Space of modular forms of level 80, weight 2, and Character 80.q

• Label: 80.2.q
• Level: $80$
• Weight: $2$
• Character orbit: 80.q
• Rep. character: $\chi_{80}(29,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $20$
• Newform subspaces: $3$
• Sturm bound: $24$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.q (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 80 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(24\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(80, [\chi])\).

	Total	New	Old
Modular forms	28	28	0
Cusp forms	20	20	0
Eisenstein series	8	8	0

Trace form

20 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^10 - 4 * q^11 - 4 * q^14 - 4 * q^15 - 12 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^24 + 32 * q^26 - 4 * q^29 - 24 * q^30 + 16 * q^31 + 32 * q^34 - 24 * q^35 + 68 * q^36 + 24 * q^40 + 16 * q^44 + 14 * q^45 + 4 * q^46 - 12 * q^49 + 36 * q^50 + 8 * q^54 - 56 * q^56 + 12 * q^59 + 48 * q^60 - 20 * q^61 - 16 * q^64 - 12 * q^65 - 96 * q^66 + 20 * q^70 - 24 * q^74 + 36 * q^75 - 96 * q^76 + 48 * q^79 - 8 * q^80 + 4 * q^81 - 80 * q^84 + 8 * q^85 - 52 * q^86 - 84 * q^90 - 16 * q^91 + 4 * q^94 + 20 * q^95 + 56 * q^96 + 76 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(80, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
80.2.q.a	$80$	$2$	80.q	80.q	$4$	$2$	$1$	$0.639$	\(\Q(\sqrt{-1}) \)	None		✓			80.2.q.a	$2$	$0$	\(-2\)	\(2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i-1)q^{2}+(i+1)q^{3}+2 i q^{4}+\cdots\)
80.2.q.b	$80$	$2$	80.q	80.q	$4$	$2$	$1$	$0.639$	\(\Q(\sqrt{-1}) \)	None		✓			80.2.q.a	$2$	$0$	\(2\)	\(-2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i+1)q^{2}+(-i-1)q^{3}+2 i q^{4}+\cdots\)
80.2.q.c	$80$	$2$	80.q	80.q	$4$	$16$	$8$	$0.639$	16.0.\(\cdots\).1	None		✓	✓		80.2.q.c	$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{12}q^{2}+(-\beta _{3}-\beta _{11}-\beta _{13}+\beta _{14}+\cdots)q^{3}+\cdots\)