Space of modular forms of level 1456, weight 2, and Character 1456.v

• Label: 1456.2.v
• Level: $1456$
• Weight: $2$
• Character orbit: 1456.v
• Rep. character: $\chi_{1456}(239,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $84$
• Newform subspaces: $3$
• Sturm bound: $448$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.v (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 52 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(448\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1456, [\chi])\).

	Total	New	Old
Modular forms	472	84	388
Cusp forms	424	84	340
Eisenstein series	48	0	48

Trace form

\( 84 q - 12 q^{5} - 84 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1456, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1456.2.v.a	$1456$	$2$	1456.v	52.f	$4$	$8$	$4$	$11.626$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\zeta_{24}-\zeta_{24}^{4}-\zeta_{24}^{5})q^{3}+(1+\zeta_{24}^{3}+\cdots)q^{5}+\cdots\)
1456.2.v.b	$1456$	$2$	1456.v	52.f	$4$	$28$	$14$	$11.626$		None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
1456.2.v.c	$1456$	$2$	1456.v	52.f	$4$	$48$	$24$	$11.626$		None		$4$	$0$	\(0\)	\(0\)	\(-16\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1456, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1456, [\chi]) \cong \)