Space of modular forms of level 2016, weight 2, and Character 2016.p

• Label: 2016.2.p
• Level: $2016$
• Weight: $2$
• Character orbit: 2016.p
• Rep. character: $\chi_{2016}(559,\cdot)$
• Character field: $\Q$
• Dimension: $38$
• Newform subspaces: $7$
• Sturm bound: $768$
• Trace bound: $43$

Defining parameters

Level:	\( N \)	\(=\)	\( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2016.p (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(768\)
Trace bound:			\(43\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2016, [\chi])\).

	Total	New	Old
Modular forms	416	42	374
Cusp forms	352	38	314
Eisenstein series	64	4	60

Trace form

\( 38 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2016, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2016.2.p.a	$2016$	$2$	2016.p	56.e	$2$	$2$	$2$	$16.098$	\(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{-7}) \)		$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{7}-4q^{11}-2\beta q^{23}-5q^{25}+\cdots\)
2016.2.p.b	$2016$	$2$	2016.p	56.e	$2$	$4$	$4$	$16.098$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\zeta_{12}q^{5}+(\zeta_{12}-\zeta_{12}^{3})q^{7}-2q^{11}+\cdots\)
2016.2.p.c	$2016$	$2$	2016.p	56.e	$2$	$4$	$4$	$16.098$	\(\Q(\sqrt{-2}, \sqrt{7})\)	\(\Q(\sqrt{-42}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{3}q^{7}-2\beta _{3}q^{13}+\beta _{2}q^{17}+\beta _{1}q^{23}+\cdots\)
2016.2.p.d	$2016$	$2$	2016.p	56.e	$2$	$4$	$4$	$16.098$	\(\Q(i, \sqrt{7})\)	\(\Q(\sqrt{-7}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{3}q^{7}-\beta _{2}q^{11}+4\beta _{1}q^{23}-5q^{25}+\cdots\)
2016.2.p.e	$2016$	$2$	2016.p	56.e	$2$	$4$	$4$	$16.098$	\(\Q(i, \sqrt{6})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}+(\beta _{1}-\beta _{3})q^{7}+2q^{11}+\beta _{3}q^{13}+\cdots\)
2016.2.p.f	$2016$	$2$	2016.p	56.e	$2$	$4$	$4$	$16.098$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\zeta_{12}q^{5}+(\zeta_{12}-\zeta_{12}^{3})q^{7}+2q^{11}+\cdots\)
2016.2.p.g	$2016$	$2$	2016.p	56.e	$2$	$16$	$16$	$16.098$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{21}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}+\beta _{6}q^{7}-\beta _{4}q^{11}+(\beta _{6}-\beta _{8}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2016, [\chi])\) into lower level spaces

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