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

• Label: 6048.2.c
• Level: $6048$
• Weight: $2$
• Character orbit: 6048.c
• Rep. character: $\chi_{6048}(3025,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $7$
• Sturm bound: $2304$
• Trace bound: $31$

Defining parameters

Level:	\( N \)	\(=\)	\( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6048.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(2304\)
Trace bound:			\(31\)
Distinguishing \(T_p\):			\(5\), \(17\)

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

\( 96 q - 96 q^{25} + 16 q^{31} + 96 q^{49} - 32 q^{55} - 80 q^{79}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
6048.2.c.a	$6048$	$2$	6048.c	8.b	$2$	$2$	$2$	$48.294$	\(\Q(\sqrt{-1}) \)	None					1512.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{5}+q^{7}-5 i q^{13}-q^{17}+4 i q^{19}+\cdots\)
6048.2.c.b	$6048$	$2$	6048.c	8.b	$2$	$2$	$2$	$48.294$	\(\Q(\sqrt{-1}) \)	None					1512.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{5}+q^{7}+5 i q^{13}+q^{17}-4 i q^{19}+\cdots\)
6048.2.c.c	$6048$	$2$	6048.c	8.b	$2$	$8$	$8$	$48.294$	8.0.3317760000.5	None					1512.2.c.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{5}+q^{7}+(2\beta _{2}+\beta _{6})q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots\)
6048.2.c.d	$6048$	$2$	6048.c	8.b	$2$	$16$	$16$	$48.294$	\(\Q(\zeta_{40})\)	None					1512.2.c.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{12}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{12}+\beta_{11})q^{5}+q^{7}-\beta_{12} q^{11}+\cdots\)
6048.2.c.e	$6048$	$2$	6048.c	8.b	$2$	$20$	$20$	$48.294$	20.0.\(\cdots\).1	None					1512.2.c.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(20\)	$2^{18}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{12}q^{5}+q^{7}+(-\beta _{4}-\beta _{10}+\beta _{12}+\cdots)q^{11}+\cdots\)
6048.2.c.f	$6048$	$2$	6048.c	8.b	$2$	$24$	$24$	$48.294$		None					1512.2.c.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-24\)		$\mathrm{SU}(2)[C_{2}]$
6048.2.c.g	$6048$	$2$	6048.c	8.b	$2$	$24$	$24$	$48.294$		None					1512.2.c.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-24\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(6048, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1512, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2016, [\chi])\)\(^{\oplus 2}\)