Space of modular forms of level 64, weight 18, and trivial character

• Label: 64.18.a
• Level: $64$
• Weight: $18$
• Character orbit: 64.a
• Rep. character: $\chi_{64}(1,\cdot)$
• Character field: $\Q$
• Dimension: $33$
• Newform subspaces: $16$
• Sturm bound: $144$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	64.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(144\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_0(64))\).

	Total	New	Old
Modular forms	142	35	107
Cusp forms	130	33	97
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
\(+\)	\(16\)
\(-\)	\(17\)

Trace form

\( 33 q + 2 q^{5} + 1334448349 q^{9} + O(q^{10}) \)

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(64))\) 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					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2
64.18.a.a	$64$	$18$	64.a	1.a	$1$	$1$	$1$	$117.262$	\(\Q\)	None	✓				2.18.a.a	$1$	$1$	\(0\)	\(-6084\)	\(-1255110\)	\(-22465912\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-78^{2}q^{3}-1255110q^{5}-22465912q^{7}+\cdots\)
64.18.a.b	$64$	$18$	64.a	1.a	$1$	$1$	$1$	$117.262$	\(\Q\)	None	✓				1.18.a.a	$1$	$0$	\(0\)	\(-4284\)	\(1025850\)	\(-3225992\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4284q^{3}+1025850q^{5}-3225992q^{7}+\cdots\)
64.18.a.c	$64$	$18$	64.a	1.a	$1$	$1$	$1$	$117.262$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓				32.18.a.a	$2$	$0$	\(0\)	\(0\)	\(1746242\)	\(0\)		$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+1746242q^{5}-3^{17}q^{9}+4948305594q^{13}+\cdots\)
64.18.a.d	$64$	$18$	64.a	1.a	$1$	$1$	$1$	$117.262$	\(\Q\)	None	✓				1.18.a.a	$1$	$1$	\(0\)	\(4284\)	\(1025850\)	\(3225992\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4284q^{3}+1025850q^{5}+3225992q^{7}+\cdots\)
64.18.a.e	$64$	$18$	64.a	1.a	$1$	$1$	$1$	$117.262$	\(\Q\)	None	✓				2.18.a.a	$1$	$0$	\(0\)	\(6084\)	\(-1255110\)	\(22465912\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+78^{2}q^{3}-1255110q^{5}+22465912q^{7}+\cdots\)
64.18.a.f	$64$	$18$	64.a	1.a	$1$	$2$	$2$	$117.262$	\(\Q(\sqrt{114}) \)	None	✓				8.18.a.b	$1$	$1$	\(0\)	\(-11592\)	\(791924\)	\(-18932592\)		$+$	$+$	$2^{7}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(-5796+\beta )q^{3}+(395962-68\beta )q^{5}+\cdots\)
64.18.a.g	$64$	$18$	64.a	1.a	$1$	$2$	$2$	$117.262$	\(\Q(\sqrt{9361}) \)	None	✓				4.18.a.a	$1$	$0$	\(0\)	\(-5880\)	\(-604044\)	\(-25350160\)		$-$	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-2940-\beta )q^{3}+(-302022-6^{2}\beta )q^{5}+\cdots\)
64.18.a.h	$64$	$18$	64.a	1.a	$1$	$2$	$2$	$117.262$	\(\Q(\sqrt{2146}) \)	None	✓				8.18.a.a	$1$	$0$	\(0\)	\(-952\)	\(53620\)	\(333168\)		$-$	$-$	$2^{8}$	$\mathrm{SU}(2)$	\(q+(-476+\beta )q^{3}+(26810-60\beta )q^{5}+\cdots\)
64.18.a.i	$64$	$18$	64.a	1.a	$1$	$2$	$2$	$117.262$	\(\Q(\sqrt{1497}) \)	None	✓				32.18.a.c	$2$	$0$	\(0\)	\(0\)	\(-1106300\)	\(0\)		$-$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-553150q^{5}+20874\beta q^{7}+\cdots\)
64.18.a.j	$64$	$18$	64.a	1.a	$1$	$2$	$2$	$117.262$	\(\Q(\sqrt{1235}) \)	None	✓				32.18.a.b	$2$	$0$	\(0\)	\(0\)	\(-476540\)	\(0\)		$-$	$-$	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-238270q^{5}+118\beta q^{7}+280603197q^{9}+\cdots\)
64.18.a.k	$64$	$18$	64.a	1.a	$1$	$2$	$2$	$117.262$	\(\Q(\sqrt{2146}) \)	None	✓				8.18.a.a	$1$	$1$	\(0\)	\(952\)	\(53620\)	\(-333168\)		$+$	$+$	$2^{8}$	$\mathrm{SU}(2)$	\(q+(476+\beta )q^{3}+(26810+60\beta )q^{5}+\cdots\)
64.18.a.l	$64$	$18$	64.a	1.a	$1$	$2$	$2$	$117.262$	\(\Q(\sqrt{9361}) \)	None	✓				4.18.a.a	$1$	$1$	\(0\)	\(5880\)	\(-604044\)	\(25350160\)		$+$	$+$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+(2940-\beta )q^{3}+(-302022+6^{2}\beta )q^{5}+\cdots\)
64.18.a.m	$64$	$18$	64.a	1.a	$1$	$2$	$2$	$117.262$	\(\Q(\sqrt{114}) \)	None	✓				8.18.a.b	$1$	$0$	\(0\)	\(11592\)	\(791924\)	\(18932592\)		$-$	$-$	$2^{7}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(5796+\beta )q^{3}+(395962+68\beta )q^{5}+\cdots\)
64.18.a.n	$64$	$18$	64.a	1.a	$1$	$4$	$4$	$117.262$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				32.18.a.d	$1$	$1$	\(0\)	\(-16352\)	\(39816\)	\(24992448\)		$+$	$+$	$2^{27}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+(-4088-\beta _{1})q^{3}+(9954+12\beta _{1}+\cdots)q^{5}+\cdots\)
64.18.a.o	$64$	$18$	64.a	1.a	$1$	$4$	$4$	$117.262$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓		✓		32.18.a.e	$2$	$0$	\(0\)	\(0\)	\(-267512\)	\(0\)		$-$	$-$	$2^{27}\cdot 3^{5}\cdot 5$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-66878+\beta _{3})q^{5}+(-73\beta _{1}+\cdots)q^{7}+\cdots\)
64.18.a.p	$64$	$18$	64.a	1.a	$1$	$4$	$4$	$117.262$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				32.18.a.d	$1$	$1$	\(0\)	\(16352\)	\(39816\)	\(-24992448\)		$+$	$+$	$2^{27}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+(4088+\beta _{1})q^{3}+(9954+12\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_0(64))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_0(64)) \simeq \) \(S_{18}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 7}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)