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

• Label: 4032.2.c
• Level: $4032$
• Weight: $2$
• Character orbit: 4032.c
• Rep. character: $\chi_{4032}(2017,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $18$
• Sturm bound: $1536$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4032.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(1536\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(17\), \(23\), \(31\)

Dimensions

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

	Total	New	Old
Modular forms	816	60	756
Cusp forms	720	60	660
Eisenstein series	96	0	96

Trace form

\( 60 q + O(q^{10}) \)

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.c.a	$4032$	$2$	4032.c	8.b	$2$	$2$	$2$	$32.196$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}-q^{7}+2iq^{11}-iq^{13}-2q^{17}+\cdots\)
4032.2.c.b	$4032$	$2$	4032.c	8.b	$2$	$2$	$2$	$32.196$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{5}-q^{7}+iq^{11}-2iq^{13}-2q^{17}+\cdots\)
4032.2.c.c	$4032$	$2$	4032.c	8.b	$2$	$2$	$2$	$32.196$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}-q^{7}-iq^{11}-iq^{13}-2q^{17}+\cdots\)
4032.2.c.d	$4032$	$2$	4032.c	8.b	$2$	$2$	$2$	$32.196$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}-q^{7}+2iq^{11}+iq^{13}+2q^{17}+\cdots\)
4032.2.c.e	$4032$	$2$	4032.c	8.b	$2$	$2$	$2$	$32.196$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}-q^{7}-iq^{11}+3iq^{13}+6q^{17}+\cdots\)
4032.2.c.f	$4032$	$2$	4032.c	8.b	$2$	$2$	$2$	$32.196$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{5}+q^{7}-iq^{11}-2iq^{13}-2q^{17}+\cdots\)
4032.2.c.g	$4032$	$2$	4032.c	8.b	$2$	$2$	$2$	$32.196$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}+q^{7}+iq^{11}-iq^{13}-2q^{17}+\cdots\)
4032.2.c.h	$4032$	$2$	4032.c	8.b	$2$	$2$	$2$	$32.196$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}+q^{7}-2iq^{11}-iq^{13}-2q^{17}+\cdots\)
4032.2.c.i	$4032$	$2$	4032.c	8.b	$2$	$2$	$2$	$32.196$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}+q^{7}-2iq^{11}+iq^{13}+2q^{17}+\cdots\)
4032.2.c.j	$4032$	$2$	4032.c	8.b	$2$	$2$	$2$	$32.196$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}+q^{7}+iq^{11}+3iq^{13}+6q^{17}+\cdots\)
4032.2.c.k	$4032$	$2$	4032.c	8.b	$2$	$4$	$4$	$32.196$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}q^{5}-q^{7}-2\zeta_{12}q^{11}+(-2\zeta_{12}+\cdots)q^{13}+\cdots\)
4032.2.c.l	$4032$	$2$	4032.c	8.b	$2$	$4$	$4$	$32.196$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{3}q^{5}-q^{7}+(-\zeta_{12}^{2}-\zeta_{12}^{3})q^{11}+\cdots\)
4032.2.c.m	$4032$	$2$	4032.c	8.b	$2$	$4$	$4$	$32.196$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{3}q^{5}-q^{7}+(\zeta_{12}^{2}+3\zeta_{12}^{3})q^{11}+\cdots\)
4032.2.c.n	$4032$	$2$	4032.c	8.b	$2$	$4$	$4$	$32.196$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}q^{5}+q^{7}+2\zeta_{12}q^{11}+(-2\zeta_{12}+\cdots)q^{13}+\cdots\)
4032.2.c.o	$4032$	$2$	4032.c	8.b	$2$	$4$	$4$	$32.196$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{3}q^{5}+q^{7}+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{11}+\cdots\)
4032.2.c.p	$4032$	$2$	4032.c	8.b	$2$	$4$	$4$	$32.196$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{3}q^{5}+q^{7}+(-\zeta_{12}^{2}-3\zeta_{12}^{3})q^{11}+\cdots\)
4032.2.c.q	$4032$	$2$	4032.c	8.b	$2$	$8$	$8$	$32.196$	8.0.897122304.10	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{5}-q^{7}+\beta _{5}q^{11}+(-\beta _{4}-\beta _{6}+\cdots)q^{13}+\cdots\)
4032.2.c.r	$4032$	$2$	4032.c	8.b	$2$	$8$	$8$	$32.196$	8.0.897122304.10	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{5}+q^{7}-\beta _{5}q^{11}+(-\beta _{4}-\beta _{6}+\cdots)q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(4032, [\chi]) \cong \)