Space of modular forms of level 784, weight 2, and Character 784.j

• Label: 784.2.j
• Level: $784$
• Weight: $2$
• Character orbit: 784.j
• Rep. character: $\chi_{784}(195,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $152$
• Newform subspaces: $2$
• Sturm bound: $224$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 112 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(224\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(784, [\chi])\).

	Total	New	Old
Modular forms	240	168	72
Cusp forms	208	152	56
Eisenstein series	32	16	16

Trace form

\( 152 q + 4 q^{2} + 4 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(784, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
784.2.j.a	$784$	$2$	784.j	112.j	$4$	$56$	$28$	$6.260$		None			112.2.v.a	$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
784.2.j.b	$784$	$2$	784.j	112.j	$4$	$96$	$48$	$6.260$		None		✓	784.2.j.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(784, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(784, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)