Space of modular forms of level 630, weight 3, and Character 630.e

• Label: 630.3.e
• Level: $630$
• Weight: $3$
• Character orbit: 630.e
• Rep. character: $\chi_{630}(71,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $432$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	630.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(432\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(630, [\chi])\).

	Total	New	Old
Modular forms	304	16	288
Cusp forms	272	16	256
Eisenstein series	32	0	32

Trace form

\( 16 q - 32 q^{4} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(630, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
630.3.e.a	$630$	$3$	630.e	3.b	$2$	$8$	$8$	$17.166$	8.0.\(\cdots\).4	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}-2q^{4}-\beta _{6}q^{5}-\beta _{2}q^{7}-2\beta _{4}q^{8}+\cdots\)
630.3.e.b	$630$	$3$	630.e	3.b	$2$	$8$	$8$	$17.166$	8.0.\(\cdots\).4	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}-2q^{4}+\beta _{6}q^{5}-\beta _{2}q^{7}-2\beta _{4}q^{8}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(630, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(630, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)