Space of modular forms of level 64, weight 17, and Character 64.c

• Label: 64.17.c
• Level: $64$
• Weight: $17$
• Character orbit: 64.c
• Rep. character: $\chi_{64}(63,\cdot)$
• Character field: $\Q$
• Dimension: $31$
• Newform subspaces: $6$
• Sturm bound: $136$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 17 \)
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:			\(136\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{17}(64, [\chi])\).

	Total	New	Old
Modular forms	134	33	101
Cusp forms	122	31	91
Eisenstein series	12	2	10

Trace form

\( 31 q + 2 q^{5} - 416118305 q^{9} + O(q^{10}) \)

Decomposition of \(S_{17}^{\mathrm{new}}(64, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
64.17.c.a	$64$	$17$	64.c	4.b	$2$	$1$	$1$	$103.888$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓		4.17.b.a	$2$	$0$	\(0\)	\(0\)	\(-329666\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-329666q^{5}+3^{16}q^{9}+1631232958q^{13}+\cdots\)
64.17.c.b	$64$	$17$	64.c	4.b	$2$	$2$	$2$	$103.888$	\(\Q(\sqrt{-3003}) \)	None			16.17.c.a	$2$	$0$	\(0\)	\(0\)	\(60\)	\(0\)	$2^{4}\cdot 3\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}+30q^{5}+462\beta q^{7}-196479q^{9}+\cdots\)
64.17.c.c	$64$	$17$	64.c	4.b	$2$	$6$	$6$	$103.888$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None			16.17.c.b	$2$	$0$	\(0\)	\(0\)	\(-531276\)	\(0\)	$2^{60}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-88546-\beta _{2})q^{5}+(139\beta _{1}+\cdots)q^{7}+\cdots\)
64.17.c.d	$64$	$17$	64.c	4.b	$2$	$6$	$6$	$103.888$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None			4.17.b.b	$2$	$0$	\(0\)	\(0\)	\(506740\)	\(0\)	$2^{62}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(84455-5\beta _{2})q^{5}+(-69\beta _{1}+\cdots)q^{7}+\cdots\)
64.17.c.e	$64$	$17$	64.c	4.b	$2$	$8$	$8$	$103.888$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None			32.17.c.b	$2$	$0$	\(0\)	\(0\)	\(-767312\)	\(0\)	$2^{90}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-95914+\beta _{3})q^{5}+(-68\beta _{1}+\cdots)q^{7}+\cdots\)
64.17.c.f	$64$	$17$	64.c	4.b	$2$	$8$	$8$	$103.888$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None			32.17.c.a	$2$	$0$	\(0\)	\(0\)	\(1121456\)	\(0\)	$2^{90}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(140182+\beta _{2})q^{5}+(221\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{17}^{\mathrm{old}}(64, [\chi])\) into lower level spaces

\( S_{17}^{\mathrm{old}}(64, [\chi]) \simeq \) \(S_{17}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)