Space of modular forms of level 16, weight 5, and Character 16.c

• Label: 16.5.c
• Level: $16$
• Weight: $5$
• Character orbit: 16.c
• Rep. character: $\chi_{16}(15,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $10$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	16.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(10\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(16, [\chi])\).

	Total	New	Old
Modular forms	11	2	9
Cusp forms	5	2	3
Eisenstein series	6	0	6

Trace form

\( 2 q + 36 q^{5} - 222 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(16, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
16.5.c.a	$16$	$5$	16.c	4.b	$2$	$2$	$2$	$1.654$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(36\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{3}+18q^{5}+2\zeta_{6}q^{7}-111q^{9}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(16, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(16, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 2}\)