Space of modular forms of level 3584, weight 2, and Character 3584.b

• Label: 3584.2.b
• Level: $3584$
• Weight: $2$
• Character orbit: 3584.b
• Rep. character: $\chi_{3584}(1793,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $12$
• Sturm bound: $1024$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 3584 = 2^{9} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3584.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(1024\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3584, [\chi])\).

	Total	New	Old
Modular forms	544	96	448
Cusp forms	480	96	384
Eisenstein series	64	0	64

Trace form

\( 96 q - 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3584, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3584.2.b.a	$3584$	$2$	3584.b	8.b	$2$	$2$	$2$	$28.618$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-q^{7}+q^{9}+\beta q^{11}-\beta q^{19}+\cdots\)
3584.2.b.b	$3584$	$2$	3584.b	8.b	$2$	$2$	$2$	$28.618$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+q^{7}+q^{9}+\beta q^{11}-\beta q^{19}+\cdots\)
3584.2.b.c	$3584$	$2$	3584.b	8.b	$2$	$4$	$4$	$28.618$	4.0.2048.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{3}q^{5}-q^{7}+(1+\beta _{2})q^{9}+\cdots\)
3584.2.b.d	$3584$	$2$	3584.b	8.b	$2$	$4$	$4$	$28.618$	4.0.2048.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{3}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots\)
3584.2.b.e	$3584$	$2$	3584.b	8.b	$2$	$8$	$8$	$28.618$	8.0.\(\cdots\).3	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{3}+(\beta _{5}-\beta _{7})q^{5}-q^{7}+(-1+\cdots)q^{9}+\cdots\)
3584.2.b.f	$3584$	$2$	3584.b	8.b	$2$	$8$	$8$	$28.618$	8.0.\(\cdots\).3	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{3}+(-\beta _{5}+\beta _{7})q^{5}+q^{7}+(-1+\cdots)q^{9}+\cdots\)
3584.2.b.g	$3584$	$2$	3584.b	8.b	$2$	$10$	$10$	$28.618$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{6}q^{5}-q^{7}+(-2-\beta _{5}+\cdots)q^{9}+\cdots\)
3584.2.b.h	$3584$	$2$	3584.b	8.b	$2$	$10$	$10$	$28.618$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(10\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{6}q^{5}+q^{7}+(-2-\beta _{5}+\cdots)q^{9}+\cdots\)
3584.2.b.i	$3584$	$2$	3584.b	8.b	$2$	$12$	$12$	$28.618$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{3}+\beta _{7}q^{5}-q^{7}+(-2+\beta _{5}+\cdots)q^{9}+\cdots\)
3584.2.b.j	$3584$	$2$	3584.b	8.b	$2$	$12$	$12$	$28.618$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{4}q^{5}-q^{7}-\beta _{2}q^{9}+\beta _{7}q^{11}+\cdots\)
3584.2.b.k	$3584$	$2$	3584.b	8.b	$2$	$12$	$12$	$28.618$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{3}-\beta _{7}q^{5}+q^{7}+(-2+\beta _{5}+\cdots)q^{9}+\cdots\)
3584.2.b.l	$3584$	$2$	3584.b	8.b	$2$	$12$	$12$	$28.618$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{4}q^{5}+q^{7}-\beta _{2}q^{9}+\beta _{7}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3584, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3584, [\chi]) \cong \)