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

• Label: 1216.2.h
• Level: $1216$
• Weight: $2$
• Character orbit: 1216.h
• Rep. character: $\chi_{1216}(1215,\cdot)$
• Character field: $\Q$
• Dimension: $38$
• Newform subspaces: $5$
• Sturm bound: $320$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
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	172	42	130
Cusp forms	148	38	110
Eisenstein series	24	4	20

Trace form

\( 38 q + 4 q^{5} + 30 q^{9} + O(q^{10}) \)

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.h.a	$1216$	$2$	1216.h	76.d	$2$	$2$	$2$	$9.710$	\(\Q(\sqrt{-19}) \)	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+q^{5}+\beta q^{7}-3q^{9}-\beta q^{11}+7q^{17}+\cdots\)
1216.2.h.b	$1216$	$2$	1216.h	76.d	$2$	$4$	$4$	$9.710$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(-1+\beta _{2})q^{5}+(2\beta _{1}+\beta _{3})q^{7}-3q^{9}+\cdots\)
1216.2.h.c	$1216$	$2$	1216.h	76.d	$2$	$4$	$4$	$9.710$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{7}+4q^{9}+2\beta _{2}q^{11}+\cdots\)
1216.2.h.d	$1216$	$2$	1216.h	76.d	$2$	$8$	$8$	$9.710$	8.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(1+\beta _{1})q^{5}-\beta _{7}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
1216.2.h.e	$1216$	$2$	1216.h	76.d	$2$	$20$	$20$	$9.710$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{25}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}+\beta _{2}q^{5}+\beta _{14}q^{7}+(1-\beta _{7}+\cdots)q^{9}+\cdots\)

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

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