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

• Label: 1216.2.t
• Level: $1216$
• Weight: $2$
• Character orbit: 1216.t
• Rep. character: $\chi_{1216}(353,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $5$
• Sturm bound: $320$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(320\)
Trace bound:			\(9\)
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.t.a	$1216$	$2$	1216.t	152.p	$6$	$8$	$4$	$9.710$	\(\Q(\zeta_{24})\)	\(\Q(\sqrt{-2}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{U}(1)[D_{6}]$	\(q+(\zeta_{24}-\zeta_{24}^{3})q^{3}+(4\zeta_{24}^{2}-\zeta_{24}^{7})q^{9}+\cdots\)
1216.2.t.b	$1216$	$2$	1216.t	152.p	$6$	$8$	$4$	$9.710$	8.0.3317760000.2	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(3\beta _{1}-3\beta _{3})q^{3}+\beta _{5}q^{5}-\beta _{7}q^{7}+\cdots\)
1216.2.t.c	$1216$	$2$	1216.t	152.p	$6$	$16$	$8$	$9.710$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{8}q^{3}-\beta _{7}q^{5}-\beta _{11}q^{7}+2\beta _{1}q^{9}+\cdots\)
1216.2.t.d	$1216$	$2$	1216.t	152.p	$6$	$24$	$12$	$9.710$		None		$4$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
1216.2.t.e	$1216$	$2$	1216.t	152.p	$6$	$24$	$12$	$9.710$		None		$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

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