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

• Label: 16.16.a
• Level: $16$
• Weight: $16$
• Character orbit: 16.a
• Rep. character: $\chi_{16}(1,\cdot)$
• Character field: $\Q$
• Dimension: $7$
• Newform subspaces: $6$
• Sturm bound: $32$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	16.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(32\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	33	8	25
Cusp forms	27	7	20
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
\(+\)	\(4\)
\(-\)	\(3\)

Trace form

\( 7 q + 2188 q^{3} - 68382 q^{5} + 1587576 q^{7} + 24885763 q^{9} + O(q^{10}) \)

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_0(16))\) 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
16.16.a.a	$16$	$16$	16.a	1.a	$1$	$1$	$1$	$22.831$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-6252\)	\(90510\)	\(-56\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-6252q^{3}+90510q^{5}-56q^{7}+24738597q^{9}+\cdots\)
16.16.a.b	$16$	$16$	16.a	1.a	$1$	$1$	$1$	$22.831$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2700\)	\(-251890\)	\(-1374072\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2700q^{3}-251890q^{5}-1374072q^{7}+\cdots\)
16.16.a.c	$16$	$16$	16.a	1.a	$1$	$1$	$1$	$22.831$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(276\)	\(-132210\)	\(3585736\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+276q^{3}-132210q^{5}+3585736q^{7}+\cdots\)
16.16.a.d	$16$	$16$	16.a	1.a	$1$	$1$	$1$	$22.831$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(3348\)	\(52110\)	\(-2822456\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3348q^{3}+52110q^{5}-2822456q^{7}+\cdots\)
16.16.a.e	$16$	$16$	16.a	1.a	$1$	$1$	$1$	$22.831$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3444\)	\(313358\)	\(2324616\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3444q^{3}+313358q^{5}+2324616q^{7}+\cdots\)
16.16.a.f	$16$	$16$	16.a	1.a	$1$	$2$	$2$	$22.831$	\(\Q(\sqrt{58}) \)	None	✓	$1$	$0$	\(0\)	\(4072\)	\(-140260\)	\(-126192\)		$+$	$+$	$2^{7}\cdot 5$	$\mathrm{SU}(2)$	\(q+(2036+\beta )q^{3}+(-70130-6^{2}\beta )q^{5}+\cdots\)

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

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