Space of modular forms of level 64, weight 15, and Character 64.c

• Label: 64.15.c
• Level: $64$
• Weight: $15$
• Character orbit: 64.c
• Rep. character: $\chi_{64}(63,\cdot)$
• Character field: $\Q$
• Dimension: $27$
• Newform subspaces: $6$
• Sturm bound: $120$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 15 \)
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:			\(120\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(64, [\chi])\).

	Total	New	Old
Modular forms	118	29	89
Cusp forms	106	27	79
Eisenstein series	12	2	10

Trace form

\( 27 q + 2 q^{5} - 39858077 q^{9} + O(q^{10}) \)

Decomposition of \(S_{15}^{\mathrm{new}}(64, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
64.15.c.a	$64$	$15$	64.c	4.b	$2$	$1$	$1$	$79.571$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(152886\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+152886q^{5}+3^{14}q^{9}+46322630q^{13}+\cdots\)
64.15.c.b	$64$	$15$	64.c	4.b	$2$	$2$	$2$	$79.571$	\(\Q(\sqrt{-3395}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-215700\)	\(0\)	$2^{5}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}-107850q^{5}-522\beta q^{7}-3039111q^{9}+\cdots\)
64.15.c.c	$64$	$15$	64.c	4.b	$2$	$4$	$4$	$79.571$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(87000\)	\(0\)	$2^{25}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(21750-\beta _{3})q^{5}+(-245\beta _{1}+\cdots)q^{7}+\cdots\)
64.15.c.d	$64$	$15$	64.c	4.b	$2$	$6$	$6$	$79.571$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-8060\)	\(0\)	$2^{60}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(-1343+\beta _{2})q^{5}+(-39\beta _{1}+\cdots)q^{7}+\cdots\)
64.15.c.e	$64$	$15$	64.c	4.b	$2$	$6$	$6$	$79.571$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(42900\)	\(0\)	$2^{47}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(7150+\beta _{3})q^{5}+(3^{3}\beta _{1}+26\beta _{2}+\cdots)q^{7}+\cdots\)
64.15.c.f	$64$	$15$	64.c	4.b	$2$	$8$	$8$	$79.571$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-59024\)	\(0\)	$2^{90}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-7378-\beta _{2})q^{5}+(-52\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{15}^{\mathrm{old}}(64, [\chi])\) into lower level spaces

\( S_{15}^{\mathrm{old}}(64, [\chi]) \cong \) \(S_{15}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)