Space of modular forms of level 20, weight 10, and Character 20.e

• Label: 20.10.e
• Level: $20$
• Weight: $10$
• Character orbit: 20.e
• Rep. character: $\chi_{20}(3,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $50$
• Newform subspaces: $2$
• Sturm bound: $30$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	20.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(30\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(20, [\chi])\).

	Total	New	Old
Modular forms	58	58	0
Cusp forms	50	50	0
Eisenstein series	8	8	0

Trace form

\( 50 q - 2 q^{2} - 4 q^{5} + 6152 q^{6} - 716 q^{8} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(20, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
20.10.e.a	$20$	$10$	20.e	20.e	$4$	$2$	$1$	$10.301$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(-32\)	\(0\)	\(1436\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-2^{4}-2^{4}i)q^{2}+2^{9}iq^{4}+(718+\cdots)q^{5}+\cdots\)
20.10.e.b	$20$	$10$	20.e	20.e	$4$	$48$	$24$	$10.301$		None		$4$	$0$	\(30\)	\(0\)	\(-1440\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$