Space of modular forms of level 63, weight 2, and trivial character

• Label: 63.2.a
• Level: $63$
• Weight: $2$
• Character orbit: 63.a
• Rep. character: $\chi_{63}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $16$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(16\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(63))\).

	Total	New	Old
Modular forms	12	3	9
Cusp forms	5	3	2
Eisenstein series	7	0	7

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
\(+\)	\(-\)	\(-\)	\(2\)
\(-\)	\(+\)	\(-\)	\(1\)
Plus space		\(+\)	\(0\)
Minus space		\(-\)	\(3\)

Trace form

3 * q + q^2 + q^4 + 2 * q^5 + q^7 - 3 * q^8 - 10 * q^10 - 4 * q^11 + 2 * q^13 - q^14 - 11 * q^16 + 6 * q^17 - 4 * q^19 - 2 * q^20 + 8 * q^22 + 13 * q^25 - 2 * q^26 + 3 * q^28 + 2 * q^29 - 8 * q^31 + 5 * q^32 + 18 * q^34 - 2 * q^35 + 10 * q^37 + 4 * q^38 + 6 * q^40 - 2 * q^41 - 12 * q^43 + 4 * q^44 - 12 * q^46 + 3 * q^49 - q^50 + 6 * q^52 - 6 * q^53 - 32 * q^55 + 3 * q^56 + 2 * q^58 - 12 * q^59 - 22 * q^61 + 9 * q^64 - 4 * q^65 - 4 * q^67 - 6 * q^68 - 14 * q^70 + 22 * q^73 + 6 * q^74 - 12 * q^76 + 4 * q^77 - 2 * q^80 + 34 * q^82 + 12 * q^83 - 12 * q^85 - 4 * q^86 + 14 * q^89 + 6 * q^91 + 24 * q^94 + 8 * q^95 + 46 * q^97 + q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(63))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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
63.2.a.a	$63$	$2$	63.a	1.a	$1$	$1$	$1$	$0.503$	\(\Q\)	None	✓		✓	✓	21.2.a.a	$1$	$0$	\(1\)	\(0\)	\(2\)	\(-1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+2q^{5}-q^{7}-3q^{8}+2q^{10}+\cdots\)
63.2.a.b	$63$	$2$	63.a	1.a	$1$	$2$	$2$	$0.503$	\(\Q(\sqrt{3}) \)	None	✓	✓	✓	✓	63.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}-2\beta q^{5}+q^{7}-\beta q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(63))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(63)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 2}\)