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

• Label: 820.2.bm
• Level: $820$
• Weight: $2$
• Character orbit: 820.bm
• Rep. character: $\chi_{820}(23,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $976$
• Newform subspaces: $3$
• Sturm bound: $252$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bm (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 820 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(252\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(3\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	1040	1040	0
Cusp forms	976	976	0
Eisenstein series	64	64	0

Trace form

976 * q - 6 * q^2 - 12 * q^5 - 20 * q^6 + 6 * q^8 + 18 * q^10 + 20 * q^12 - 20 * q^13 - 12 * q^16 - 20 * q^17 - 12 * q^18 - 22 * q^20 - 8 * q^21 - 10 * q^22 - 32 * q^25 - 20 * q^26 - 10 * q^28 - 10 * q^30 - 56 * q^32 - 48 * q^33 + 36 * q^36 + 18 * q^37 - 120 * q^40 - 24 * q^41 + 64 * q^42 + 68 * q^45 - 12 * q^46 - 40 * q^48 - 56 * q^50 + 90 * q^52 - 20 * q^53 - 160 * q^56 + 24 * q^57 - 10 * q^58 - 110 * q^60 - 24 * q^61 - 14 * q^62 - 20 * q^65 + 168 * q^66 - 310 * q^70 - 40 * q^72 - 84 * q^73 - 20 * q^76 + 44 * q^77 - 40 * q^78 - 46 * q^80 - 704 * q^81 + 118 * q^82 - 44 * q^86 + 100 * q^88 + 58 * q^90 - 64 * q^92 - 160 * q^93 + 30 * q^97 + 90 * 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.bm.a	$820$	$2$	820.bm	820.am	$20$	$8$	$1$	$6.548$	\(\Q(\zeta_{20})\)	\(\Q(\sqrt{-1}) \)		✓			820.2.bm.a	$4$	$0$	\(2\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{20}]$	\(q+(-\zeta_{20}+\zeta_{20}^{6})q^{2}-2\zeta_{20}^{7}q^{4}+\cdots\)
820.2.bm.b	$820$	$2$	820.bm	820.am	$20$	$8$	$1$	$6.548$	\(\Q(\zeta_{20})\)	\(\Q(\sqrt{-1}) \)		✓			820.2.bm.a	$4$	$0$	\(2\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{20}]$	\(q+(-\zeta_{20}+\zeta_{20}^{6})q^{2}-2\zeta_{20}^{7}q^{4}+\cdots\)
820.2.bm.c	$820$	$2$	820.bm	820.am	$20$	$960$	$120$	$6.548$		None		✓	✓		820.2.bm.c	$8$	$0$	\(-10\)	\(0\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$