Space of modular forms of level 2240, weight 2, and Character 2240.n

• Label: 2240.2.n
• Level: $2240$
• Weight: $2$
• Character orbit: 2240.n
• Rep. character: $\chi_{2240}(1119,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $10$
• Sturm bound: $768$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2240.n (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 280 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(768\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(3\), \(11\), \(17\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2240, [\chi])\).

	Total	New	Old
Modular forms	408	96	312
Cusp forms	360	96	264
Eisenstein series	48	0	48

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(2240, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2240.2.n.a	$2240$	$2$	2240.n	280.n	$2$	$8$	$8$	$17.886$	8.0.1731891456.1	None		$4$	$0$	\(0\)	\(-4\)	\(-16\)	\(16\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{1})q^{3}+(-2-\beta _{5})q^{5}+(2+\cdots)q^{7}+\cdots\)
2240.2.n.b	$2240$	$2$	2240.n	280.n	$2$	$8$	$8$	$17.886$	8.0.1731891456.1	None		$4$	$0$	\(0\)	\(-4\)	\(16\)	\(-16\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{1})q^{3}+(2+\beta _{5})q^{5}+(-2+\cdots)q^{7}+\cdots\)
2240.2.n.c	$2240$	$2$	2240.n	280.n	$2$	$8$	$8$	$17.886$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{24}^{3}q^{5}-\zeta_{24}^{4}q^{7}-3q^{9}+2\zeta_{24}q^{11}+\cdots\)
2240.2.n.d	$2240$	$2$	2240.n	280.n	$2$	$8$	$8$	$17.886$	8.0.384160000.1	\(\Q(\sqrt{-70}) \)		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{5}-\beta _{3}q^{7}-3q^{9}-\beta _{2}q^{17}+\cdots\)
2240.2.n.e	$2240$	$2$	2240.n	280.n	$2$	$8$	$8$	$17.886$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{24}^{3}q^{5}+(-\zeta_{24}^{2}-\zeta_{24}^{4})q^{7}+\cdots\)
2240.2.n.f	$2240$	$2$	2240.n	280.n	$2$	$8$	$8$	$17.886$	8.0.384160000.1	\(\Q(\sqrt{-35}) \)		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}+\beta _{6}q^{5}-\beta _{3}q^{7}+2q^{9}-\beta _{5}q^{11}+\cdots\)
2240.2.n.g	$2240$	$2$	2240.n	280.n	$2$	$8$	$8$	$17.886$	8.0.1731891456.1	None		$4$	$0$	\(0\)	\(4\)	\(-16\)	\(-16\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-2+\beta _{5})q^{5}+(-2-\beta _{2}+\cdots)q^{7}+\cdots\)
2240.2.n.h	$2240$	$2$	2240.n	280.n	$2$	$8$	$8$	$17.886$	8.0.1731891456.1	None		$4$	$0$	\(0\)	\(4\)	\(16\)	\(16\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(2+\beta _{5})q^{5}+(2+\beta _{2})q^{7}+\cdots\)
2240.2.n.i	$2240$	$2$	2240.n	280.n	$2$	$16$	$16$	$17.886$	16.0.\(\cdots\).7	\(\Q(\sqrt{-14}) \)		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{22}$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta _{6}-\beta _{7})q^{3}-\beta _{11}q^{5}-\beta _{3}q^{7}+(3+\cdots)q^{9}+\cdots\)
2240.2.n.j	$2240$	$2$	2240.n	280.n	$2$	$16$	$16$	$17.886$	16.0.\(\cdots\).1	\(\Q(\sqrt{-35}) \)		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{24}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{3}q^{3}-\beta _{7}q^{5}+(\beta _{2}-\beta _{9})q^{7}+(3+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2240, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)