Space of modular forms of level 1020, weight 2, and Character 1020.v

• Label: 1020.2.v
• Level: $1020$
• Weight: $2$
• Character orbit: 1020.v
• Rep. character: $\chi_{1020}(137,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $64$
• Newform subspaces: $1$
• Sturm bound: $432$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1020.v (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(432\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1020, [\chi])\).

	Total	New	Old
Modular forms	456	64	392
Cusp forms	408	64	344
Eisenstein series	48	0	48

Trace form

\( 64 q - 4 q^{3} + 8 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1020, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1020.2.v.a	$1020$	$2$	1020.v	15.e	$4$	$64$	$32$	$8.145$		None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1020, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1020, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)