Space of modular forms of level 1428, weight 2, and Character 1428.bd

• Label: 1428.2.bd
• Level: $1428$
• Weight: $2$
• Character orbit: 1428.bd
• Rep. character: $\chi_{1428}(341,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $84$
• Newform subspaces: $2$
• Sturm bound: $576$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 1428 = 2^{2} \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1428.bd (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(576\)
Trace bound:			\(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1428, [\chi])\).

	Total	New	Old
Modular forms	600	84	516
Cusp forms	552	84	468
Eisenstein series	48	0	48

Trace form

\( 84 q - 6 q^{7} + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1428, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1428.2.bd.a	$1428$	$2$	1428.bd	21.g	$6$	$42$	$21$	$11.403$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-3\)		$\mathrm{SU}(2)[C_{6}]$
1428.2.bd.b	$1428$	$2$	1428.bd	21.g	$6$	$42$	$21$	$11.403$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-3\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1428, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1428, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)