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

• Label: 1216.2.n
• Level: $1216$
• Weight: $2$
• Character orbit: 1216.n
• Rep. character: $\chi_{1216}(255,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $76$
• Newform subspaces: $7$
• Sturm bound: $320$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(320\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	344	84	260
Cusp forms	296	76	220
Eisenstein series	48	8	40

Trace form

\( 76 q + 2 q^{5} - 36 q^{9} + O(q^{10}) \)

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.n.a	$1216$	$2$	1216.n	76.f	$6$	$2$	$1$	$9.710$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{6})q^{3}+(3-3\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
1216.2.n.b	$1216$	$2$	1216.n	76.f	$6$	$2$	$1$	$9.710$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{3}+(3-3\zeta_{6})q^{5}+(2-4\zeta_{6})q^{7}+\cdots\)
1216.2.n.c	$1216$	$2$	1216.n	76.f	$6$	$4$	$2$	$9.710$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{5}+2\zeta_{12}^{3}q^{7}+\cdots\)
1216.2.n.d	$1216$	$2$	1216.n	76.f	$6$	$6$	$3$	$9.710$	6.0.31726512.1	None		$2$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{3})q^{5}+(\beta _{4}+\cdots)q^{7}+\cdots\)
1216.2.n.e	$1216$	$2$	1216.n	76.f	$6$	$6$	$3$	$9.710$	6.0.31726512.1	None		$2$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{3})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)
1216.2.n.f	$1216$	$2$	1216.n	76.f	$6$	$16$	$8$	$9.710$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{7}q^{3}+(-\beta _{5}+\beta _{10})q^{5}-\beta _{9}q^{7}+\cdots\)
1216.2.n.g	$1216$	$2$	1216.n	76.f	$6$	$40$	$20$	$9.710$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(1216, [\chi]) \cong \)