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

• Label: 1216.2.c
• Level: $1216$
• Weight: $2$
• Character orbit: 1216.c
• Rep. character: $\chi_{1216}(609,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $9$
• Sturm bound: $320$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(320\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	172	36	136
Cusp forms	148	36	112
Eisenstein series	24	0	24

Trace form

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

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.c.a	$1216$	$2$	1216.c	8.b	$2$	$2$	$2$	$9.710$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-3q^{7}+2q^{9}-3iq^{13}+3q^{17}+\cdots\)
1216.2.c.b	$1216$	$2$	1216.c	8.b	$2$	$2$	$2$	$9.710$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}-4iq^{5}-q^{7}-6q^{9}+5iq^{13}+\cdots\)
1216.2.c.c	$1216$	$2$	1216.c	8.b	$2$	$2$	$2$	$9.710$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}+4iq^{5}+q^{7}-6q^{9}-5iq^{13}+\cdots\)
1216.2.c.d	$1216$	$2$	1216.c	8.b	$2$	$2$	$2$	$9.710$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+3q^{7}+2q^{9}+3iq^{13}+3q^{17}+\cdots\)
1216.2.c.e	$1216$	$2$	1216.c	8.b	$2$	$4$	$4$	$9.710$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)
1216.2.c.f	$1216$	$2$	1216.c	8.b	$2$	$4$	$4$	$9.710$	\(\Q(i, \sqrt{11})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{1}q^{3}-\beta _{3}q^{5}+\beta _{2}q^{7}-q^{9}-5\beta _{1}q^{11}+\cdots\)
1216.2.c.g	$1216$	$2$	1216.c	8.b	$2$	$4$	$4$	$9.710$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{3}+2\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+\cdots\)
1216.2.c.h	$1216$	$2$	1216.c	8.b	$2$	$8$	$8$	$9.710$	8.0.303595776.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+\beta _{1}q^{5}+(-\beta _{3}+2\beta _{6})q^{7}+\cdots\)
1216.2.c.i	$1216$	$2$	1216.c	8.b	$2$	$8$	$8$	$9.710$	8.0.2702336256.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}+\beta _{5}q^{7}+3q^{9}+(-\beta _{2}-2\beta _{4}+\cdots)q^{11}+\cdots\)

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

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