Space of modular forms of level 8280, weight 2, and trivial character

• Label: 8280.2.a
• Level: $8280$
• Weight: $2$
• Character orbit: 8280.a
• Rep. character: $\chi_{8280}(1,\cdot)$
• Character field: $\Q$
• Dimension: $110$
• Newform subspaces: $49$
• Sturm bound: $3456$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8280.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 49 \)
Sturm bound:			\(3456\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8280))\).

	Total	New	Old
Modular forms	1760	110	1650
Cusp forms	1697	110	1587
Eisenstein series	63	0	63

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

\(2\)	\(3\)	\(5\)	\(23\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(7\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(4\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(4\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(7\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(9\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(8\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(8\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(9\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(7\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(4\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(7\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(6\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(10\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(10\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(6\)
Plus space				\(+\)	\(50\)
Minus space				\(-\)	\(60\)

Trace form

110 * q - 8 * q^7 + 4 * q^11 - 12 * q^13 - 20 * q^17 - 20 * q^19 + 110 * q^25 - 8 * q^29 + 16 * q^31 - 12 * q^35 - 8 * q^37 - 12 * q^41 + 4 * q^43 + 94 * q^49 + 24 * q^53 - 4 * q^59 + 16 * q^61 - 28 * q^67 + 20 * q^73 + 16 * q^77 - 20 * q^83 - 4 * q^85 - 36 * q^89 - 8 * q^91 - 8 * q^95 + 44 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8280))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	23
8280.2.a.a	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	\(\Q\)	None	✓				2760.2.a.j	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-3\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{7}+4q^{11}-3q^{17}-4q^{19}+\cdots\)
8280.2.a.b	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	\(\Q\)	None	✓	✓			8280.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-2q^{13}-6q^{17}+q^{23}+\cdots\)
8280.2.a.c	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	\(\Q\)	None	✓	✓			8280.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-2q^{13}+2q^{17}-4q^{19}+\cdots\)
8280.2.a.d	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	\(\Q\)	None	✓				920.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}+q^{13}-q^{23}+q^{25}+\cdots\)
8280.2.a.e	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	\(\Q\)	None	✓				920.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{11}-5q^{13}+4q^{17}-2q^{19}+\cdots\)
8280.2.a.f	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	\(\Q\)	None	✓				2760.2.a.k	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{11}-6q^{17}+8q^{19}+q^{23}+\cdots\)
8280.2.a.g	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	\(\Q\)	None	✓				2760.2.a.e	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{11}-2q^{13}-2q^{17}+4q^{19}+\cdots\)
8280.2.a.h	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	\(\Q\)	None	✓	✓			8280.2.a.h	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{11}+4q^{13}+4q^{17}+4q^{19}+\cdots\)
8280.2.a.i	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	\(\Q\)	None	✓				2760.2.a.f	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-4q^{13}+q^{17}-q^{23}+\cdots\)
8280.2.a.j	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	\(\Q\)	None	✓				920.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+6q^{11}-2q^{13}+3q^{17}+\cdots\)
8280.2.a.k	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	\(\Q\)	None	✓	✓			8280.2.a.k	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-4q^{11}+2q^{13}+2q^{17}+\cdots\)
8280.2.a.l	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	\(\Q\)	None	✓				2760.2.a.g	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}+2q^{11}+2q^{13}+8q^{17}+\cdots\)
