Space of modular forms of level 12, weight 16, and trivial character

• Label: 12.16.a
• Level: $12$
• Weight: $16$
• Character orbit: 12.a
• Rep. character: $\chi_{12}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $32$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	12.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(32\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_0(12))\).

	Total	New	Old
Modular forms	33	3	30
Cusp forms	27	3	24
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.

\(2\)	\(3\)	Fricke	Dim
\(-\)	\(+\)	$-$	\(1\)
\(-\)	\(-\)	$+$	\(2\)
Plus space		\(+\)	\(2\)
Minus space		\(-\)	\(1\)

Trace form

\( 3 q + 2187 q^{3} + 115362 q^{5} + 3709392 q^{7} + 14348907 q^{9} + O(q^{10}) \)

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_0(12))\) 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	3
12.16.a.a	$12$	$16$	12.a	1.a	$1$	$1$	$1$	$17.123$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2187\)	\(45702\)	\(1217888\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3^{7}q^{3}+45702q^{5}+1217888q^{7}+\cdots\)
12.16.a.b	$12$	$16$	12.a	1.a	$1$	$2$	$2$	$17.123$	\(\Q(\sqrt{8017}) \)	None	✓	$1$	$0$	\(0\)	\(4374\)	\(69660\)	\(2491504\)		$-$	$-$	$+$	$2^{7}\cdot 3^{2}\cdot 5$	$\mathrm{SU}(2)$	\(q+3^{7}q^{3}+(34830-\beta )q^{5}+(1245752+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_0(12))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_0(12)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)