Space of modular forms of level 4032, weight 2, and Character 4032.j

• Label: 4032.2.j
• Level: $4032$
• Weight: $2$
• Character orbit: 4032.j
• Rep. character: $\chi_{4032}(2591,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $6$
• Sturm bound: $1536$
• Trace bound: $43$

Defining parameters

Level:	\( N \)	\(=\)	\( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4032.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1536\)
Trace bound:			\(43\)
Distinguishing \(T_p\):			\(5\), \(19\), \(43\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4032, [\chi])\).

	Total	New	Old
Modular forms	816	48	768
Cusp forms	720	48	672
Eisenstein series	96	0	96

Trace form

\( 48 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4032, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4032.2.j.a	$4032$	$2$	4032.j	24.f	$2$	$4$	$4$	$32.196$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\zeta_{8}^{3}q^{5}-\zeta_{8}q^{7}-\zeta_{8}^{2}q^{11}-2\zeta_{8}q^{13}+\cdots\)
4032.2.j.b	$4032$	$2$	4032.j	24.f	$2$	$4$	$4$	$32.196$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}q^{7}-\zeta_{8}^{2}q^{11}-6\zeta_{8}q^{13}-\zeta_{8}^{3}q^{23}+\cdots\)
4032.2.j.c	$4032$	$2$	4032.j	24.f	$2$	$4$	$4$	$32.196$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}q^{7}+\zeta_{8}^{2}q^{11}+6\zeta_{8}q^{13}-\zeta_{8}^{3}q^{23}+\cdots\)
4032.2.j.d	$4032$	$2$	4032.j	24.f	$2$	$4$	$4$	$32.196$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\zeta_{8}^{3}q^{5}-\zeta_{8}q^{7}-\zeta_{8}^{2}q^{11}+2\zeta_{8}q^{13}+\cdots\)
4032.2.j.e	$4032$	$2$	4032.j	24.f	$2$	$16$	$16$	$32.196$	16.0.\(\cdots\).1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{13}q^{5}+\beta _{1}q^{7}+\beta _{9}q^{11}-\beta _{5}q^{13}+\cdots\)
4032.2.j.f	$4032$	$2$	4032.j	24.f	$2$	$16$	$16$	$32.196$	16.0.\(\cdots\).1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{12}q^{5}+\beta _{8}q^{7}+(-\beta _{11}-\beta _{13}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4032, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4032, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1344, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2016, [\chi])\)\(^{\oplus 2}\)