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

• Label: 20.10.c
• Level: $20$
• Weight: $10$
• Character orbit: 20.c
• Rep. character: $\chi_{20}(9,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $30$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	20.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(30\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	30	4	26
Cusp forms	24	4	20
Eisenstein series	6	0	6

Trace form

\( 4 q + 660 q^{5} - 9044 q^{9} + O(q^{10}) \)

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.c.a	$20$	$10$	20.c	5.b	$2$	$4$	$4$	$10.301$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(660\)	\(0\)	$2^{7}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(165+\beta _{1}-\beta _{3})q^{5}+(3\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(20, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(20, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)