Space of modular forms of level 1216, weight 2, and Character 1216.s

• Label: 1216.2.s
• Level: $1216$
• Weight: $2$
• Character orbit: 1216.s
• Rep. character: $\chi_{1216}(31,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $9$
• Sturm bound: $320$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(320\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1216, [\chi])\).

	Total	New	Old
Modular forms	344	80	264
Cusp forms	296	80	216
Eisenstein series	48	0	48

Trace form

\( 80 q + 40 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1216, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1216.2.s.a	$1216$	$2$	1216.s	152.o	$6$	$4$	$2$	$9.710$	\(\Q(\zeta_{12})\)	None		$2$	$1$	\(0\)	\(-6\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\zeta_{12}^{2})q^{3}+(-2+\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
1216.2.s.b	$1216$	$2$	1216.s	152.o	$6$	$4$	$2$	$9.710$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(-6\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\zeta_{12}^{2})q^{3}+(2-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
1216.2.s.c	$1216$	$2$	1216.s	152.o	$6$	$4$	$2$	$9.710$	\(\Q(\zeta_{12})\)	None		$4$	$1$	\(0\)	\(0\)	\(-12\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{3}+(-2-2\zeta_{12}^{2})q^{5}+2\zeta_{12}^{3}q^{7}+\cdots\)
1216.2.s.d	$1216$	$2$	1216.s	152.o	$6$	$4$	$2$	$9.710$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{3}+(2+2\zeta_{12}^{2})q^{5}-2\zeta_{12}^{3}q^{7}+\cdots\)
1216.2.s.e	$1216$	$2$	1216.s	152.o	$6$	$4$	$2$	$9.710$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(6\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-\zeta_{12}^{2})q^{3}+(-2-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
1216.2.s.f	$1216$	$2$	1216.s	152.o	$6$	$4$	$2$	$9.710$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(6\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{12}^{2})q^{3}+(1-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
1216.2.s.g	$1216$	$2$	1216.s	152.o	$6$	$12$	$6$	$9.710$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-18\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{9}q^{3}+(-1-\beta _{5})q^{5}+(-\beta _{6}-\beta _{8}+\cdots)q^{7}+\cdots\)
1216.2.s.h	$1216$	$2$	1216.s	152.o	$6$	$12$	$6$	$9.710$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(18\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{9}q^{3}+(1+\beta _{5})q^{5}+(\beta _{6}+\beta _{8})q^{7}+\cdots\)
1216.2.s.i	$1216$	$2$	1216.s	152.o	$6$	$32$	$16$	$9.710$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1216, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1216, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(608, [\chi])\)\(^{\oplus 2}\)