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

• Label: 2016.2.c
• Level: $2016$
• Weight: $2$
• Character orbit: 2016.c
• Rep. character: $\chi_{2016}(1009,\cdot)$
• Character field: $\Q$
• Dimension: $30$
• Newform subspaces: $6$
• Sturm bound: $768$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2016.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(768\)
Trace bound:			\(17\)
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	30	386
Cusp forms	352	30	322
Eisenstein series	64	0	64

Trace form

\( 30 q + 2 q^{7} + O(q^{10}) \)

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.c.a	$2016$	$2$	2016.c	8.b	$2$	$2$	$2$	$16.098$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-q^{7}+2\beta q^{11}-3\beta q^{13}+6q^{17}+\cdots\)
2016.2.c.b	$2016$	$2$	2016.c	8.b	$2$	$4$	$4$	$16.098$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}-q^{7}+\beta _{1}q^{11}+\beta _{2}q^{17}+\cdots\)
2016.2.c.c	$2016$	$2$	2016.c	8.b	$2$	$4$	$4$	$16.098$	4.0.2312.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}+q^{7}+(-\beta _{1}+\beta _{2})q^{11}+\beta _{2}q^{13}+\cdots\)
2016.2.c.d	$2016$	$2$	2016.c	8.b	$2$	$4$	$4$	$16.098$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{3}q^{5}+q^{7}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{11}+\cdots\)
2016.2.c.e	$2016$	$2$	2016.c	8.b	$2$	$8$	$8$	$16.098$	8.0.386672896.3	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}-q^{7}+\beta _{6}q^{11}-\beta _{4}q^{13}+\cdots\)
2016.2.c.f	$2016$	$2$	2016.c	8.b	$2$	$8$	$8$	$16.098$	8.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+q^{7}-\beta _{2}q^{11}-\beta _{4}q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2016, [\chi]) \cong \)