Space of modular forms of level 20, weight 12, and trivial character

• Label: 20.12.a
• Level: $20$
• Weight: $12$
• Character orbit: 20.a
• Rep. character: $\chi_{20}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $36$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	20.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(36\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(20))\).

	Total	New	Old
Modular forms	36	3	33
Cusp forms	30	3	27
Eisenstein series	6	0	6

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(5\)	Fricke	Dim
\(-\)	\(+\)	$-$	\(1\)
\(-\)	\(-\)	$+$	\(2\)
Plus space		\(+\)	\(2\)
Minus space		\(-\)	\(1\)

Trace form

\( 3 q + 526 q^{3} + 3125 q^{5} - 28734 q^{7} - 39773 q^{9} + O(q^{10}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(20))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	5
20.12.a.a	$20$	$12$	20.a	1.a	$1$	$1$	$1$	$15.367$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(306\)	\(-3125\)	\(-32074\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+306q^{3}-5^{5}q^{5}-32074q^{7}-83511q^{9}+\cdots\)
20.12.a.b	$20$	$12$	20.a	1.a	$1$	$2$	$2$	$15.367$	\(\Q(\sqrt{46729}) \)	None	✓	$1$	$0$	\(0\)	\(220\)	\(6250\)	\(3340\)		$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(110-\beta )q^{3}+5^{5}q^{5}+(1670-111\beta )q^{7}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(20))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(20)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 2}\)