])\).

	Total	New	Old
Modular forms	18	4	14
Cusp forms	6	2	4
Eisenstein series	12	2	10

Trace form

2 * q - 2 * q^5 - 2 * q^9 + 8 * q^11 - 8 * q^15 - 8 * q^19 + 8 * q^21 - 6 * q^25 - 4 * q^29 + 8 * q^35 + 16 * q^39 + 4 * q^41 + 2 * q^45 + 6 * q^49 - 8 * q^55 - 24 * q^59 - 20 * q^61 + 16 * q^65 + 8 * q^69 - 16 * q^71 + 16 * q^75 + 32 * q^79 - 22 * q^81 - 12 * q^89 - 16 * q^91 + 8 * q^95 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(80, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
80.2.c.a	$80$	$2$	80.c	5.b	$2$	$2$	$2$	$0.639$	\(\Q(\sqrt{-1}) \)	None			✓	✓	40.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+(\beta-1)q^{5}-\beta q^{7}-q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(80, [\chi])\) into lower level spaces

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