Space of modular forms of level 63, weight 3, and Character 63.d

• Label: 63.3.d
• Level: $63$
• Weight: $3$
• Character orbit: 63.d
• Rep. character: $\chi_{63}(55,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $3$
• Sturm bound: $24$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	63.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(24\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(63, [\chi])\).

	Total	New	Old
Modular forms	20	7	13
Cusp forms	12	5	7
Eisenstein series	8	2	6

Trace form

\( 5 q + q^{2} + 5 q^{4} + 9 q^{7} + 17 q^{8} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(63, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
63.3.d.a	$63$	$3$	63.d	7.b	$2$	$1$	$1$	$1.717$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(3\)	\(0\)	\(0\)	\(-7\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3q^{2}+5q^{4}-7q^{7}+3q^{8}+6q^{11}+\cdots\)
63.3.d.b	$63$	$3$	63.d	7.b	$2$	$2$	$2$	$1.717$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(2\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-3q^{4}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
63.3.d.c	$63$	$3$	63.d	7.b	$2$	$2$	$2$	$1.717$	\(\Q(\sqrt{7}) \)	\(\Q(\sqrt{-7}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(14\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{2}+3q^{4}+7q^{7}-\beta q^{8}-8\beta q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(63, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(63, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)