Space of modular forms of level 2280, weight 2, and Character 2280.j

• Label: 2280.2.j
• Level: $2280$
• Weight: $2$
• Character orbit: 2280.j
• Rep. character: $\chi_{2280}(1369,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $9$
• Sturm bound: $960$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2280.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(960\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2280, [\chi])\).

	Total	New	Old
Modular forms	496	56	440
Cusp forms	464	56	408
Eisenstein series	32	0	32

Trace form

\( 56 q - 8 q^{5} - 56 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2280, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2280.2.j.a	$2280$	$2$	2280.j	5.b	$2$	$2$	$2$	$18.206$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(-2+i)q^{5}+4iq^{7}-q^{9}+\cdots\)
2280.2.j.b	$2280$	$2$	2280.j	5.b	$2$	$2$	$2$	$18.206$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(-1+2i)q^{5}+2iq^{7}-q^{9}+\cdots\)
2280.2.j.c	$2280$	$2$	2280.j	5.b	$2$	$2$	$2$	$18.206$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+(-1-2i)q^{5}+2iq^{7}-q^{9}+\cdots\)
2280.2.j.d	$2280$	$2$	2280.j	5.b	$2$	$2$	$2$	$18.206$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+(-1-2i)q^{5}+2iq^{7}-q^{9}+\cdots\)
2280.2.j.e	$2280$	$2$	2280.j	5.b	$2$	$2$	$2$	$18.206$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(-1-2i)q^{5}+4iq^{7}-q^{9}+\cdots\)
2280.2.j.f	$2280$	$2$	2280.j	5.b	$2$	$6$	$6$	$18.206$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(\beta _{1}-\beta _{4})q^{5}+(-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
2280.2.j.g	$2280$	$2$	2280.j	5.b	$2$	$10$	$10$	$18.206$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{3}+(1-\beta _{2}-\beta _{4})q^{5}+(\beta _{6}+\beta _{9})q^{7}+\cdots\)
2280.2.j.h	$2280$	$2$	2280.j	5.b	$2$	$12$	$12$	$18.206$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}+\beta _{10}q^{5}+\beta _{2}q^{7}-q^{9}-\beta _{8}q^{11}+\cdots\)
2280.2.j.i	$2280$	$2$	2280.j	5.b	$2$	$18$	$18$	$18.206$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{9}q^{3}+\beta _{2}q^{5}-\beta _{5}q^{7}-q^{9}-\beta _{3}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2280, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)