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

• Label: 420.2.w
• Level: $420$
• Weight: $2$
• Character orbit: 420.w
• Rep. character: $\chi_{420}(83,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $176$
• Newform subspaces: $3$
• Sturm bound: $192$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.w (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 420 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(192\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(11\)

Dimensions

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

	Total	New	Old
Modular forms	208	208	0
Cusp forms	176	176	0
Eisenstein series	32	32	0

Trace form

\( 176 q + O(q^{10}) \)

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.w.a	$420$	$2$	420.w	420.w	$4$	$8$	$4$	$3.354$	8.0.\(\cdots\).1	\(\Q(\sqrt{-21}) \)		$8$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{4}]$	\(q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+\cdots\)
420.2.w.b	$420$	$2$	420.w	420.w	$4$	$8$	$4$	$3.354$	8.0.\(\cdots\).1	\(\Q(\sqrt{-21}) \)		$8$	$0$	\(8\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{4}]$	\(q+(1-\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
420.2.w.c	$420$	$2$	420.w	420.w	$4$	$160$	$80$	$3.354$		None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$