Space of modular forms of level 6240, weight 2, and Character 6240.w

• Label: 6240.2.w
• Level: $6240$
• Weight: $2$
• Character orbit: 6240.w
• Rep. character: $\chi_{6240}(3121,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $8$
• Sturm bound: $2688$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 6240 = 2^{5} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6240.w (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(2688\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(6240, [\chi])\).

	Total	New	Old
Modular forms	1376	96	1280
Cusp forms	1312	96	1216
Eisenstein series	64	0	64

Trace form

\( 96 q + 16 q^{7} - 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(6240, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
6240.2.w.a	$6240$	$2$	6240.w	8.b	$2$	$2$	$2$	$49.827$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}-iq^{5}-q^{9}+2iq^{11}-iq^{13}+\cdots\)
6240.2.w.b	$6240$	$2$	6240.w	8.b	$2$	$2$	$2$	$49.827$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-iq^{5}-q^{9}+6iq^{11}+iq^{13}+\cdots\)
6240.2.w.c	$6240$	$2$	6240.w	8.b	$2$	$4$	$4$	$49.827$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}q^{3}-\zeta_{12}q^{5}+(-3+\zeta_{12}^{3})q^{7}+\cdots\)
6240.2.w.d	$6240$	$2$	6240.w	8.b	$2$	$4$	$4$	$49.827$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}q^{3}+\zeta_{8}q^{5}+(2+\zeta_{8}^{3})q^{7}-q^{9}+\cdots\)
6240.2.w.e	$6240$	$2$	6240.w	8.b	$2$	$16$	$16$	$49.827$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{3}-\beta _{9}q^{5}+\beta _{1}q^{7}-q^{9}+(-\beta _{9}+\cdots)q^{11}+\cdots\)
6240.2.w.f	$6240$	$2$	6240.w	8.b	$2$	$20$	$20$	$49.827$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{23}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}-\beta _{2}q^{5}+(1+\beta _{10})q^{7}-q^{9}+\cdots\)
6240.2.w.g	$6240$	$2$	6240.w	8.b	$2$	$22$	$22$	$49.827$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{2}]$
6240.2.w.h	$6240$	$2$	6240.w	8.b	$2$	$26$	$26$	$49.827$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(6240, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(6240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1040, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2080, [\chi])\)\(^{\oplus 2}\)