Space of modular forms of level 420, weight 2, and Character 420.bh

• Label: 420.2.bh
• Level: $420$
• Weight: $2$
• Character orbit: 420.bh
• Rep. character: $\chi_{420}(101,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $20$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.bh (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(420, [\chi])\).

	Total	New	Old
Modular forms	216	20	196
Cusp forms	168	20	148
Eisenstein series	48	0	48

Trace form

\( 20 q - 10 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(420, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
420.2.bh.a	$420$	$2$	420.bh	21.g	$6$	$10$	$5$	$3.354$	10.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(-1\)	\(-5\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{5}q^{3}+(-1-\beta _{7})q^{5}+(-1+\beta _{2}+\cdots)q^{7}+\cdots\)
420.2.bh.b	$420$	$2$	420.bh	21.g	$6$	$10$	$5$	$3.354$	10.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(1\)	\(5\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{6}q^{3}+(1+\beta _{7})q^{5}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(420, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(420, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)