Space of modular forms of level 64, weight 9, and Character 64.c

• Label: 64.9.c
• Level: $64$
• Weight: $9$
• Character orbit: 64.c
• Rep. character: $\chi_{64}(63,\cdot)$
• Character field: $\Q$
• Dimension: $15$
• Newform subspaces: $6$
• Sturm bound: $72$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	64.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(72\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(64, [\chi])\).

	Total	New	Old
Modular forms	70	17	53
Cusp forms	58	15	43
Eisenstein series	12	2	10

Trace form

\( 15 q + 2 q^{5} - 28433 q^{9} + O(q^{10}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(64, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
64.9.c.a	$64$	$9$	64.c	4.b	$2$	$1$	$1$	$26.072$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓				4.9.b.a	$2$	$0$	\(0\)	\(0\)	\(1054\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+1054q^{5}+3^{8}q^{9}+478q^{13}-63358q^{17}+\cdots\)
64.9.c.b	$64$	$9$	64.c	4.b	$2$	$2$	$2$	$26.072$	\(\Q(\sqrt{-39}) \)	None					4.9.b.b	$2$	$0$	\(0\)	\(0\)	\(-1220\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}-610q^{5}+14\beta q^{7}-3423q^{9}+\cdots\)
64.9.c.c	$64$	$9$	64.c	4.b	$2$	$2$	$2$	$26.072$	\(\Q(\sqrt{-3}) \)	None					16.9.c.b	$2$	$0$	\(0\)	\(0\)	\(-516\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{3}-258q^{5}+238\zeta_{6}q^{7}+6369q^{9}+\cdots\)
64.9.c.d	$64$	$9$	64.c	4.b	$2$	$2$	$2$	$26.072$	\(\Q(\sqrt{-35}) \)	None					16.9.c.a	$2$	$0$	\(0\)	\(0\)	\(1020\)	\(0\)	$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}+510q^{5}-18\beta q^{7}-13599q^{9}+\cdots\)
64.9.c.e	$64$	$9$	64.c	4.b	$2$	$4$	$4$	$26.072$	\(\Q(i, \sqrt{19})\)	None					32.9.c.b	$2$	$0$	\(0\)	\(0\)	\(-1064\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(-266-3\beta _{2})q^{5}+(7\beta _{1}+\cdots)q^{7}+\cdots\)
64.9.c.f	$64$	$9$	64.c	4.b	$2$	$4$	$4$	$26.072$	\(\Q(i, \sqrt{39})\)	None					32.9.c.a	$2$	$0$	\(0\)	\(0\)	\(728\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{3})q^{3}+(182-\beta _{2})q^{5}+(-17\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(64, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(64, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)