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

• Label: 4032.2.h
• Level: $4032$
• Weight: $2$
• Character orbit: 4032.h
• Rep. character: $\chi_{4032}(575,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $8$
• 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.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(1536\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\)

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.h.a	$4032$	$2$	4032.h	12.b	$2$	$4$	$4$	$32.196$	\(\Q(\zeta_{8})\)	None		$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}-\zeta_{8}^{3}q^{11}-6q^{13}+\cdots\)
4032.2.h.b	$4032$	$2$	4032.h	12.b	$2$	$4$	$4$	$32.196$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}+2\zeta_{8}^{3}q^{11}+5\zeta_{8}^{2}q^{17}+\cdots\)
4032.2.h.c	$4032$	$2$	4032.h	12.b	$2$	$4$	$4$	$32.196$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}+\zeta_{8}^{3}q^{11}+2q^{13}+\cdots\)
4032.2.h.d	$4032$	$2$	4032.h	12.b	$2$	$4$	$4$	$32.196$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{7}+3\zeta_{8}^{3}q^{11}+2q^{13}+2\zeta_{8}^{2}q^{17}+\cdots\)
4032.2.h.e	$4032$	$2$	4032.h	12.b	$2$	$4$	$4$	$32.196$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}+4\zeta_{8}^{3}q^{11}+4q^{13}+\cdots\)
4032.2.h.f	$4032$	$2$	4032.h	12.b	$2$	$8$	$8$	$32.196$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\zeta_{24}^{2}+\zeta_{24}^{7})q^{5}+\zeta_{24}q^{7}+(\zeta_{24}^{3}+\cdots)q^{11}+\cdots\)
4032.2.h.g	$4032$	$2$	4032.h	12.b	$2$	$8$	$8$	$32.196$	8.0.5473632256.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{5}+\beta _{6})q^{5}-\beta _{1}q^{7}+(-\beta _{4}-2\beta _{7})q^{11}+\cdots\)
4032.2.h.h	$4032$	$2$	4032.h	12.b	$2$	$12$	$12$	$32.196$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}+\beta _{3}q^{7}+(-\beta _{5}-\beta _{6})q^{11}+\cdots\)

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

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