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

• Label: 2016.2.s
• Level: $2016$
• Weight: $2$
• Character orbit: 2016.s
• Rep. character: $\chi_{2016}(289,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $80$
• Newform subspaces: $24$
• Sturm bound: $768$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2016.s (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 24 \)
Sturm bound:			\(768\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	832	80	752
Cusp forms	704	80	624
Eisenstein series	128	0	128

Trace form

\( 80 q + O(q^{10}) \)

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.s.a	$2016$	$2$	2016.s	7.c	$3$	$2$	$1$	$16.098$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-4\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
2016.2.s.b	$2016$	$2$	2016.s	7.c	$3$	$2$	$1$	$16.098$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-4\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
2016.2.s.c	$2016$	$2$	2016.s	7.c	$3$	$2$	$1$	$16.098$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(0\)	\(-3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-3\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots\)
2016.2.s.d	$2016$	$2$	2016.s	7.c	$3$	$2$	$1$	$16.098$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(5-5\zeta_{6})q^{11}+\cdots\)
2016.2.s.e	$2016$	$2$	2016.s	7.c	$3$	$2$	$1$	$16.098$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2-\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2016.2.s.f	$2016$	$2$	2016.s	7.c	$3$	$2$	$1$	$16.098$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+3\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2016.2.s.g	$2016$	$2$	2016.s	7.c	$3$	$2$	$1$	$16.098$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-3\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+5q^{13}+\cdots\)
2016.2.s.h	$2016$	$2$	2016.s	7.c	$3$	$2$	$1$	$16.098$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2+\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+q^{13}+\cdots\)
2016.2.s.i	$2016$	$2$	2016.s	7.c	$3$	$2$	$1$	$16.098$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots\)
2016.2.s.j	$2016$	$2$	2016.s	7.c	$3$	$2$	$1$	$16.098$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+(1-\zeta_{6})q^{11}+\cdots\)
2016.2.s.k	$2016$	$2$	2016.s	7.c	$3$	$2$	$1$	$16.098$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+3\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+(1-\zeta_{6})q^{11}+\cdots\)
2016.2.s.l	$2016$	$2$	2016.s	7.c	$3$	$2$	$1$	$16.098$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+3\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+(5-5\zeta_{6})q^{11}+\cdots\)
2016.2.s.m	$2016$	$2$	2016.s	7.c	$3$	$2$	$1$	$16.098$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots\)
2016.2.s.n	$2016$	$2$	2016.s	7.c	$3$	$2$	$1$	$16.098$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots\)
2016.2.s.o	$2016$	$2$	2016.s	7.c	$3$	$4$	$2$	$16.098$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$4$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+3\beta _{2}q^{5}+\beta _{3}q^{7}-\beta _{1}q^{11}-4q^{13}+\cdots\)
2016.2.s.p	$2016$	$2$	2016.s	7.c	$3$	$4$	$2$	$16.098$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\beta _{2}q^{5}+\beta _{3}q^{7}-3q^{13}+(2-2\beta _{2}+\cdots)q^{17}+\cdots\)
2016.2.s.q	$2016$	$2$	2016.s	7.c	$3$	$4$	$2$	$16.098$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+2\beta _{1}+\beta _{2})q^{5}+(-1-2\beta _{1}-\beta _{3})q^{7}+\cdots\)
2016.2.s.r	$2016$	$2$	2016.s	7.c	$3$	$4$	$2$	$16.098$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{12}^{2})q^{5}+(2\zeta_{12}-3\zeta_{12}^{3})q^{7}+\cdots\)
2016.2.s.s	$2016$	$2$	2016.s	7.c	$3$	$4$	$2$	$16.098$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+2\beta _{1}+\beta _{2})q^{5}+(1+2\beta _{1}+\beta _{3})q^{7}+\cdots\)
2016.2.s.t	$2016$	$2$	2016.s	7.c	$3$	$4$	$2$	$16.098$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\beta _{2}q^{5}+\beta _{3}q^{7}-3q^{13}+(-2+2\beta _{2}+\cdots)q^{17}+\cdots\)
2016.2.s.u	$2016$	$2$	2016.s	7.c	$3$	$6$	$3$	$16.098$	6.0.1156923.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-3\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{4}q^{5}+(-1+\beta _{3}-\beta _{4})q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
2016.2.s.v	$2016$	$2$	2016.s	7.c	$3$	$6$	$3$	$16.098$	6.0.1156923.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(3\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{4}q^{5}+(1-\beta _{3}+\beta _{4})q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
2016.2.s.w	$2016$	$2$	2016.s	7.c	$3$	$8$	$4$	$16.098$	8.0.1445900625.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{7}q^{5}+(\beta _{1}-\beta _{4}+\beta _{5})q^{7}+\beta _{6}q^{11}+\cdots\)
2016.2.s.x	$2016$	$2$	2016.s	7.c	$3$	$8$	$4$	$16.098$	8.0.1445900625.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{7}q^{5}+(-\beta _{1}+\beta _{4}-\beta _{5})q^{7}-\beta _{6}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2016, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)