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

• Label: 820.2.bi
• Level: $820$
• Weight: $2$
• Character orbit: 820.bi
• Rep. character: $\chi_{820}(189,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $80$
• Newform subspaces: $1$
• Sturm bound: $252$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bi (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 205 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(252\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	528	80	448
Cusp forms	480	80	400
Eisenstein series	48	0	48

Trace form

\( 80 q + 68 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
820.2.bi.a	$820$	$2$	820.bi	205.r	$10$	$80$	$20$	$6.548$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

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

\( S_{2}^{\mathrm{old}}(820, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(205, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(410, [\chi])\)\(^{\oplus 2}\)