Space of modular forms of level 16, weight 11, and Character 16.c

• Label: 16.11.c
• Level: $16$
• Weight: $11$
• Character orbit: 16.c
• Rep. character: $\chi_{16}(15,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $2$
• Sturm bound: $22$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 11 \)
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:			\(22\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(16, [\chi])\).

	Total	New	Old
Modular forms	23	5	18
Cusp forms	17	5	12
Eisenstein series	6	0	6

Trace form

\( 5 q + 4674 q^{5} - 130227 q^{9} + O(q^{10}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(16, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
16.11.c.a	$16$	$11$	16.c	4.b	$2$	$1$	$1$	$10.166$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(474\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+474q^{5}+3^{10}q^{9}+683050q^{13}+\cdots\)
16.11.c.b	$16$	$11$	16.c	4.b	$2$	$4$	$4$	$10.166$	\(\Q(\sqrt{-3}, \sqrt{505})\)	None		$2$	$0$	\(0\)	\(0\)	\(4200\)	\(0\)	$2^{25}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(1050+\beta _{2})q^{5}+(-12\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(16, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(16, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 2}\)