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

• Label: 2280.2.bg
• Level: $2280$
• Weight: $2$
• Character orbit: 2280.bg
• Rep. character: $\chi_{2280}(121,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $80$
• Newform subspaces: $22$
• Sturm bound: $960$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2280.bg (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 22 \)
Sturm bound:			\(960\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	992	80	912
Cusp forms	928	80	848
Eisenstein series	64	0	64

Trace form

\( 80 q - 4 q^{3} - 8 q^{7} - 40 q^{9} + O(q^{10}) \)

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.bg.a	$2280$	$2$	2280.bg	19.c	$3$	$2$	$1$	$18.206$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-2q^{7}+\cdots\)
2280.2.bg.b	$2280$	$2$	2280.bg	19.c	$3$	$2$	$1$	$18.206$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-2q^{7}+\cdots\)
2280.2.bg.c	$2280$	$2$	2280.bg	19.c	$3$	$2$	$1$	$18.206$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-2q^{7}+\cdots\)
2280.2.bg.d	$2280$	$2$	2280.bg	19.c	$3$	$2$	$1$	$18.206$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}+3q^{7}+\cdots\)
2280.2.bg.e	$2280$	$2$	2280.bg	19.c	$3$	$2$	$1$	$18.206$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}+3q^{7}+\cdots\)
2280.2.bg.f	$2280$	$2$	2280.bg	19.c	$3$	$2$	$1$	$18.206$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(1\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+q^{7}+\cdots\)
2280.2.bg.g	$2280$	$2$	2280.bg	19.c	$3$	$2$	$1$	$18.206$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-2q^{7}+\cdots\)
2280.2.bg.h	$2280$	$2$	2280.bg	19.c	$3$	$2$	$1$	$18.206$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(-1\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-q^{7}+\cdots\)
2280.2.bg.i	$2280$	$2$	2280.bg	19.c	$3$	$2$	$1$	$18.206$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
2280.2.bg.j	$2280$	$2$	2280.bg	19.c	$3$	$2$	$1$	$18.206$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(-1\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}+3q^{7}+\cdots\)
2280.2.bg.k	$2280$	$2$	2280.bg	19.c	$3$	$2$	$1$	$18.206$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(-1\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}+3q^{7}+\cdots\)
2280.2.bg.l	$2280$	$2$	2280.bg	19.c	$3$	$4$	$2$	$18.206$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(-2\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{2})q^{3}+(-1+\beta _{2})q^{5}+(1+\cdots)q^{7}+\cdots\)
2280.2.bg.m	$2280$	$2$	2280.bg	19.c	$3$	$4$	$2$	$18.206$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(-2\)	\(2\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{2})q^{3}+(1-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
2280.2.bg.n	$2280$	$2$	2280.bg	19.c	$3$	$4$	$2$	$18.206$	\(\Q(\sqrt{-3}, \sqrt{65})\)	None		$2$	$0$	\(0\)	\(-2\)	\(2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{2})q^{3}+(1-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
2280.2.bg.o	$2280$	$2$	2280.bg	19.c	$3$	$4$	$2$	$18.206$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(-2\)	\(2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{2})q^{3}+(1-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots\)
2280.2.bg.p	$2280$	$2$	2280.bg	19.c	$3$	$4$	$2$	$18.206$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(2\)	\(2\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{2})q^{3}+(1-\beta _{2})q^{5}+(-1+\beta _{3})q^{7}+\cdots\)
2280.2.bg.q	$2280$	$2$	2280.bg	19.c	$3$	$4$	$2$	$18.206$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(2\)	\(2\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{2})q^{3}+(1-\beta _{2})q^{5}+(-1+\beta _{3})q^{7}+\cdots\)
2280.2.bg.r	$2280$	$2$	2280.bg	19.c	$3$	$4$	$2$	$18.206$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(2\)	\(2\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{3}+\beta _{2}q^{5}+(2-\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots\)
2280.2.bg.s	$2280$	$2$	2280.bg	19.c	$3$	$6$	$3$	$18.206$	6.0.2696112.1	None		$2$	$0$	\(0\)	\(3\)	\(3\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{4}q^{3}+\beta _{4}q^{5}+(-1-\beta _{2})q^{7}+(-1+\cdots)q^{9}+\cdots\)
2280.2.bg.t	$2280$	$2$	2280.bg	19.c	$3$	$8$	$4$	$18.206$	8.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(-4\)	\(-4\)	\(-6\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{5})q^{3}+(-1-\beta _{5})q^{5}+(-1+\cdots)q^{7}+\cdots\)
2280.2.bg.u	$2280$	$2$	2280.bg	19.c	$3$	$8$	$4$	$18.206$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(-4\)	\(4\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{3})q^{3}+(1-\beta _{3})q^{5}+(1-\beta _{5}+\cdots)q^{7}+\cdots\)
2280.2.bg.v	$2280$	$2$	2280.bg	19.c	$3$	$8$	$4$	$18.206$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(4\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{3})q^{3}+(-1-\beta _{3})q^{5}+(\beta _{2}+\beta _{5}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)