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

• Label: 630.2.t
• Level: $630$
• Weight: $2$
• Character orbit: 630.t
• Rep. character: $\chi_{630}(311,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $64$
• Newform subspaces: $3$
• Sturm bound: $288$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(288\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(11\)

Dimensions

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

	Total	New	Old
Modular forms	304	64	240
Cusp forms	272	64	208
Eisenstein series	32	0	32

Trace form

64 * q + 32 * q^4 - 4 * q^7 + 6 * q^9 + 12 * q^13 + 6 * q^14 + 4 * q^15 - 32 * q^16 - 8 * q^18 + 22 * q^21 + 6 * q^24 + 64 * q^25 + 24 * q^26 + 36 * q^27 + 4 * q^28 - 6 * q^29 + 4 * q^30 - 12 * q^31 + 24 * q^33 + 4 * q^37 + 36 * q^39 - 6 * q^41 - 32 * q^42 + 4 * q^43 - 12 * q^44 + 6 * q^45 - 6 * q^46 + 36 * q^47 - 8 * q^49 + 8 * q^51 - 72 * q^53 - 36 * q^54 - 12 * q^57 - 60 * q^59 + 8 * q^60 + 102 * q^61 - 80 * q^63 - 64 * q^64 - 12 * q^65 - 48 * q^66 - 28 * q^67 - 6 * q^70 + 8 * q^72 - 12 * q^77 + 16 * q^78 + 8 * q^79 - 38 * q^81 + 14 * q^84 + 12 * q^85 + 96 * q^87 + 6 * q^89 + 24 * q^91 - 36 * q^92 + 8 * q^93 + 6 * q^96 + 12 * q^97 - 48 * q^98 - 48 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
630.2.t.a	$630$	$2$	630.t	63.s	$6$	$4$	$2$	$5.031$	\(\Q(\zeta_{12})\)	None		✓			630.2.t.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}q^{2}+(-\zeta_{12}+2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
630.2.t.b	$630$	$2$	630.t	63.s	$6$	$28$	$14$	$5.031$		None		✓			630.2.t.b	$2$	$0$	\(0\)	\(-2\)	\(-28\)	\(-4\)		$\mathrm{SU}(2)[C_{6}]$
630.2.t.c	$630$	$2$	630.t	63.s	$6$	$32$	$16$	$5.031$		None		✓	✓		630.2.t.c	$2$	$0$	\(0\)	\(2\)	\(32\)	\(-2\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(630, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)