Space of modular forms of level 63, weight 2, and Character 63.p

• Label: 63.2.p
• Level: $63$
• Weight: $2$
• Character orbit: 63.p
• Rep. character: $\chi_{63}(17,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.p (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(16\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(63, [\chi])\).

	Total	New	Old
Modular forms	24	4	20
Cusp forms	8	4	4
Eisenstein series	16	0	16

Trace form

4 * q - 2 * q^7 - 12 * q^10 + 8 * q^16 + 6 * q^19 - 8 * q^22 - 2 * q^25 + 6 * q^31 + 2 * q^37 + 24 * q^40 - 4 * q^43 + 16 * q^46 - 26 * q^49 - 8 * q^58 - 12 * q^61 - 32 * q^64 - 22 * q^67 + 24 * q^70 + 6 * q^73 - 10 * q^79 - 36 * q^82 + 48 * q^85 + 8 * q^88 + 54 * q^91 + 60 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(63, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
63.2.p.a	$63$	$2$	63.p	21.g	$6$	$4$	$2$	$0.503$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		✓	✓	✓	63.2.p.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}+2\beta _{3})q^{5}+(1-3\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(63, [\chi])\) into lower level spaces

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