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

• Label: 63.2.c
• Level: $63$
• Weight: $2$
• Character orbit: 63.c
• Rep. character: $\chi_{63}(62,\cdot)$
• Character field: $\Q$
• 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.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
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	12	4	8
Cusp forms	4	4	0
Eisenstein series	8	0	8

Trace form

\( 4 q - 8 q^{4} + 12 q^{16} + 20 q^{22} - 20 q^{25} - 28 q^{28} + 44 q^{46} + 28 q^{49} - 52 q^{58} - 24 q^{64} - 16 q^{67} + 32 q^{79} + 28 q^{88}+O(q^{100}) \)

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.c.a	$63$	$2$	63.c	21.c	$2$	$4$	$4$	$0.503$	\(\Q(\sqrt{-2}, \sqrt{7})\)	\(\Q(\sqrt{-7}) \)		✓	✓	✓	63.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}-\beta _{2}q^{7}+(-2\beta _{1}+\cdots)q^{8}+\cdots\)