Space of modular forms of level 63, weight 5, and Character 63.m

• Label: 63.5.m
• Level: $63$
• Weight: $5$
• Character orbit: 63.m
• Rep. character: $\chi_{63}(10,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $24$
• Newform subspaces: $6$
• Sturm bound: $40$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	63.m (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(40\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(63, [\chi])\).

	Total	New	Old
Modular forms	72	28	44
Cusp forms	56	24	32
Eisenstein series	16	4	12

Trace form

\( 24 q - 2 q^{2} - 84 q^{4} - 24 q^{5} + 78 q^{7} + 248 q^{8} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(63, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
63.5.m.a	$63$	$5$	63.m	7.d	$6$	$2$	$1$	$6.512$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-5\)	\(0\)	\(3\)	\(-91\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-5\zeta_{6}q^{2}+(-9+9\zeta_{6})q^{4}+(2-\zeta_{6})q^{5}+\cdots\)
63.5.m.b	$63$	$5$	63.m	7.d	$6$	$2$	$1$	$6.512$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-71\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(2^{4}-2^{4}\zeta_{6})q^{4}+(-2^{4}-39\zeta_{6})q^{7}+\cdots\)
63.5.m.c	$63$	$5$	63.m	7.d	$6$	$2$	$1$	$6.512$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(0\)	\(-18\)	\(77\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+2\zeta_{6}q^{2}+(12-12\zeta_{6})q^{4}+(-12+\cdots)q^{5}+\cdots\)
63.5.m.d	$63$	$5$	63.m	7.d	$6$	$4$	$2$	$6.512$	\(\Q(\sqrt{-3}, \sqrt{22})\)	None		$2$	$0$	\(4\)	\(0\)	\(30\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2+\beta _{1}+2\beta _{2})q^{2}+(4\beta _{1}+10\beta _{2}+\cdots)q^{4}+\cdots\)
63.5.m.e	$63$	$5$	63.m	7.d	$6$	$6$	$3$	$6.512$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(-3\)	\(0\)	\(-39\)	\(23\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{2})q^{2}+(-10-4\beta _{1}+10\beta _{2}+\cdots)q^{4}+\cdots\)
63.5.m.f	$63$	$5$	63.m	7.d	$6$	$8$	$4$	$6.512$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(140\)	$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{4}q^{2}+(-1+2\beta _{2}-13\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(63, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(63, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)