Space of modular forms of level 80, weight 5, and Character 80.h

• Label: 80.5.h
• Level: $80$
• Weight: $5$
• Character orbit: 80.h
• Rep. character: $\chi_{80}(79,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $3$
• Sturm bound: $60$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	80.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(60\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(80, [\chi])\).

	Total	New	Old
Modular forms	54	12	42
Cusp forms	42	12	30
Eisenstein series	12	0	12

Trace form

\( 12 q - 36 q^{5} + 324 q^{9} + 912 q^{21} + 1356 q^{25} - 936 q^{29} - 2952 q^{41} - 6924 q^{45} + 132 q^{49} - 6600 q^{61} + 11520 q^{65} - 624 q^{69} + 34716 q^{81} - 3840 q^{85} - 11880 q^{89}+O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(80, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
80.5.h.a	$80$	$5$	80.h	20.d	$2$	$2$	$2$	$8.270$	\(\Q(\sqrt{5}) \)	\(\Q(\sqrt{-5}) \)	✓	✓			80.5.h.a	$4$	$0$	\(0\)	\(0\)	\(-50\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{3}-5^{2}q^{5}-3\beta q^{7}+239q^{9}+\cdots\)
80.5.h.b	$80$	$5$	80.h	20.d	$2$	$2$	$2$	$8.270$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		✓			80.5.h.b	$4$	$0$	\(0\)	\(0\)	\(14\)	\(0\)	$2^{3}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta+7)q^{5}-81 q^{9}+10\beta q^{13}+\cdots\)
80.5.h.c	$80$	$5$	80.h	20.d	$2$	$8$	$8$	$8.270$	8.0.\(\cdots\).10	None		✓	✓		80.5.h.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{28}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+\beta _{4}q^{5}+(2\beta _{3}-\beta _{7})q^{7}+(1+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(80, [\chi])\) into lower level spaces

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