Space of modular forms of level 663, weight 2, and Character 663.z

• Label: 663.2.z
• Level: $663$
• Weight: $2$
• Character orbit: 663.z
• Rep. character: $\chi_{663}(205,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $76$
• Newform subspaces: $6$
• Sturm bound: $168$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 663 = 3 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	663.z (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(168\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(663, [\chi])\).

	Total	New	Old
Modular forms	176	76	100
Cusp forms	160	76	84
Eisenstein series	16	0	16

Trace form

\( 76 q - 2 q^{3} + 40 q^{4} + 6 q^{7} - 38 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(663, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
663.2.z.a	$663$	$2$	663.z	13.e	$6$	$2$	$1$	$5.294$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+(1-2\zeta_{6})q^{5}+\cdots\)
663.2.z.b	$663$	$2$	663.z	13.e	$6$	$4$	$2$	$5.294$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$1$	\(0\)	\(-2\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(-1+2\beta _{2}+\cdots)q^{5}+\cdots\)
663.2.z.c	$663$	$2$	663.z	13.e	$6$	$12$	$6$	$5.294$	12.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(-3\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{11}q^{2}+\beta _{2}q^{3}+(1-\beta _{1}-\beta _{2}-\beta _{5}+\cdots)q^{4}+\cdots\)
663.2.z.d	$663$	$2$	663.z	13.e	$6$	$16$	$8$	$5.294$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{2})q^{2}+(-1+\beta _{10})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots\)
663.2.z.e	$663$	$2$	663.z	13.e	$6$	$20$	$10$	$5.294$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(-10\)	\(0\)	\(12\)	$5^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{2}+\beta _{8}q^{3}+(1+\beta _{8}+\beta _{10})q^{4}+\cdots\)
663.2.z.f	$663$	$2$	663.z	13.e	$6$	$22$	$11$	$5.294$		None		$2$	$0$	\(0\)	\(11\)	\(0\)	\(3\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(663, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(663, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)