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

• Label: 2016.2.bs
• Level: $2016$
• Weight: $2$
• Character orbit: 2016.bs
• Rep. character: $\chi_{2016}(271,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $76$
• Newform subspaces: $3$
• 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.bs (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(768\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	832	84	748
Cusp forms	704	76	628
Eisenstein series	128	8	120

Trace form

\( 76 q + 2 q^{11} + 6 q^{17} + 6 q^{19} - 32 q^{25} - 6 q^{35} + 4 q^{49} - 54 q^{59} + 12 q^{65} - 14 q^{67} - 30 q^{73} - 18 q^{89} + 24 q^{91}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2016.2.bs.a	$2016$	$2$	2016.bs	56.m	$6$	$12$	$6$	$16.098$	12.0.\(\cdots\).2	None					56.2.m.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{7}q^{5}+(\beta _{5}+\beta _{10}-\beta _{11})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots\)
2016.2.bs.b	$2016$	$2$	2016.bs	56.m	$6$	$32$	$16$	$16.098$		None					504.2.bk.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
2016.2.bs.c	$2016$	$2$	2016.bs	56.m	$6$	$32$	$16$	$16.098$		None					168.2.t.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

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