Space of modular forms of level 80, weight 20, and Character 80.c

• Label: 80.20.c
• Level: $80$
• Weight: $20$
• Character orbit: 80.c
• Rep. character: $\chi_{80}(49,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $4$
• Sturm bound: $240$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 20 \)
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:			\(240\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(80, [\chi])\).

	Total	New	Old
Modular forms	234	58	176
Cusp forms	222	56	166
Eisenstein series	12	2	10

Trace form

\( 56 q - 1782960 q^{5} - 20920706408 q^{9} + O(q^{10}) \)

Decomposition of \(S_{20}^{\mathrm{new}}(80, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
80.20.c.a	$80$	$20$	80.c	5.b	$2$	$8$	$8$	$183.053$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(147000\)	\(0\)	$2^{34}\cdot 3^{8}\cdot 5^{13}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(18375-\beta _{1}-3^{3}\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
80.20.c.b	$80$	$20$	80.c	5.b	$2$	$10$	$10$	$183.053$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-897466\)	\(0\)	$2^{56}\cdot 3^{6}\cdot 5^{17}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-89747+8\beta _{1}+\beta _{2})q^{5}+\cdots\)
80.20.c.c	$80$	$20$	80.c	5.b	$2$	$10$	$10$	$183.053$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(2902670\)	\(0\)	$2^{69}\cdot 3^{6}\cdot 5^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(290267+11\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
80.20.c.d	$80$	$20$	80.c	5.b	$2$	$28$	$28$	$183.053$		None		$2$	$0$	\(0\)	\(0\)	\(-3935164\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{20}^{\mathrm{old}}(80, [\chi])\) into lower level spaces

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