Space of modular forms of level 64, weight 24, and trivial character

• Label: 64.24.a
• Level: $64$
• Weight: $24$
• Character orbit: 64.a
• Rep. character: $\chi_{64}(1,\cdot)$
• Character field: $\Q$
• Dimension: $45$
• Newform subspaces: $15$
• Sturm bound: $192$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	64.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 15 \)
Sturm bound:			\(192\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_0(64))\).

	Total	New	Old
Modular forms	190	47	143
Cusp forms	178	45	133
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
\(+\)	\(23\)
\(-\)	\(22\)

Trace form

\( 45 q + 2 q^{5} + 1349385563185 q^{9} + O(q^{10}) \)

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(64))\) 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
64.24.a.a	$64$	$24$	64.a	1.a	$1$	$1$	$1$	$214.531$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-505908\)	\(90135570\)	\(-6872255096\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-505908q^{3}+90135570q^{5}-6872255096q^{7}+\cdots\)
64.24.a.b	$64$	$24$	64.a	1.a	$1$	$1$	$1$	$214.531$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$1$	\(0\)	\(0\)	\(206464378\)	\(0\)		$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+206464378q^{5}-3^{23}q^{9}-7436301651582q^{13}+\cdots\)
64.24.a.c	$64$	$24$	64.a	1.a	$1$	$1$	$1$	$214.531$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(505908\)	\(90135570\)	\(6872255096\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+505908q^{3}+90135570q^{5}+6872255096q^{7}+\cdots\)
64.24.a.d	$64$	$24$	64.a	1.a	$1$	$2$	$2$	$214.531$	\(\Q(\sqrt{144169}) \)	None	✓	$1$	$0$	\(0\)	\(-339480\)	\(-73069020\)	\(-1359184400\)		$+$	$+$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-169740-3\beta )q^{3}+(-36534510+\cdots)q^{5}+\cdots\)
64.24.a.e	$64$	$24$	64.a	1.a	$1$	$2$	$2$	$214.531$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-170520\)	\(92266020\)	\(192083440\)		$+$	$+$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-85260-\beta )q^{3}+(46133010+540\beta )q^{5}+\cdots\)
64.24.a.f	$64$	$24$	64.a	1.a	$1$	$2$	$2$	$214.531$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(170520\)	\(92266020\)	\(-192083440\)		$-$	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+(85260-\beta )q^{3}+(46133010-540\beta )q^{5}+\cdots\)
64.24.a.g	$64$	$24$	64.a	1.a	$1$	$2$	$2$	$214.531$	\(\Q(\sqrt{144169}) \)	None	✓	$1$	$1$	\(0\)	\(339480\)	\(-73069020\)	\(1359184400\)		$-$	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+(169740-3\beta )q^{3}+(-36534510+\cdots)q^{5}+\cdots\)
64.24.a.h	$64$	$24$	64.a	1.a	$1$	$3$	$3$	$214.531$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-213948\)	\(-95628618\)	\(8647912920\)		$-$	$-$	$2^{21}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+(-71316-\beta _{1})q^{3}+(-31876206+\cdots)q^{5}+\cdots\)
64.24.a.i	$64$	$24$	64.a	1.a	$1$	$3$	$3$	$214.531$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-32708\)	\(-31480650\)	\(993025320\)		$+$	$+$	$2^{21}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+(-10903-\beta _{1})q^{3}+(-10493544+\cdots)q^{5}+\cdots\)
64.24.a.j	$64$	$24$	64.a	1.a	$1$	$3$	$3$	$214.531$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(32708\)	\(-31480650\)	\(-993025320\)		$-$	$-$	$2^{21}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+(10903+\beta _{1})q^{3}+(-10493544+\cdots)q^{5}+\cdots\)
64.24.a.k	$64$	$24$	64.a	1.a	$1$	$3$	$3$	$214.531$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(213948\)	\(-95628618\)	\(-8647912920\)		$+$	$+$	$2^{21}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+(71316+\beta _{1})q^{3}+(-31876206+\cdots)q^{5}+\cdots\)
64.24.a.l	$64$	$24$	64.a	1.a	$1$	$4$	$4$	$214.531$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(-19990040\)	\(0\)		$-$	$-$	$2^{30}\cdot 3^{7}\cdot 5$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-4997510-5\beta _{2})q^{5}+\cdots\)
64.24.a.m	$64$	$24$	64.a	1.a	$1$	$6$	$6$	$214.531$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-483920\)	\(6100380\)	\(-347289696\)		$+$	$+$	$2^{71}\cdot 3^{4}\cdot 5^{4}$	$\mathrm{SU}(2)$	\(q+(-80653+\beta _{1})q^{3}+(1016775+135\beta _{1}+\cdots)q^{5}+\cdots\)
64.24.a.n	$64$	$24$	64.a	1.a	$1$	$6$	$6$	$214.531$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(-163121700\)	\(0\)		$-$	$-$	$2^{71}\cdot 3^{6}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-27186950-\beta _{2})q^{5}+\cdots\)
64.24.a.o	$64$	$24$	64.a	1.a	$1$	$6$	$6$	$214.531$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(483920\)	\(6100380\)	\(347289696\)		$+$	$+$	$2^{71}\cdot 3^{4}\cdot 5^{4}$	$\mathrm{SU}(2)$	\(q+(80653-\beta _{1})q^{3}+(1016775+135\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_0(64))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_0(64)) \cong \) \(S_{24}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 7}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)