Space of modular forms of level 840, weight 2, and Character 840.cp

• Label: 840.2.cp
• Level: $840$
• Weight: $2$
• Character orbit: 840.cp
• Rep. character: $\chi_{840}(521,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $64$
• Newform subspaces: $2$
• Sturm bound: $384$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.cp (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(384\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(840, [\chi])\).

	Total	New	Old
Modular forms	416	64	352
Cusp forms	352	64	288
Eisenstein series	64	0	64

Trace form

\( 64 q - 4 q^{7} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(840, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
840.2.cp.a	$840$	$2$	840.cp	21.g	$6$	$32$	$16$	$6.707$		None		$2$	$0$	\(0\)	\(0\)	\(-16\)	\(-2\)		$\mathrm{SU}(2)[C_{6}]$
840.2.cp.b	$840$	$2$	840.cp	21.g	$6$	$32$	$16$	$6.707$		None		$2$	$0$	\(0\)	\(0\)	\(16\)	\(-2\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(840, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 3}\)