Space of modular forms of level 1664, weight 2, and Character 1664.b

• Label: 1664.2.b
• Level: $1664$
• Weight: $2$
• Character orbit: 1664.b
• Rep. character: $\chi_{1664}(833,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $11$
• Sturm bound: $448$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1664 = 2^{7} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1664.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(448\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1664, [\chi])\).

	Total	New	Old
Modular forms	240	48	192
Cusp forms	208	48	160
Eisenstein series	32	0	32

Trace form

\( 48 q - 48 q^{9} - 48 q^{25} + 32 q^{33} - 32 q^{41} + 48 q^{49} - 32 q^{57} + 16 q^{81} + 64 q^{89} + 64 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1664, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1664.2.b.a	$1664$	$2$	1664.b	8.b	$2$	$2$	$2$	$13.287$	\(\Q(\sqrt{-1}) \)	None		✓			1664.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{3}+i q^{5}-3 q^{7}-6 q^{9}-6 i q^{11}+\cdots\)
1664.2.b.b	$1664$	$2$	1664.b	8.b	$2$	$2$	$2$	$13.287$	\(\Q(\sqrt{-1}) \)	None		✓			1664.2.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+i q^{5}-q^{7}+2 q^{9}-2 i q^{11}+\cdots\)
1664.2.b.c	$1664$	$2$	1664.b	8.b	$2$	$2$	$2$	$13.287$	\(\Q(\sqrt{-1}) \)	None		✓			1664.2.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-i q^{5}+q^{7}+2 q^{9}-2 i q^{11}+\cdots\)
1664.2.b.d	$1664$	$2$	1664.b	8.b	$2$	$2$	$2$	$13.287$	\(\Q(\sqrt{-1}) \)	None		✓			1664.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{3}-i q^{5}+3 q^{7}-6 q^{9}-6 i q^{11}+\cdots\)
1664.2.b.e	$1664$	$2$	1664.b	8.b	$2$	$4$	$4$	$13.287$	\(\Q(\zeta_{8})\)	None		✓			1664.2.b.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{3}+(-\beta_{2}-\beta_1)q^{5}+(-\beta_{3}-1)q^{7}+\cdots\)
1664.2.b.f	$1664$	$2$	1664.b	8.b	$2$	$4$	$4$	$13.287$	\(\Q(\zeta_{8})\)	None		✓			1664.2.b.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta_{2} q^{3}+2\beta_1 q^{5}+3\beta_{3} q^{7}+\cdots\)
1664.2.b.g	$1664$	$2$	1664.b	8.b	$2$	$4$	$4$	$13.287$	\(\Q(i, \sqrt{5})\)	None		✓			1664.2.b.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}-\beta _{1}q^{5}+\beta _{3}q^{7}-2q^{9}+2\beta _{2}q^{11}+\cdots\)
1664.2.b.h	$1664$	$2$	1664.b	8.b	$2$	$4$	$4$	$13.287$	\(\Q(\zeta_{8})\)	None		✓			1664.2.b.h	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta_1 q^{5}+\beta_{3} q^{7}+3 q^{9}+\beta_{2} q^{11}+\cdots\)
1664.2.b.i	$1664$	$2$	1664.b	8.b	$2$	$4$	$4$	$13.287$	\(\Q(\zeta_{8})\)	None		✓			1664.2.b.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{3}+(\beta_{2}-\beta_1)q^{5}+(-\beta_{3}+1)q^{7}+\cdots\)
1664.2.b.j	$1664$	$2$	1664.b	8.b	$2$	$8$	$8$	$13.287$	8.0.\(\cdots\).3	None		✓			1664.2.b.j	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+(\beta _{2}+\beta _{3})q^{5}+\beta _{7}q^{7}+(-4+\cdots)q^{9}+\cdots\)
1664.2.b.k	$1664$	$2$	1664.b	8.b	$2$	$12$	$12$	$13.287$	12.0.\(\cdots\).1	None		✓	✓		1664.2.b.k	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{9}q^{3}+(-\beta _{4}+\beta _{7})q^{5}-\beta _{1}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1664, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1664, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(832, [\chi])\)\(^{\oplus 2}\)