Space of modular forms of level 2016, weight 3, and Character 2016.l

• Label: 2016.3.l
• Level: $2016$
• Weight: $3$
• Character orbit: 2016.l
• Rep. character: $\chi_{2016}(433,\cdot)$
• Character field: $\Q$
• Dimension: $78$
• Newform subspaces: $8$
• Sturm bound: $1152$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2016.l (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(1152\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2016, [\chi])\).

	Total	New	Old
Modular forms	800	82	718
Cusp forms	736	78	658
Eisenstein series	64	4	60

Trace form

\( 78 q + 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2016, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2016.3.l.a	$2016$	$3$	2016.l	56.h	$2$	$2$	$2$	$54.932$	\(\Q(\sqrt{7}) \)	\(\Q(\sqrt{-14}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-14\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{5}-7q^{7}-\beta q^{13}+7\beta q^{19}-10q^{23}+\cdots\)
2016.3.l.b	$2016$	$3$	2016.l	56.h	$2$	$2$	$2$	$54.932$	\(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-14\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-7q^{7}-\beta q^{11}+18q^{23}-5^{2}q^{25}+\cdots\)
2016.3.l.c	$2016$	$3$	2016.l	56.h	$2$	$2$	$2$	$54.932$	\(\Q(\sqrt{2}) \)	\(\Q(\sqrt{-14}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(14\)	$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{5}+7q^{7}+3\beta q^{13}+\beta q^{19}-10q^{23}+\cdots\)
2016.3.l.d	$2016$	$3$	2016.l	56.h	$2$	$4$	$4$	$54.932$	\(\Q(i, \sqrt{6})\)	\(\Q(\sqrt{-6}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(20\)	$2^{5}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{3}q^{5}+(5+\beta _{2})q^{7}-5\beta _{1}q^{11}+71q^{25}+\cdots\)
2016.3.l.e	$2016$	$3$	2016.l	56.h	$2$	$4$	$4$	$54.932$	\(\Q(i, \sqrt{7})\)	\(\Q(\sqrt{-7}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(28\)	$2^{10}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+7q^{7}+\beta _{1}q^{11}-\beta _{2}q^{23}-5^{2}q^{25}+\cdots\)
2016.3.l.f	$2016$	$3$	2016.l	56.h	$2$	$8$	$8$	$54.932$	8.0.\(\cdots\).51	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{2}+\beta _{3})q^{5}+(2+\beta _{4})q^{7}+(\beta _{5}+\cdots)q^{11}+\cdots\)
2016.3.l.g	$2016$	$3$	2016.l	56.h	$2$	$24$	$24$	$54.932$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(-48\)		$\mathrm{SU}(2)[C_{2}]$
2016.3.l.h	$2016$	$3$	2016.l	56.h	$2$	$32$	$32$	$54.932$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(2016, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2016, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)