Space of modular forms of level 820, weight 2, and Character 820.k

• Label: 820.2.k
• Level: $820$
• Weight: $2$
• Character orbit: 820.k
• Rep. character: $\chi_{820}(83,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $240$
• Newform subspaces: $4$
• Sturm bound: $252$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(252\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(820, [\chi])\).

	Total	New	Old
Modular forms	260	240	20
Cusp forms	244	240	4
Eisenstein series	16	0	16

Trace form

240 * q - 8 * q^6 + 8 * q^16 + 28 * q^18 + 20 * q^20 + 20 * q^22 - 16 * q^26 - 32 * q^28 + 20 * q^32 + 16 * q^33 - 20 * q^40 - 8 * q^46 + 8 * q^48 - 16 * q^50 - 36 * q^52 - 48 * q^53 - 64 * q^56 - 32 * q^57 - 12 * q^58 + 60 * q^60 - 64 * q^61 + 4 * q^62 - 32 * q^65 + 32 * q^66 + 80 * q^68 + 36 * q^70 + 60 * q^72 - 16 * q^73 - 24 * q^76 + 48 * q^77 - 24 * q^78 - 96 * q^80 - 240 * q^81 + 48 * q^85 - 40 * q^86 + 48 * q^88 + 60 * q^90 + 16 * q^92 + 48 * q^93 + 48 * q^96 - 80 * q^97 - 20 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(820, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
820.2.k.a	$820$	$2$	820.k	20.e	$4$	$4$	$2$	$6.548$	\(\Q(i, \sqrt{5})\)	None		✓			820.2.k.a	$4$	$0$	\(-4\)	\(0\)	\(-8\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}-2\beta _{1}q^{4}+\cdots\)
820.2.k.b	$820$	$2$	820.k	20.e	$4$	$8$	$4$	$6.548$	8.0.\(\cdots\).8	None		✓			820.2.k.b	$4$	$0$	\(-8\)	\(0\)	\(8\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}+2\beta _{2}q^{4}+\cdots\)
820.2.k.c	$820$	$2$	820.k	20.e	$4$	$108$	$54$	$6.548$		None		✓			820.2.k.c	$4$	$0$	\(12\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
820.2.k.d	$820$	$2$	820.k	20.e	$4$	$120$	$60$	$6.548$		None		✓	✓		820.2.k.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(820, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(820, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)