Space of modular forms of level 630, weight 2, and Character 630.bv

• Label: 630.2.bv
• Level: $630$
• Weight: $2$
• Character orbit: 630.bv
• Rep. character: $\chi_{630}(73,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $80$
• Newform subspaces: $4$
• Sturm bound: $288$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bv (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(288\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(630, [\chi])\).

	Total	New	Old
Modular forms	640	80	560
Cusp forms	512	80	432
Eisenstein series	128	0	128

Trace form

\( 80 q - 12 q^{5} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(630, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
630.2.bv.a	$630$	$2$	630.bv	35.k	$12$	$16$	$4$	$5.031$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-12\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\beta _{15}q^{2}+(\beta _{5}-\beta _{13})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
630.2.bv.b	$630$	$2$	630.bv	35.k	$12$	$16$	$4$	$5.031$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-12\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q-\beta _{6}q^{2}+(-\beta _{5}+\beta _{13})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
630.2.bv.c	$630$	$2$	630.bv	35.k	$12$	$16$	$4$	$5.031$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(12\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\beta _{13}q^{2}+(\beta _{11}-\beta _{14})q^{4}+(\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots\)
630.2.bv.d	$630$	$2$	630.bv	35.k	$12$	$32$	$8$	$5.031$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(630, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(630, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)