Space of modular forms of level 63, weight 2, and Character 63.e

• Label: 63.2.e
• Level: $63$
• Weight: $2$
• Character orbit: 63.e
• Rep. character: $\chi_{63}(37,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $16$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(16\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(63, [\chi])\).

	Total	New	Old
Modular forms	24	8	16
Cusp forms	8	4	4
Eisenstein series	16	4	12

Trace form

\( 4 q + 2 q^{2} - 2 q^{5} - 6 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(63, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
63.2.e.a	$63$	$2$	63.e	7.c	$3$	$2$	$1$	$0.503$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q+2\zeta_{6}q^{4}+(1-3\zeta_{6})q^{7}-7q^{13}+(-4+\cdots)q^{16}+\cdots\)
63.2.e.b	$63$	$2$	63.e	7.c	$3$	$2$	$1$	$0.503$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(0\)	\(-2\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(63, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(63, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)