Space of modular forms of level 63, weight 12, and Character 63.e

• Label: 63.12.e
• Level: $63$
• Weight: $12$
• Character orbit: 63.e
• Rep. character: $\chi_{63}(37,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $72$
• Newform subspaces: $5$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(63, [\chi])\).

	Total	New	Old
Modular forms	184	76	108
Cusp forms	168	72	96
Eisenstein series	16	4	12

Trace form

\( 72 q + 24 q^{2} - 35324 q^{4} + 3720 q^{5} - 71918 q^{7} + 88824 q^{8} + O(q^{10}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(63, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
63.12.e.a	$63$	$12$	63.e	7.c	$3$	$2$	$1$	$48.406$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(77153\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q+2^{11}\zeta_{6}q^{4}+(25807+25539\zeta_{6})q^{7}+\cdots\)
63.12.e.b	$63$	$12$	63.e	7.c	$3$	$12$	$6$	$48.406$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-22\)	\(0\)	\(8782\)	\(-504\)	$2^{20}\cdot 3^{5}\cdot 7^{6}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-4+\beta _{1}-4\beta _{2})q^{2}+(\beta _{1}+426\beta _{2}+\cdots)q^{4}+\cdots\)
63.12.e.c	$63$	$12$	63.e	7.c	$3$	$14$	$7$	$48.406$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(-9\)	\(0\)	\(-7218\)	\(9219\)	$2^{12}\cdot 3^{7}\cdot 7^{8}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{1}-\beta _{2})q^{2}+(1241\beta _{2}+11\beta _{3}+\cdots)q^{4}+\cdots\)
63.12.e.d	$63$	$12$	63.e	7.c	$3$	$16$	$8$	$48.406$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(55\)	\(0\)	\(2156\)	\(-6560\)	$2^{10}\cdot 3^{9}\cdot 7^{10}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(7+7\beta _{2}+\beta _{4})q^{2}+(7\beta _{1}+1346\beta _{2}+\cdots)q^{4}+\cdots\)
63.12.e.e	$63$	$12$	63.e	7.c	$3$	$28$	$14$	$48.406$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-151226\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{12}^{\mathrm{old}}(63, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(63, [\chi]) \cong \) \(S_{12}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)