Space of modular forms of level 80, weight 6, and trivial character

• Label: 80.6.a
• Level: $80$
• Weight: $6$
• Character orbit: 80.a
• Rep. character: $\chi_{80}(1,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $9$
• Sturm bound: $72$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	80.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(72\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(80))\).

	Total	New	Old
Modular forms	66	10	56
Cusp forms	54	10	44
Eisenstein series	12	0	12

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(5\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(2\)
\(+\)	\(-\)	$-$	\(3\)
\(-\)	\(+\)	$-$	\(3\)
\(-\)	\(-\)	$+$	\(2\)
Plus space		\(+\)	\(4\)
Minus space		\(-\)	\(6\)

Trace form

\( 10 q + 18 q^{3} - 222 q^{7} + 854 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(80))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	5
80.6.a.a	$80$	$6$	80.a	1.a	$1$	$1$	$1$	$12.831$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-24\)	\(25\)	\(172\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-24q^{3}+5^{2}q^{5}+172q^{7}+333q^{9}+\cdots\)
80.6.a.b	$80$	$6$	80.a	1.a	$1$	$1$	$1$	$12.831$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-22\)	\(-25\)	\(-218\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-22q^{3}-5^{2}q^{5}-218q^{7}+241q^{9}+\cdots\)
80.6.a.c	$80$	$6$	80.a	1.a	$1$	$1$	$1$	$12.831$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-6\)	\(-25\)	\(118\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-6q^{3}-5^{2}q^{5}+118q^{7}-207q^{9}+\cdots\)
80.6.a.d	$80$	$6$	80.a	1.a	$1$	$1$	$1$	$12.831$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-25\)	\(62\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-5^{2}q^{5}+62q^{7}-239q^{9}+\cdots\)
80.6.a.e	$80$	$6$	80.a	1.a	$1$	$1$	$1$	$12.831$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(4\)	\(25\)	\(-192\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{3}+5^{2}q^{5}-192q^{7}-227q^{9}+\cdots\)
80.6.a.f	$80$	$6$	80.a	1.a	$1$	$1$	$1$	$12.831$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(8\)	\(25\)	\(108\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+8q^{3}+5^{2}q^{5}+108q^{7}-179q^{9}+\cdots\)
80.6.a.g	$80$	$6$	80.a	1.a	$1$	$1$	$1$	$12.831$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(18\)	\(-25\)	\(-242\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+18q^{3}-5^{2}q^{5}-242q^{7}+3^{4}q^{9}+\cdots\)
80.6.a.h	$80$	$6$	80.a	1.a	$1$	$1$	$1$	$12.831$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(26\)	\(-25\)	\(22\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+26q^{3}-5^{2}q^{5}+22q^{7}+433q^{9}+\cdots\)
80.6.a.i	$80$	$6$	80.a	1.a	$1$	$2$	$2$	$12.831$	\(\Q(\sqrt{129}) \)	None	✓	$1$	$0$	\(0\)	\(12\)	\(50\)	\(-52\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(6+\beta )q^{3}+5^{2}q^{5}+(-26+3\beta )q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(80))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(80)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 2}\)