Space of modular forms of level 64, weight 12, and trivial character

• Label: 64.12.a
• Level: $64$
• Weight: $12$
• Character orbit: 64.a
• Rep. character: $\chi_{64}(1,\cdot)$
• Character field: $\Q$
• Dimension: $21$
• Newform subspaces: $13$
• Sturm bound: $96$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	64.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(96\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(64))\).

	Total	New	Old
Modular forms	94	23	71
Cusp forms	82	21	61
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
\(+\)	\(11\)
\(-\)	\(10\)

Trace form

\( 21 q + 2 q^{5} + 1121929 q^{9} + O(q^{10}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(64))\) 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
64.12.a.a	$64$	$12$	64.a	1.a	$1$	$1$	$1$	$49.174$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-516\)	\(10530\)	\(-49304\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-516q^{3}+10530q^{5}-49304q^{7}+\cdots\)
64.12.a.b	$64$	$12$	64.a	1.a	$1$	$1$	$1$	$49.174$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-252\)	\(-4830\)	\(-16744\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-252q^{3}-4830q^{5}-16744q^{7}+\cdots\)
64.12.a.c	$64$	$12$	64.a	1.a	$1$	$1$	$1$	$49.174$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-36\)	\(3490\)	\(55464\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-6^{2}q^{3}+3490q^{5}+55464q^{7}-175851q^{9}+\cdots\)
64.12.a.d	$64$	$12$	64.a	1.a	$1$	$1$	$1$	$49.174$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$1$	\(0\)	\(0\)	\(12938\)	\(0\)		$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+12938q^{5}-3^{11}q^{9}-2631822q^{13}+\cdots\)
64.12.a.e	$64$	$12$	64.a	1.a	$1$	$1$	$1$	$49.174$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(36\)	\(3490\)	\(-55464\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+6^{2}q^{3}+3490q^{5}-55464q^{7}-175851q^{9}+\cdots\)
64.12.a.f	$64$	$12$	64.a	1.a	$1$	$1$	$1$	$49.174$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(252\)	\(-4830\)	\(16744\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+252q^{3}-4830q^{5}+16744q^{7}+\cdots\)
64.12.a.g	$64$	$12$	64.a	1.a	$1$	$1$	$1$	$49.174$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(516\)	\(10530\)	\(49304\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+516q^{3}+10530q^{5}+49304q^{7}+\cdots\)
64.12.a.h	$64$	$12$	64.a	1.a	$1$	$2$	$2$	$49.174$	\(\Q(\sqrt{109}) \)	None	✓	$1$	$0$	\(0\)	\(-56\)	\(-7868\)	\(91056\)		$+$	$+$	$2^{7}$	$\mathrm{SU}(2)$	\(q+(-28-\beta )q^{3}+(-3934+12\beta )q^{5}+\cdots\)
64.12.a.i	$64$	$12$	64.a	1.a	$1$	$2$	$2$	$49.174$	\(\Q(\sqrt{273}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(-14060\)	\(0\)		$-$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-7030q^{5}+66\beta q^{7}+102405q^{9}+\cdots\)
64.12.a.j	$64$	$12$	64.a	1.a	$1$	$2$	$2$	$49.174$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(20\)	\(0\)		$-$	$-$	$2^{4}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+10q^{5}+62\beta q^{7}-4347q^{9}+\cdots\)
64.12.a.k	$64$	$12$	64.a	1.a	$1$	$2$	$2$	$49.174$	\(\Q(\sqrt{109}) \)	None	✓	$1$	$1$	\(0\)	\(56\)	\(-7868\)	\(-91056\)		$-$	$-$	$2^{7}$	$\mathrm{SU}(2)$	\(q+(28+\beta )q^{3}+(-3934+12\beta )q^{5}+\cdots\)
64.12.a.l	$64$	$12$	64.a	1.a	$1$	$3$	$3$	$49.174$	3.3.1056820.1	None	✓	$1$	$0$	\(0\)	\(-440\)	\(-770\)	\(-6032\)		$+$	$+$	$2^{14}$	$\mathrm{SU}(2)$	\(q+(-147-\beta _{1})q^{3}+(-257+\beta _{2})q^{5}+\cdots\)
64.12.a.m	$64$	$12$	64.a	1.a	$1$	$3$	$3$	$49.174$	3.3.1056820.1	None	✓	$1$	$0$	\(0\)	\(440\)	\(-770\)	\(6032\)		$+$	$+$	$2^{14}$	$\mathrm{SU}(2)$	\(q+(147+\beta _{1})q^{3}+(-257+\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(64))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(64)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 7}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)