Space of modular forms of level 6048, weight 2, and Character 6048.h

• Label: 6048.2.h
• Level: $6048$
• Weight: $2$
• Character orbit: 6048.h
• Rep. character: $\chi_{6048}(2591,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $9$
• Sturm bound: $2304$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6048.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(2304\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(6048, [\chi])\).

	Total	New	Old
Modular forms	1200	96	1104
Cusp forms	1104	96	1008
Eisenstein series	96	0	96

Trace form

\( 96 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(6048, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
6048.2.h.a	$6048$	$2$	6048.h	12.b	$2$	$8$	$8$	$48.294$	\(\Q(\zeta_{24})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\zeta_{24}+\zeta_{24}^{2}+\zeta_{24}^{7})q^{5}+\zeta_{24}q^{7}+\cdots\)
6048.2.h.b	$6048$	$2$	6048.h	12.b	$2$	$8$	$8$	$48.294$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2\zeta_{24}^{3}+3\zeta_{24}^{5})q^{5}-\zeta_{24}q^{7}+(3\zeta_{24}^{6}+\cdots)q^{11}+\cdots\)
6048.2.h.c	$6048$	$2$	6048.h	12.b	$2$	$8$	$8$	$48.294$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{24}^{2}+\zeta_{24}^{3})q^{5}-\zeta_{24}q^{7}+\zeta_{24}^{6}q^{11}+\cdots\)
6048.2.h.d	$6048$	$2$	6048.h	12.b	$2$	$8$	$8$	$48.294$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\zeta_{24}^{2}-\zeta_{24}^{3})q^{5}-\zeta_{24}q^{7}+(2\zeta_{24}^{4}+\cdots)q^{11}+\cdots\)
6048.2.h.e	$6048$	$2$	6048.h	12.b	$2$	$8$	$8$	$48.294$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\zeta_{24}^{3}q^{5}+\zeta_{24}q^{7}+(2\zeta_{24}^{4}+2\zeta_{24}^{6}+\cdots)q^{11}+\cdots\)
6048.2.h.f	$6048$	$2$	6048.h	12.b	$2$	$8$	$8$	$48.294$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2\zeta_{24}^{4}-\zeta_{24}^{7})q^{5}+\zeta_{24}q^{7}+\cdots\)
6048.2.h.g	$6048$	$2$	6048.h	12.b	$2$	$8$	$8$	$48.294$	\(\Q(\zeta_{24})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\zeta_{24}+\zeta_{24}^{2}+\zeta_{24}^{3}+\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
6048.2.h.h	$6048$	$2$	6048.h	12.b	$2$	$16$	$16$	$48.294$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{12}q^{5}+\beta _{3}q^{7}+(-\beta _{11}+\beta _{13}+\cdots)q^{11}+\cdots\)
6048.2.h.i	$6048$	$2$	6048.h	12.b	$2$	$24$	$24$	$48.294$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(6048, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(6048, [\chi]) \cong \)