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

• Label: 420.2.bv
• Level: $420$
• Weight: $2$
• Character orbit: 420.bv
• Rep. character: $\chi_{420}(53,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $64$
• Newform subspaces: $3$
• 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.bv (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(192\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(11\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	432	64	368
Cusp forms	336	64	272
Eisenstein series	96	0	96

Trace form

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

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.bv.a	$420$	$2$	420.bv	105.x	$12$	$8$	$2$	$3.354$	8.0.303595776.1	None		$4$	$0$	\(0\)	\(0\)	\(-8\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\beta _{1}q^{3}+(-2-\beta _{3}-2\beta _{4})q^{5}+(1+\cdots)q^{7}+\cdots\)
420.2.bv.b	$420$	$2$	420.bv	105.x	$12$	$8$	$2$	$3.354$	8.0.303595776.1	None		$4$	$0$	\(0\)	\(2\)	\(8\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1-\beta _{2}+\beta _{4}+\beta _{6})q^{3}+(-2\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\)
420.2.bv.c	$420$	$2$	420.bv	105.x	$12$	$48$	$12$	$3.354$		None		$8$	$0$	\(0\)	\(-2\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{12}]$

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

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