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

• Label: 630.2.g
• Level: $630$
• Weight: $2$
• Character orbit: 630.g
• Rep. character: $\chi_{630}(379,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $7$
• Sturm bound: $288$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(288\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(11\), \(29\)

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 - 4 * q^5 + 4 * q^14 + 16 * q^16 + 16 * q^19 + 4 * q^20 - 12 * q^25 - 8 * q^26 + 8 * q^29 + 32 * q^31 + 4 * q^35 + 8 * q^41 + 8 * q^46 - 16 * q^49 - 12 * q^50 + 8 * q^55 - 4 * q^56 - 48 * q^59 - 48 * q^61 - 16 * q^64 + 20 * q^65 + 4 * q^70 + 64 * q^71 + 16 * q^74 - 16 * q^76 + 40 * q^79 - 4 * q^80 - 16 * q^85 - 8 * q^86 - 40 * q^89 - 8 * q^91 - 4 * q^95

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.g.a	$630$	$2$	630.g	5.b	$2$	$2$	$2$	$5.031$	\(\Q(\sqrt{-1}) \)	None		✓			630.2.g.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+(-i-2)q^{5}+i q^{7}+\cdots\)
630.2.g.b	$630$	$2$	630.g	5.b	$2$	$2$	$2$	$5.031$	\(\Q(\sqrt{-1}) \)	None		✓			630.2.g.b	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+(2 i-1)q^{5}-i q^{7}+\cdots\)
630.2.g.c	$630$	$2$	630.g	5.b	$2$	$2$	$2$	$5.031$	\(\Q(\sqrt{-1}) \)	None					210.2.g.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+(-2 i-1)q^{5}+i q^{7}+\cdots\)
630.2.g.d	$630$	$2$	630.g	5.b	$2$	$2$	$2$	$5.031$	\(\Q(\sqrt{-1}) \)	None					210.2.g.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+(2 i+1)q^{5}-i q^{7}+\cdots\)
630.2.g.e	$630$	$2$	630.g	5.b	$2$	$2$	$2$	$5.031$	\(\Q(\sqrt{-1}) \)	None		✓			630.2.g.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+(2 i+1)q^{5}+i q^{7}+\cdots\)
630.2.g.f	$630$	$2$	630.g	5.b	$2$	$2$	$2$	$5.031$	\(\Q(\sqrt{-1}) \)	None		✓			630.2.g.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+(-i+2)q^{5}-i q^{7}+\cdots\)
630.2.g.g	$630$	$2$	630.g	5.b	$2$	$4$	$4$	$5.031$	\(\Q(i, \sqrt{6})\)	None			✓		70.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-q^{4}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(630, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)