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

• Label: 630.2.d
• Level: $630$
• Weight: $2$
• Character orbit: 630.d
• Rep. character: $\chi_{630}(629,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $288$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(288\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(11\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	160	16	144
Cusp forms	128	16	112
Eisenstein series	32	0	32

Trace form

\( 16 q + 16 q^{4} + O(q^{10}) \)

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.d.a	$630$	$2$	630.d	105.g	$2$	$4$	$4$	$5.031$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
630.2.d.b	$630$	$2$	630.d	105.g	$2$	$4$	$4$	$5.031$	\(\Q(\sqrt{-2}, \sqrt{5})\)	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots\)
630.2.d.c	$630$	$2$	630.d	105.g	$2$	$4$	$4$	$5.031$	\(\Q(\sqrt{-2}, \sqrt{5})\)	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots\)
630.2.d.d	$630$	$2$	630.d	105.g	$2$	$4$	$4$	$5.031$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)

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

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