Space of modular forms of level 5040, weight 2, and Character 5040.d

• Label: 5040.2.d
• Level: $5040$
• Weight: $2$
• Character orbit: 5040.d
• Rep. character: $\chi_{5040}(4591,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $8$
• Sturm bound: $2304$
• Trace bound: $29$

Defining parameters

Level:	\( N \)	\(=\)	\( 5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5040.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(2304\)
Trace bound:			\(29\)
Distinguishing \(T_p\):			\(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5040, [\chi])\).

	Total	New	Old
Modular forms	1200	80	1120
Cusp forms	1104	80	1024
Eisenstein series	96	0	96

Trace form

\( 80 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5040, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5040.2.d.a	$5040$	$2$	5040.d	28.d	$2$	$4$	$4$	$40.245$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{11}+\cdots\)
5040.2.d.b	$5040$	$2$	5040.d	28.d	$2$	$4$	$4$	$40.245$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+(\beta _{1}+\beta _{3})q^{7}-\beta _{2}q^{11}+(-2\beta _{1}+\cdots)q^{13}+\cdots\)
5040.2.d.c	$5040$	$2$	5040.d	28.d	$2$	$8$	$8$	$40.245$	8.0.40960000.1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+(-\beta _{3}+\beta _{5})q^{7}-\beta _{4}q^{11}+\cdots\)
5040.2.d.d	$5040$	$2$	5040.d	28.d	$2$	$8$	$8$	$40.245$	8.0.\(\cdots\).7	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}+(\beta _{1}-\beta _{6})q^{7}+(-\beta _{1}-\beta _{4}+\cdots)q^{11}+\cdots\)
5040.2.d.e	$5040$	$2$	5040.d	28.d	$2$	$8$	$8$	$40.245$	8.0.303595776.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{5}+(-\beta _{1}+\beta _{5}+\beta _{6})q^{7}-\beta _{1}q^{11}+\cdots\)
5040.2.d.f	$5040$	$2$	5040.d	28.d	$2$	$12$	$12$	$40.245$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+\beta _{9}q^{7}-\beta _{7}q^{11}+(2\beta _{1}+\beta _{5}+\cdots)q^{13}+\cdots\)
5040.2.d.g	$5040$	$2$	5040.d	28.d	$2$	$12$	$12$	$40.245$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}-\beta _{8}q^{7}-\beta _{7}q^{11}+(-2\beta _{1}+\cdots)q^{13}+\cdots\)
5040.2.d.h	$5040$	$2$	5040.d	28.d	$2$	$24$	$24$	$40.245$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(5040, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5040, [\chi]) \cong \)