Space of Modular Forms of Level 80, Weight 1, and Character 80.h

• Label: 80.1.h
• Level: 80
• Weight: 1
• Character orbit: h
• Rep. character: \(\chi_{80}(79,\cdot)\)
• Character field: \(\Q\)
• Dimension: 1
• Newforms: 1
• Sturm bound: 12
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	=	\( 1 \)
Character orbit:	\([\chi]\)	=	80.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	=	\( 20 \)
Character field:			\(\Q\)
Newforms:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(80, [\chi])\).

	Total	New	Old
Modular forms	7	1	6
Cusp forms	1	1	0
Eisenstein series	6	0	6

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	1	0	0	0

Trace form

\(q \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut -\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(80, [\chi])\) into irreducible Hecke orbits

Label	Dim.	\(A\)	Field	Image	CM	RM	Traces				$q$-expansion
							\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)
80.1.h.a	\(1\)	\(0.040\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{5}) \)	\(0\)	\(0\)	\(-1\)	\(0\)	\(q-q^{5}-q^{9}+q^{25}+2q^{29}-2q^{41}+\cdots\)