Space of modular forms of level 16, weight 3, and Character 16.c

• Label: 16.3.c
• Level: $16$
• Weight: $3$
• Character orbit: 16.c
• Rep. character: $\chi_{16}(15,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $6$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
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:			\(6\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(16, [\chi])\).

	Total	New	Old
Modular forms	7	1	6
Cusp forms	1	1	0
Eisenstein series	6	0	6

Trace form

\( q - 6 q^{5} + 9 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(16, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
16.3.c.a	$16$	$3$	16.c	4.b	$2$	$1$	$1$	$0.436$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-6q^{5}+9q^{9}+10q^{13}-30q^{17}+\cdots\)