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

• Label: 80.3.h
• Level: $80$
• Weight: $3$
• Character orbit: 80.h
• Rep. character: $\chi_{80}(79,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $36$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	80.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(36\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	30	6	24
Cusp forms	18	6	12
Eisenstein series	12	0	12

Trace form

\( 6 q + 6 q^{5} + 18 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
80.3.h.a	$80$	$3$	80.h	20.d	$2$	$2$	$2$	$2.180$	\(\Q(\sqrt{5}) \)	\(\Q(\sqrt{-5}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(10\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{3}+5q^{5}+3\beta q^{7}+11q^{9}-5\beta q^{15}+\cdots\)
80.3.h.b	$80$	$3$	80.h	20.d	$2$	$4$	$4$	$2.180$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+3\beta _{1}q^{7}+\cdots\)

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

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