Space of modular forms of level 2280, weight 2, and trivial character

• Label: 2280.2.a
• Level: $2280$
• Weight: $2$
• Character orbit: 2280.a
• Rep. character: $\chi_{2280}(1,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $21$
• 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.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 21 \)
Sturm bound:			\(960\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2280))\).

	Total	New	Old
Modular forms	496	36	460
Cusp forms	465	36	429
Eisenstein series	31	0	31

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	\(5\)	\(19\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(2\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(3\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(1\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(1\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(4\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(2\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(2\)
Plus space				\(+\)	\(14\)
Minus space				\(-\)	\(22\)

Trace form

\( 36 q + 36 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2280))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	5	19
2280.2.a.a	$2280$	$2$	2280.a	1.a	$1$	$1$	$1$	$18.206$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}-2q^{13}-q^{15}-6q^{17}+\cdots\)
2280.2.a.b	$2280$	$2$	2280.a	1.a	$1$	$1$	$1$	$18.206$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
2280.2.a.c	$2280$	$2$	2280.a	1.a	$1$	$1$	$1$	$18.206$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
2280.2.a.d	$2280$	$2$	2280.a	1.a	$1$	$1$	$1$	$18.206$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}+q^{9}+6q^{11}+4q^{13}+\cdots\)
2280.2.a.e	$2280$	$2$	2280.a	1.a	$1$	$1$	$1$	$18.206$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
2280.2.a.f	$2280$	$2$	2280.a	1.a	$1$	$1$	$1$	$18.206$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
2280.2.a.g	$2280$	$2$	2280.a	1.a	$1$	$1$	$1$	$18.206$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
2280.2.a.h	$2280$	$2$	2280.a	1.a	$1$	$1$	$1$	$18.206$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
2280.2.a.i	$2280$	$2$	2280.a	1.a	$1$	$1$	$1$	$18.206$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(4\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
2280.2.a.j	$2280$	$2$	2280.a	1.a	$1$	$1$	$1$	$18.206$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+4q^{7}+q^{9}+2q^{13}+q^{15}+\cdots\)
2280.2.a.k	$2280$	$2$	2280.a	1.a	$1$	$2$	$2$	$18.206$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
2280.2.a.l	$2280$	$2$	2280.a	1.a	$1$	$2$	$2$	$18.206$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+\beta q^{7}+q^{9}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
2280.2.a.m	$2280$	$2$	2280.a	1.a	$1$	$2$	$2$	$18.206$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(2\)		$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
2280.2.a.n	$2280$	$2$	2280.a	1.a	$1$	$2$	$2$	$18.206$	\(\Q(\sqrt{7}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(-2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(-1+\beta )q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
2280.2.a.o	$2280$	$2$	2280.a	1.a	$1$	$2$	$2$	$18.206$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(-2+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
2280.2.a.p	$2280$	$2$	2280.a	1.a	$1$	$2$	$2$	$18.206$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(6\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(3+\beta )q^{7}+q^{9}+(1-\beta )q^{11}+\cdots\)
2280.2.a.q	$2280$	$2$	2280.a	1.a	$1$	$2$	$2$	$18.206$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(-6\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(-3+\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
2280.2.a.r	$2280$	$2$	2280.a	1.a	$1$	$3$	$3$	$18.206$	3.3.568.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-3\)	\(-2\)		$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(-1-\beta _{2})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
2280.2.a.s	$2280$	$2$	2280.a	1.a	$1$	$3$	$3$	$18.206$	3.3.316.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(3\)	\(-2\)		$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(-1+\beta _{1})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
2280.2.a.t	$2280$	$2$	2280.a	1.a	$1$	$3$	$3$	$18.206$	3.3.1016.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+\beta _{2}q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
2280.2.a.u	$2280$	$2$	2280.a	1.a	$1$	$3$	$3$	$18.206$	3.3.1772.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(3\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+\beta _{2}q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2280))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2280)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(285))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(380))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(456))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(570))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(760))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1140))\)\(^{\oplus 2}\)