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

• Label: 784.2.bp
• Level: $784$
• Weight: $2$
• Character orbit: 784.bp
• Rep. character: $\chi_{784}(47,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $336$
• Newform subspaces: $3$
• Sturm bound: $224$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.bp (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 196 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(224\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	1416	336	1080
Cusp forms	1272	336	936
Eisenstein series	144	0	144

Trace form

\( 336 q + 28 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
784.2.bp.a	$784$	$2$	784.bp	196.p	$42$	$108$	$9$	$6.260$		None		$2$	$0$	\(0\)	\(-1\)	\(-3\)	\(4\)		$\mathrm{SU}(2)[C_{42}]$
784.2.bp.b	$784$	$2$	784.bp	196.p	$42$	$108$	$9$	$6.260$		None		$2$	$0$	\(0\)	\(1\)	\(-3\)	\(-4\)		$\mathrm{SU}(2)[C_{42}]$
784.2.bp.c	$784$	$2$	784.bp	196.p	$42$	$120$	$10$	$6.260$		None		$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$\mathrm{SU}(2)[C_{42}]$

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

\( S_{2}^{\mathrm{old}}(784, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 2}\)