Space of modular forms of level 8064, weight 2, and Character 8064.j

• Label: 8064.2.j
• Level: $8064$
• Weight: $2$
• Character orbit: 8064.j
• Rep. character: $\chi_{8064}(575,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $9$
• Sturm bound: $3072$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 8064 = 2^{7} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8064.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(3072\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(5\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(8064, [\chi])\).

	Total	New	Old
Modular forms	1600	96	1504
Cusp forms	1472	96	1376
Eisenstein series	128	0	128

Trace form

\( 96 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(8064, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
8064.2.j.a	$8064$	$2$	8064.j	24.f	$2$	$4$	$4$	$64.391$	\(\Q(\zeta_{8})\)	None		✓			8064.2.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}^{3}q^{5}+\zeta_{8}q^{7}+2\zeta_{8}^{2}q^{11}+2\zeta_{8}q^{13}+\cdots\)
8064.2.j.b	$8064$	$2$	8064.j	24.f	$2$	$4$	$4$	$64.391$	\(\Q(\zeta_{8})\)	None		✓			8064.2.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}^{3}q^{5}+\zeta_{8}q^{7}+2\zeta_{8}^{2}q^{11}-2\zeta_{8}q^{13}+\cdots\)
8064.2.j.c	$8064$	$2$	8064.j	24.f	$2$	$12$	$12$	$64.391$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			8064.2.j.c	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{9})q^{5}+\beta _{2}q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
8064.2.j.d	$8064$	$2$	8064.j	24.f	$2$	$12$	$12$	$64.391$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			8064.2.j.c	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{9})q^{5}+\beta _{2}q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
8064.2.j.e	$8064$	$2$	8064.j	24.f	$2$	$12$	$12$	$64.391$	12.0.\(\cdots\).1	None		✓			8064.2.j.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{9}q^{5}-\beta _{3}q^{7}+(-\beta _{4}-\beta _{10})q^{11}+\cdots\)
8064.2.j.f	$8064$	$2$	8064.j	24.f	$2$	$12$	$12$	$64.391$	12.0.\(\cdots\).1	None		✓			8064.2.j.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{9}q^{5}+\beta _{3}q^{7}+(\beta _{4}+\beta _{10})q^{11}+\cdots\)
8064.2.j.g	$8064$	$2$	8064.j	24.f	$2$	$12$	$12$	$64.391$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			8064.2.j.c	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{9})q^{5}-\beta _{2}q^{7}+(\beta _{1}+\beta _{2})q^{11}+\cdots\)
8064.2.j.h	$8064$	$2$	8064.j	24.f	$2$	$12$	$12$	$64.391$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			8064.2.j.c	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{9})q^{5}-\beta _{2}q^{7}+(\beta _{1}+\beta _{2})q^{11}+\cdots\)
8064.2.j.i	$8064$	$2$	8064.j	24.f	$2$	$16$	$16$	$64.391$	16.0.\(\cdots\).1	None		✓	✓		8064.2.j.i	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{26}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{13}q^{5}-\beta _{5}q^{7}+(-\beta _{7}-\beta _{12})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(8064, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(8064, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1344, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2016, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2688, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4032, [\chi])\)\(^{\oplus 2}\)