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

• Label: 4032.2.k
• Level: $4032$
• Weight: $2$
• Character orbit: 4032.k
• Rep. character: $\chi_{4032}(3905,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $8$
• Sturm bound: $1536$
• Trace bound: $67$

Defining parameters

Level:	\( N \)	\(=\)	\( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4032.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(1536\)
Trace bound:			\(67\)
Distinguishing \(T_p\):			\(5\), \(43\), \(67\)

Dimensions

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

	Total	New	Old
Modular forms	816	64	752
Cusp forms	720	64	656
Eisenstein series	96	0	96

Trace form

\( 64 q + O(q^{10}) \)

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.k.a	$4032$	$2$	4032.k	21.c	$2$	$4$	$4$	$32.196$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}+(-1+\beta _{1})q^{7}-\beta _{2}q^{11}+\cdots\)
4032.2.k.b	$4032$	$2$	4032.k	21.c	$2$	$4$	$4$	$32.196$	\(\Q(\sqrt{-2}, \sqrt{7})\)	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{7}+(-\beta _{1}+\beta _{3})q^{11}+(\beta _{1}+\beta _{3})q^{23}+\cdots\)
4032.2.k.c	$4032$	$2$	4032.k	21.c	$2$	$4$	$4$	$32.196$	\(\Q(\sqrt{-2}, \sqrt{7})\)	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{7}+(\beta _{1}-\beta _{3})q^{11}+(-\beta _{1}-\beta _{3})q^{23}+\cdots\)
4032.2.k.d	$4032$	$2$	4032.k	21.c	$2$	$4$	$4$	$32.196$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}+(1-\beta _{1})q^{7}+\beta _{2}q^{11}-2\beta _{1}q^{13}+\cdots\)
4032.2.k.e	$4032$	$2$	4032.k	21.c	$2$	$8$	$8$	$32.196$	\(\Q(\zeta_{16})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{16}^{7}q^{5}+(-1-\zeta_{16}^{6})q^{7}+(\zeta_{16}+\cdots)q^{11}+\cdots\)
4032.2.k.f	$4032$	$2$	4032.k	21.c	$2$	$8$	$8$	$32.196$	\(\Q(\zeta_{16})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{16}^{7}q^{5}+(1+\zeta_{16}^{4})q^{7}+(\zeta_{16}+\zeta_{16}^{2}+\cdots)q^{11}+\cdots\)
4032.2.k.g	$4032$	$2$	4032.k	21.c	$2$	$16$	$16$	$32.196$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{25}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}+\beta _{6}q^{7}-\beta _{3}q^{11}+\beta _{13}q^{13}+\cdots\)
4032.2.k.h	$4032$	$2$	4032.k	21.c	$2$	$16$	$16$	$32.196$	16.0.\(\cdots\).7	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{26}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+\beta _{3}q^{7}+\beta _{4}q^{11}+\beta _{9}q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(4032, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1344, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2016, [\chi])\)\(^{\oplus 2}\)