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

• Label: 4032.2.v
• Level: $4032$
• Weight: $2$
• Character orbit: 4032.v
• Rep. character: $\chi_{4032}(1583,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $96$
• Newform subspaces: $5$
• Sturm bound: $1536$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4032.v (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 48 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(1536\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	1600	96	1504
Cusp forms	1472	96	1376
Eisenstein series	128	0	128

Trace form

\( 96 q + 32 q^{19} - 64 q^{43} + 96 q^{49} - 128 q^{55} + 64 q^{61} - 16 q^{67} + 64 q^{85}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4032.2.v.a	$4032$	$2$	4032.v	48.k	$4$	$4$	$2$	$32.196$	\(\Q(\zeta_{8})\)	None					1008.2.v.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta_{3}+\beta_{2})q^{5}-q^{7}+(\beta_{3}-\beta_{2})q^{11}+\cdots\)
4032.2.v.b	$4032$	$2$	4032.v	48.k	$4$	$4$	$2$	$32.196$	\(\Q(\zeta_{8})\)	None					1008.2.v.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta_{3}+\beta_{2})q^{5}-q^{7}+(-2\beta_{3}+2\beta_{2})q^{11}+\cdots\)
4032.2.v.c	$4032$	$2$	4032.v	48.k	$4$	$12$	$6$	$32.196$	12.0.\(\cdots\).1	None					1008.2.v.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$2^{12}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta _{3}-\beta _{5})q^{5}+q^{7}+(\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{11}+\cdots\)
4032.2.v.d	$4032$	$2$	4032.v	48.k	$4$	$36$	$18$	$32.196$		None					1008.2.v.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(36\)		$\mathrm{SU}(2)[C_{4}]$
4032.2.v.e	$4032$	$2$	4032.v	48.k	$4$	$40$	$20$	$32.196$		None			✓		1008.2.v.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-40\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(4032, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1344, [\chi])\)\(^{\oplus 2}\)