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

• Label: 820.2.b
• Level: $820$
• Weight: $2$
• Character orbit: 820.b
• Rep. character: $\chi_{820}(81,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $2$
• Sturm bound: $252$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 41 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
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	132	14	118
Cusp forms	120	14	106
Eisenstein series	12	0	12

Trace form

14 * q + 2 * q^5 - 22 * q^9 + 12 * q^21 - 8 * q^23 + 14 * q^25 + 12 * q^31 + 28 * q^33 - 16 * q^37 - 4 * q^39 - 2 * q^41 + 6 * q^45 - 26 * q^49 + 48 * q^51 - 36 * q^57 + 4 * q^59 + 36 * q^61 + 12 * q^73 - 28 * q^77 + 38 * q^81 - 28 * q^83 - 20 * q^87 - 44 * q^91

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.b.a	$820$	$2$	820.b	41.b	$2$	$6$	$6$	$6.548$	6.0.36433296.1	None		✓			820.2.b.a	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}-q^{5}-\beta _{4}q^{7}+(-2-\beta _{3}+\cdots)q^{9}+\cdots\)
820.2.b.b	$820$	$2$	820.b	41.b	$2$	$8$	$8$	$6.548$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓	✓		820.2.b.b	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{3}+q^{5}-\beta _{4}q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(820, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(82, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(164, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(205, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(410, [\chi])\)\(^{\oplus 2}\)