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

• Label: 80.3.k
• Level: $80$
• Weight: $3$
• Character orbit: 80.k
• Rep. character: $\chi_{80}(19,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $44$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	80.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 80 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(36\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	52	52	0
Cusp forms	44	44	0
Eisenstein series	8	8	0

Trace form

44 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 - 20 * q^10 - 4 * q^11 + 4 * q^14 - 32 * q^16 - 36 * q^19 + 40 * q^20 + 32 * q^21 + 16 * q^24 - 56 * q^26 - 4 * q^29 - 160 * q^30 - 192 * q^34 + 212 * q^36 - 8 * q^39 - 184 * q^40 + 224 * q^44 + 30 * q^45 + 124 * q^46 - 148 * q^49 + 100 * q^50 + 128 * q^51 + 24 * q^54 - 260 * q^55 + 360 * q^56 - 68 * q^59 - 80 * q^60 + 28 * q^61 - 16 * q^64 - 20 * q^65 + 448 * q^66 + 128 * q^69 + 396 * q^70 - 264 * q^71 + 480 * q^74 + 60 * q^75 - 464 * q^76 + 504 * q^80 - 116 * q^81 - 496 * q^84 + 48 * q^85 - 852 * q^86 + 144 * q^90 + 384 * q^91 - 340 * q^94 - 1128 * q^96 + 484 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
80.3.k.a	$80$	$3$	80.k	80.k	$4$	$44$	$22$	$2.180$		None		✓	✓	✓	80.3.k.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$