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

• Label: 630.2.u
• Level: $630$
• Weight: $2$
• Character orbit: 630.u
• Rep. character: $\chi_{630}(109,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $40$
• Newform subspaces: $6$
• 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.u (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(288\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(11\), \(37\)

Dimensions

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

	Total	New	Old
Modular forms	320	40	280
Cusp forms	256	40	216
Eisenstein series	64	0	64

Trace form

\( 40 q + 20 q^{4} + 2 q^{5} + O(q^{10}) \)

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.u.a	$630$	$2$	630.u	35.j	$6$	$4$	$2$	$5.031$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-2-\zeta_{12}+\cdots)q^{5}+\cdots\)
630.2.u.b	$630$	$2$	630.u	35.j	$6$	$4$	$2$	$5.031$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(1+2\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
630.2.u.c	$630$	$2$	630.u	35.j	$6$	$4$	$2$	$5.031$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(2-\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
630.2.u.d	$630$	$2$	630.u	35.j	$6$	$8$	$4$	$5.031$	8.0.2702336256.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{4}q^{2}-\beta _{2}q^{4}+\beta _{1}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
630.2.u.e	$630$	$2$	630.u	35.j	$6$	$8$	$4$	$5.031$	8.0.2702336256.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{4}-\beta _{6})q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
630.2.u.f	$630$	$2$	630.u	35.j	$6$	$12$	$6$	$5.031$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{2}+\beta _{8})q^{2}-\beta _{10}q^{4}+(\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\)

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

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