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

• Label: 3584.2.m
• Level: $3584$
• Weight: $2$
• Character orbit: 3584.m
• Rep. character: $\chi_{3584}(897,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $192$
• Newform subspaces: $40$
• Sturm bound: $1024$
• Trace bound: $35$

Defining parameters

Level:	\( N \)	\(=\)	\( 3584 = 2^{9} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3584.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 40 \)
Sturm bound:			\(1024\)
Trace bound:			\(35\)
Distinguishing \(T_p\):			\(3\), \(5\), \(11\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	1088	192	896
Cusp forms	960	192	768
Eisenstein series	128	0	128

Trace form

\( 192 q + O(q^{10}) \)

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.m.a	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-4\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2+2i)q^{3}+(-1-i)q^{5}+iq^{7}+\cdots\)
3584.2.m.b	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-4\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2+2i)q^{3}+(1+i)q^{5}-iq^{7}+\cdots\)
3584.2.m.c	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(-2\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+i)q^{3}+(-2-2i)q^{5}+iq^{7}+\cdots\)
3584.2.m.d	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(-2\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+i)q^{3}+(-2-2i)q^{5}-iq^{7}+\cdots\)
3584.2.m.e	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(-2\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+i)q^{3}+(-2-2i)q^{5}+iq^{7}+\cdots\)
3584.2.m.f	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+i)q^{3}+(-2-2i)q^{5}-iq^{7}+\cdots\)
3584.2.m.g	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+i)q^{3}+iq^{7}+iq^{9}+(2+2i)q^{11}+\cdots\)
3584.2.m.h	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+i)q^{3}-iq^{7}+iq^{9}+(2+2i)q^{11}+\cdots\)
3584.2.m.i	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(-2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+i)q^{3}+(2+2i)q^{5}-iq^{7}+\cdots\)
3584.2.m.j	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(-2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+i)q^{3}+(2+2i)q^{5}+iq^{7}+\cdots\)
3584.2.m.k	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+i)q^{3}+(2+2i)q^{5}+iq^{7}+\cdots\)
3584.2.m.l	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+i)q^{3}+(2+2i)q^{5}-iq^{7}+\cdots\)
3584.2.m.m	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-i)q^{5}+iq^{7}+3iq^{9}+(-4+\cdots)q^{11}+\cdots\)
3584.2.m.n	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-i)q^{5}-iq^{7}+3iq^{9}+(4+4i)q^{11}+\cdots\)
3584.2.m.o	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+i)q^{5}-iq^{7}+3iq^{9}+(-4-4i)q^{11}+\cdots\)
3584.2.m.p	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+i)q^{5}+iq^{7}+3iq^{9}+(4+4i)q^{11}+\cdots\)
3584.2.m.q	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-i)q^{3}+(-2-2i)q^{5}-iq^{7}+\cdots\)
3584.2.m.r	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-i)q^{3}+(-2-2i)q^{5}+iq^{7}+\cdots\)
3584.2.m.s	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-i)q^{3}+(-2-2i)q^{5}+iq^{7}+\cdots\)
3584.2.m.t	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-i)q^{3}+(-2-2i)q^{5}-iq^{7}+\cdots\)
3584.2.m.u	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-i)q^{3}-iq^{7}+iq^{9}+(-2-2i)q^{11}+\cdots\)
3584.2.m.v	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-i)q^{3}+iq^{7}+iq^{9}+(-2-2i)q^{11}+\cdots\)
3584.2.m.w	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-i)q^{3}+(2+2i)q^{5}-iq^{7}+iq^{9}+\cdots\)
3584.2.m.x	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-i)q^{3}+(2+2i)q^{5}+iq^{7}+iq^{9}+\cdots\)
3584.2.m.y	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-i)q^{3}+(2+2i)q^{5}-iq^{7}+iq^{9}+\cdots\)
3584.2.m.z	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-i)q^{3}+(2+2i)q^{5}+iq^{7}+iq^{9}+\cdots\)
3584.2.m.ba	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(4\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2-2i)q^{3}+(-1-i)q^{5}-iq^{7}+\cdots\)
3584.2.m.bb	$3584$	$2$	3584.m	16.e	$4$	$2$	$1$	$28.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(4\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2-2i)q^{3}+(1+i)q^{5}+iq^{7}-5iq^{9}+\cdots\)
3584.2.m.bc	$3584$	$2$	3584.m	16.e	$4$	$4$	$2$	$28.618$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{12}^{2}q^{3}+(-1+\zeta_{12}+\zeta_{12}^{3})q^{5}+\cdots\)
3584.2.m.bd	$3584$	$2$	3584.m	16.e	$4$	$4$	$2$	$28.618$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{12}^{2}q^{3}+(-1+\zeta_{12}-\zeta_{12}^{3})q^{5}+\cdots\)
3584.2.m.be	$3584$	$2$	3584.m	16.e	$4$	$4$	$2$	$28.618$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{12}^{2}q^{3}+(1-\zeta_{12}-\zeta_{12}^{3})q^{5}+\cdots\)
3584.2.m.bf	$3584$	$2$	3584.m	16.e	$4$	$4$	$2$	$28.618$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{12}^{2}q^{3}+(1-\zeta_{12}+\zeta_{12}^{3})q^{5}+\cdots\)
3584.2.m.bg	$3584$	$2$	3584.m	16.e	$4$	$6$	$3$	$28.618$	6.0.399424.1	None		$2$	$0$	\(0\)	\(-2\)	\(-4\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{3}+(-1-\beta _{1}-\beta _{5})q^{5}+\beta _{1}q^{7}+\cdots\)
3584.2.m.bh	$3584$	$2$	3584.m	16.e	$4$	$6$	$3$	$28.618$	6.0.399424.1	None		$2$	$0$	\(0\)	\(-2\)	\(4\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{3}+(1+\beta _{1}+\beta _{5})q^{5}-\beta _{1}q^{7}+\cdots\)
3584.2.m.bi	$3584$	$2$	3584.m	16.e	$4$	$6$	$3$	$28.618$	6.0.399424.1	None		$2$	$0$	\(0\)	\(2\)	\(-4\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{5}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+\beta _{1}q^{7}+\cdots\)
3584.2.m.bj	$3584$	$2$	3584.m	16.e	$4$	$6$	$3$	$28.618$	6.0.399424.1	None		$2$	$0$	\(0\)	\(2\)	\(4\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{5}q^{3}+(1-\beta _{1}+\beta _{2})q^{5}-\beta _{1}q^{7}+\cdots\)
3584.2.m.bk	$3584$	$2$	3584.m	16.e	$4$	$24$	$12$	$28.618$		None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
3584.2.m.bl	$3584$	$2$	3584.m	16.e	$4$	$24$	$12$	$28.618$		None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
3584.2.m.bm	$3584$	$2$	3584.m	16.e	$4$	$24$	$12$	$28.618$		None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
3584.2.m.bn	$3584$	$2$	3584.m	16.e	$4$	$24$	$12$	$28.618$		None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(3584, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(512, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(896, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1792, [\chi])\)\(^{\oplus 2}\)