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

• Label: 2240.2.b
• Level: $2240$
• Weight: $2$
• Character orbit: 2240.b
• Rep. character: $\chi_{2240}(1121,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $8$
• Sturm bound: $768$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2240.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(768\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(23\), \(31\)

Dimensions

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

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

Trace form

\( 48 q - 48 q^{9} + O(q^{10}) \)

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.b.a	$2240$	$2$	2240.b	8.b	$2$	$2$	$2$	$17.886$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}-q^{7}+3q^{9}-2iq^{11}-2iq^{13}+\cdots\)
2240.2.b.b	$2240$	$2$	2240.b	8.b	$2$	$2$	$2$	$17.886$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}+q^{7}+3q^{9}+2iq^{11}-2iq^{13}+\cdots\)
2240.2.b.c	$2240$	$2$	2240.b	8.b	$2$	$4$	$4$	$17.886$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}-q^{7}-\zeta_{12}q^{11}+\cdots\)
2240.2.b.d	$2240$	$2$	2240.b	8.b	$2$	$4$	$4$	$17.886$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}+q^{7}+\zeta_{12}q^{11}+\cdots\)
2240.2.b.e	$2240$	$2$	2240.b	8.b	$2$	$6$	$6$	$17.886$	6.0.3534400.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}+\beta _{4}q^{5}-q^{7}+(-2-\beta _{1}+\cdots)q^{9}+\cdots\)
2240.2.b.f	$2240$	$2$	2240.b	8.b	$2$	$6$	$6$	$17.886$	6.0.3534400.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}-\beta _{4}q^{5}+q^{7}+(-2-\beta _{1}+\cdots)q^{9}+\cdots\)
2240.2.b.g	$2240$	$2$	2240.b	8.b	$2$	$12$	$12$	$17.886$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{11}q^{3}+\beta _{9}q^{5}-q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)
2240.2.b.h	$2240$	$2$	2240.b	8.b	$2$	$12$	$12$	$17.886$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{11}q^{3}-\beta _{9}q^{5}+q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)