Space of modular forms of level 64, weight 20, and trivial character

• Label: 64.20.a
• Level: $64$
• Weight: $20$
• Character orbit: 64.a
• Rep. character: $\chi_{64}(1,\cdot)$
• Character field: $\Q$
• Dimension: $37$
• Newform subspaces: $17$
• Sturm bound: $160$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	64.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(160\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_0(64))\).

	Total	New	Old
Modular forms	158	39	119
Cusp forms	146	37	109
Eisenstein series	12	2	10

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	Dim
\(+\)	\(19\)
\(-\)	\(18\)

Trace form

\( 37 q + 2 q^{5} + 13559717113 q^{9} + O(q^{10}) \)

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_0(64))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2
64.20.a.a	$64$	$20$	64.a	1.a	$1$	$1$	$1$	$146.443$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-53028\)	\(5556930\)	\(44496424\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-53028q^{3}+5556930q^{5}+44496424q^{7}+\cdots\)
64.20.a.b	$64$	$20$	64.a	1.a	$1$	$1$	$1$	$146.443$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-50652\)	\(2377410\)	\(-16917544\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-50652q^{3}+2377410q^{5}-16917544q^{7}+\cdots\)
64.20.a.c	$64$	$20$	64.a	1.a	$1$	$1$	$1$	$146.443$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-13092\)	\(-6546750\)	\(-96674264\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-13092q^{3}-6546750q^{5}-96674264q^{7}+\cdots\)
64.20.a.d	$64$	$20$	64.a	1.a	$1$	$1$	$1$	$146.443$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-36\)	\(196290\)	\(35905576\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-6^{2}q^{3}+196290q^{5}+35905576q^{7}+\cdots\)
64.20.a.e	$64$	$20$	64.a	1.a	$1$	$1$	$1$	$146.443$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$1$	\(0\)	\(0\)	\(-5042902\)	\(0\)		$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-5042902q^{5}-3^{19}q^{9}-13425142062q^{13}+\cdots\)
64.20.a.f	$64$	$20$	64.a	1.a	$1$	$1$	$1$	$146.443$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(36\)	\(196290\)	\(-35905576\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+6^{2}q^{3}+196290q^{5}-35905576q^{7}+\cdots\)
64.20.a.g	$64$	$20$	64.a	1.a	$1$	$1$	$1$	$146.443$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(13092\)	\(-6546750\)	\(96674264\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+13092q^{3}-6546750q^{5}+96674264q^{7}+\cdots\)
64.20.a.h	$64$	$20$	64.a	1.a	$1$	$1$	$1$	$146.443$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(50652\)	\(2377410\)	\(16917544\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+50652q^{3}+2377410q^{5}+16917544q^{7}+\cdots\)
64.20.a.i	$64$	$20$	64.a	1.a	$1$	$1$	$1$	$146.443$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(53028\)	\(5556930\)	\(-44496424\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+53028q^{3}+5556930q^{5}-44496424q^{7}+\cdots\)
64.20.a.j	$64$	$20$	64.a	1.a	$1$	$2$	$2$	$146.443$	\(\Q(\sqrt{1453}) \)	None	✓	$1$	$1$	\(0\)	\(-27912\)	\(-1226620\)	\(-88510512\)		$-$	$-$	$2^{7}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+(-13956-\beta )q^{3}+(-613310-44\beta )q^{5}+\cdots\)
64.20.a.k	$64$	$20$	64.a	1.a	$1$	$2$	$2$	$146.443$	\(\Q(\sqrt{1453}) \)	None	✓	$1$	$0$	\(0\)	\(27912\)	\(-1226620\)	\(88510512\)		$+$	$+$	$2^{7}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+(13956-\beta )q^{3}+(-613310+44\beta )q^{5}+\cdots\)
64.20.a.l	$64$	$20$	64.a	1.a	$1$	$3$	$3$	$146.443$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-23732\)	\(-2140218\)	\(55851720\)		$+$	$+$	$2^{21}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(-7911+\beta _{1})q^{3}+(-713429+70\beta _{1}+\cdots)q^{5}+\cdots\)
64.20.a.m	$64$	$20$	64.a	1.a	$1$	$3$	$3$	$146.443$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(23732\)	\(-2140218\)	\(-55851720\)		$-$	$-$	$2^{21}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(7911-\beta _{1})q^{3}+(-713429+70\beta _{1}+\cdots)q^{5}+\cdots\)
64.20.a.n	$64$	$20$	64.a	1.a	$1$	$4$	$4$	$146.443$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(-4924760\)	\(0\)		$-$	$-$	$2^{27}\cdot 3^{4}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1231190-\beta _{2})q^{5}+(-830\beta _{1}+\cdots)q^{7}+\cdots\)
64.20.a.o	$64$	$20$	64.a	1.a	$1$	$4$	$4$	$146.443$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(5322920\)	\(0\)		$-$	$-$	$2^{30}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1330730-5\beta _{2})q^{5}+(941\beta _{1}+\cdots)q^{7}+\cdots\)
64.20.a.p	$64$	$20$	64.a	1.a	$1$	$5$	$5$	$146.443$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-6424\)	\(4105330\)	\(-107158480\)		$+$	$+$	$2^{48}\cdot 3^{4}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+(-1285-\beta _{1})q^{3}+(821058-39\beta _{1}+\cdots)q^{5}+\cdots\)
64.20.a.q	$64$	$20$	64.a	1.a	$1$	$5$	$5$	$146.443$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(6424\)	\(4105330\)	\(107158480\)		$+$	$+$	$2^{48}\cdot 3^{4}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+(1285+\beta _{1})q^{3}+(821058-39\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_0(64))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_0(64)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 7}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)