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

• Label: 2240.2.e
• Level: $2240$
• Weight: $2$
• Character orbit: 2240.e
• Rep. character: $\chi_{2240}(2239,\cdot)$
• Character field: $\Q$
• Dimension: $92$
• Newform subspaces: $7$
• Sturm bound: $768$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2240.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 140 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(768\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	408	100	308
Cusp forms	360	92	268
Eisenstein series	48	8	40

Trace form

\( 92 q - 92 q^{9} + O(q^{10}) \)

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.e.a	$2240$	$2$	2240.e	140.c	$2$	$4$	$4$	$17.886$	\(\Q(\sqrt{2}, \sqrt{-5})\)	\(\Q(\sqrt{-5}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(2\beta _{1}+\beta _{2})q^{3}-\beta _{3}q^{5}+(\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)
2240.2.e.b	$2240$	$2$	2240.e	140.c	$2$	$4$	$4$	$17.886$	\(\Q(\sqrt{5}, \sqrt{-7})\)	\(\Q(\sqrt{-35}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}-4q^{9}+\beta _{3}q^{11}+\cdots\)
2240.2.e.c	$2240$	$2$	2240.e	140.c	$2$	$4$	$4$	$17.886$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-5}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{3}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
2240.2.e.d	$2240$	$2$	2240.e	140.c	$2$	$8$	$8$	$17.886$	8.0.121550625.1	\(\Q(\sqrt{-35}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{6}q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{6})q^{7}+(-3+\cdots)q^{9}+\cdots\)
2240.2.e.e	$2240$	$2$	2240.e	140.c	$2$	$8$	$8$	$17.886$	8.0.\(\cdots\).5	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}+\beta _{4}q^{5}-\beta _{1}q^{7}+q^{9}+2\beta _{3}q^{11}+\cdots\)
2240.2.e.f	$2240$	$2$	2240.e	140.c	$2$	$16$	$16$	$17.886$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{3}-\beta _{10}q^{5}+(-\beta _{6}+\beta _{8})q^{7}+\cdots\)
2240.2.e.g	$2240$	$2$	2240.e	140.c	$2$	$48$	$48$	$17.886$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(2240, [\chi]) \cong \)