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

• Label: 2016.2.h
• Level: $2016$
• Weight: $2$
• Character orbit: 2016.h
• Rep. character: $\chi_{2016}(575,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $5$
• Sturm bound: $768$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2016.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(768\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	416	24	392
Cusp forms	352	24	328
Eisenstein series	64	0	64

Trace form

\( 24 q + O(q^{10}) \)

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.h.a	$2016$	$2$	2016.h	12.b	$2$	$4$	$4$	$16.098$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}-\zeta_{8}^{3}q^{11}-2q^{13}+\cdots\)
2016.2.h.b	$2016$	$2$	2016.h	12.b	$2$	$4$	$4$	$16.098$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}q^{7}+3\zeta_{8}^{3}q^{11}-2q^{13}+2\zeta_{8}^{2}q^{17}+\cdots\)
2016.2.h.c	$2016$	$2$	2016.h	12.b	$2$	$4$	$4$	$16.098$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}+2\zeta_{8}^{3}q^{11}-5\zeta_{8}^{2}q^{17}+\cdots\)
2016.2.h.d	$2016$	$2$	2016.h	12.b	$2$	$4$	$4$	$16.098$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}-\zeta_{8}^{3}q^{11}+6q^{13}+\cdots\)
2016.2.h.e	$2016$	$2$	2016.h	12.b	$2$	$8$	$8$	$16.098$	8.0.5473632256.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{5}+\beta _{6})q^{5}+\beta _{1}q^{7}+(\beta _{4}+2\beta _{7})q^{11}+\cdots\)

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

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