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

• Label: 16.12.a
• Level: $16$
• Weight: $12$
• Character orbit: 16.a
• Rep. character: $\chi_{16}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $4$
• Sturm bound: $24$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	16.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(24\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	25	6	19
Cusp forms	19	5	14
Eisenstein series	6	1	5

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

\(2\)	Dim
\(+\)	\(3\)
\(-\)	\(2\)

Trace form

\( 5 q + 244 q^{3} - 1322 q^{5} - 68152 q^{7} + 339817 q^{9} + O(q^{10}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(16))\) 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
16.12.a.a	$16$	$12$	16.a	1.a	$1$	$1$	$1$	$12.293$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-252\)	\(4830\)	\(16744\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-252q^{3}+4830q^{5}+16744q^{7}+\cdots\)
16.12.a.b	$16$	$12$	16.a	1.a	$1$	$1$	$1$	$12.293$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(36\)	\(-3490\)	\(55464\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+6^{2}q^{3}-3490q^{5}+55464q^{7}-175851q^{9}+\cdots\)
16.12.a.c	$16$	$12$	16.a	1.a	$1$	$1$	$1$	$12.293$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(516\)	\(-10530\)	\(-49304\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+516q^{3}-10530q^{5}-49304q^{7}+\cdots\)
16.12.a.d	$16$	$12$	16.a	1.a	$1$	$2$	$2$	$12.293$	\(\Q(\sqrt{109}) \)	None	✓	$1$	$0$	\(0\)	\(-56\)	\(7868\)	\(-91056\)		$+$	$+$	$2^{7}$	$\mathrm{SU}(2)$	\(q+(-28-\beta )q^{3}+(3934-12\beta )q^{5}+\cdots\)

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

\( S_{12}^{\mathrm{old}}(\Gamma_0(16)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)