Space of modular forms of level 63, weight 12, and trivial character

• Label: 63.12.a
• Level: $63$
• Weight: $12$
• Character orbit: 63.a
• Rep. character: $\chi_{63}(1,\cdot)$
• Character field: $\Q$
• Dimension: $27$
• Newform subspaces: $9$
• Sturm bound: $96$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	63.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(96\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(63))\).

	Total	New	Old
Modular forms	92	27	65
Cusp forms	84	27	57
Eisenstein series	8	0	8

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)	\(7\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(6\)
\(+\)	\(-\)	$-$	\(4\)
\(-\)	\(+\)	$-$	\(8\)
\(-\)	\(-\)	$+$	\(9\)
Plus space		\(+\)	\(15\)
Minus space		\(-\)	\(12\)

Trace form

\( 27 q + 87 q^{2} + 24209 q^{4} - 12390 q^{5} - 16807 q^{7} + 417387 q^{8} + O(q^{10}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(63))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	7
63.12.a.a	$63$	$12$	63.a	1.a	$1$	$1$	$1$	$48.406$	\(\Q\)	None	✓	$1$	$1$	\(-8\)	\(0\)	\(-4390\)	\(-16807\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-8q^{2}-1984q^{4}-4390q^{5}-7^{5}q^{7}+\cdots\)
63.12.a.b	$63$	$12$	63.a	1.a	$1$	$1$	$1$	$48.406$	\(\Q\)	None	✓	$1$	$1$	\(62\)	\(0\)	\(3310\)	\(-16807\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+62q^{2}+1796q^{4}+3310q^{5}-7^{5}q^{7}+\cdots\)
63.12.a.c	$63$	$12$	63.a	1.a	$1$	$2$	$2$	$48.406$	\(\Q(\sqrt{3369}) \)	None	✓	$1$	$0$	\(54\)	\(0\)	\(13500\)	\(33614\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(3^{3}-\beta )q^{2}+(2050-54\beta )q^{4}+(6750+\cdots)q^{5}+\cdots\)
63.12.a.d	$63$	$12$	63.a	1.a	$1$	$3$	$3$	$48.406$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(-77\)	\(0\)	\(-5026\)	\(-50421\)		$-$	$+$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(-26-\beta _{2})q^{2}+(1834+7\beta _{1}+2^{4}\beta _{2})q^{4}+\cdots\)
63.12.a.e	$63$	$12$	63.a	1.a	$1$	$3$	$3$	$48.406$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(33\)	\(0\)	\(-3102\)	\(50421\)		$-$	$-$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(11+\beta _{2})q^{2}+(255+13\beta _{1}+4\beta _{2})q^{4}+\cdots\)
63.12.a.f	$63$	$12$	63.a	1.a	$1$	$3$	$3$	$48.406$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(68\)	\(0\)	\(-3326\)	\(-50421\)		$-$	$+$	$-$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q+(23+\beta _{1})q^{2}+(664+72\beta _{1}+4\beta _{2})q^{4}+\cdots\)
63.12.a.g	$63$	$12$	63.a	1.a	$1$	$4$	$4$	$48.406$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(-45\)	\(0\)	\(-13356\)	\(67228\)		$-$	$-$	$+$	$2^{2}\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)$	\(q+(-11-\beta _{1})q^{2}+(1196+18\beta _{1}+\beta _{3})q^{4}+\cdots\)
63.12.a.h	$63$	$12$	63.a	1.a	$1$	$4$	$4$	$48.406$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(67228\)		$+$	$-$	$-$	$2^{5}\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(370-\beta _{3})q^{4}+(80\beta _{1}+5\beta _{2}+\cdots)q^{5}+\cdots\)
63.12.a.i	$63$	$12$	63.a	1.a	$1$	$6$	$6$	$48.406$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-100842\)		$+$	$+$	$+$	$2^{5}\cdot 3^{8}\cdot 7$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(973+\beta _{4})q^{4}+(-19\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(63))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(63)) \simeq \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 2}\)