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

• Label: 10.20.b
• Level: $10$
• Weight: $20$
• Character orbit: 10.b
• Rep. character: $\chi_{10}(9,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $1$
• Sturm bound: $30$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	10.b (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 \(M_{20}(10, [\chi])\).

	Total	New	Old
Modular forms	30	10	20
Cusp forms	26	10	16
Eisenstein series	4	0	4

Trace form

\( 10 q - 2621440 q^{4} + 2902670 q^{5} + 23152640 q^{6} - 8718754970 q^{9} + O(q^{10}) \)

Decomposition of \(S_{20}^{\mathrm{new}}(10, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
10.20.b.a	$10$	$20$	10.b	5.b	$2$	$10$	$10$	$22.882$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		✓	10.20.b.a	$2$	$0$	\(0\)	\(0\)	\(2902670\)	\(0\)	$2^{59}\cdot 3^{6}\cdot 5^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-9\beta _{1}+\beta _{2})q^{3}-2^{18}q^{4}+\cdots\)

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

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