Space of modular forms of level 16, weight 7, and Character 16.c

• Label: 16.7.c
• Level: $16$
• Weight: $7$
• Character orbit: 16.c
• Rep. character: $\chi_{16}(15,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $14$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	16.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(14\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(16, [\chi])\).

	Total	New	Old
Modular forms	15	3	12
Cusp forms	9	3	6
Eisenstein series	6	0	6

Trace form

\( 3 q - 66 q^{5} + 651 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(16, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
16.7.c.a	$16$	$7$	16.c	4.b	$2$	$1$	$1$	$3.681$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(234\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+234q^{5}+3^{6}q^{9}-4070q^{13}-990q^{17}+\cdots\)
16.7.c.b	$16$	$7$	16.c	4.b	$2$	$2$	$2$	$3.681$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-300\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{3}-150q^{5}-22\zeta_{6}q^{7}-39q^{9}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(16, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(16, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 2}\)