8280.2.a.m	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	\(\Q\)	None	✓	✓			8280.2.a.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-2q^{13}-2q^{17}-4q^{19}+\cdots\)
8280.2.a.n	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	\(\Q\)	None	✓	✓			8280.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-2q^{13}+6q^{17}-q^{23}+\cdots\)
8280.2.a.o	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	\(\Q\)	None	✓				920.2.a.d	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+q^{13}+4q^{17}-4q^{19}+\cdots\)
8280.2.a.p	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	\(\Q\)	None	✓				2760.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{11}+2q^{13}-2q^{17}+q^{23}+\cdots\)
8280.2.a.q	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	\(\Q\)	None	✓	✓			8280.2.a.h	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{11}+4q^{13}-4q^{17}+4q^{19}+\cdots\)
8280.2.a.r	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	\(\Q\)	None	✓				2760.2.a.h	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{13}+6q^{17}+q^{23}+q^{25}+\cdots\)
8280.2.a.s	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	\(\Q\)	None	✓	✓			8280.2.a.k	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
8280.2.a.t	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	\(\Q\)	None	✓				2760.2.a.b	$1$	$0$	\(0\)	\(0\)	\(1\)	\(3\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+3q^{7}+2q^{11}+2q^{13}+q^{17}+\cdots\)
8280.2.a.u	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	\(\Q\)	None	✓				2760.2.a.i	$1$	$0$	\(0\)	\(0\)	\(1\)	\(3\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+3q^{7}+6q^{11}-2q^{13}-3q^{17}+\cdots\)
8280.2.a.v	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	\(\Q\)	None	✓				2760.2.a.d	$1$	$0$	\(0\)	\(0\)	\(1\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}-4q^{11}+6q^{13}+2q^{17}+\cdots\)
8280.2.a.w	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	\(\Q\)	None	✓				2760.2.a.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}+6q^{11}-4q^{13}-2q^{17}+\cdots\)
8280.2.a.x	$8280$	$2$	8280.a	1.a	$1$	$2$	$2$	$66.116$	\(\Q(\sqrt{2}) \)	None	✓				2760.2.a.n	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(-1+2\beta )q^{7}+\beta q^{11}+(2-\beta )q^{13}+\cdots\)
8280.2.a.y	$8280$	$2$	8280.a	1.a	$1$	$2$	$2$	$66.116$	\(\Q(\sqrt{2}) \)	None	✓				2760.2.a.q	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}+(2-3\beta )q^{11}+(-4-\beta )q^{13}+\cdots\)
8280.2.a.z	$8280$	$2$	8280.a	1.a	$1$	$2$	$2$	$66.116$	\(\Q(\sqrt{33}) \)	None	✓				2760.2.a.o	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta q^{7}-4q^{11}+(-2+2\beta )q^{13}+\cdots\)
8280.2.a.ba	$8280$	$2$	8280.a	1.a	$1$	$2$	$2$	$66.116$	\(\Q(\sqrt{6}) \)	None	✓	✓	✓		8280.2.a.ba	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(1+\beta )q^{7}+\beta q^{11}+(-2-\beta )q^{13}+\cdots\)
8280.2.a.bb	$8280$	$2$	8280.a	1.a	$1$	$2$	$2$	$66.116$	\(\Q(\sqrt{17}) \)	None	✓				920.2.a.f	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2\beta q^{7}+4q^{11}+(2-\beta )q^{13}+\cdots\)
8280.2.a.bc	$8280$	$2$	8280.a	1.a	$1$	$2$	$2$	$66.116$	\(\Q(\sqrt{11}) \)	None	✓				2760.2.a.l	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-6\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{7}+(1+\beta )q^{11}+(1-\beta )q^{13}+\cdots\)
8280.2.a.bd	$8280$	$2$	8280.a	1.a	$1$	$2$	$2$	$66.116$	\(\Q(\sqrt{17}) \)	None	✓				2760.2.a.m	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-3\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(-1-\beta )q^{7}-2q^{11}-2q^{13}+\cdots\)
8280.2.a.be	$8280$	$2$	8280.a	1.a	$1$	$2$	$2$	$66.116$	\(\Q(\sqrt{17}) \)	None	✓				2760.2.a.p	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-\beta q^{7}+2\beta q^{11}+2q^{13}+(-2+\cdots)q^{17}+\cdots\)
8280.2.a.bf	$8280$	$2$	8280.a	1.a	$1$	$2$	$2$	$66.116$	\(\Q(\sqrt{17}) \)	None	✓				920.2.a.e	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-\beta q^{7}+2q^{11}+(-1-\beta )q^{13}+\cdots\)
8280.2.a.bg	$8280$	$2$	8280.a	1.a	$1$	$2$	$2$	$66.116$	\(\Q(\sqrt{6}) \)	None	✓	✓	✓		8280.2.a.ba	$1$	$1$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(1+\beta )q^{7}-\beta q^{11}+(-2-\beta )q^{13}+\cdots\)
8280.2.a.bh	$8280$	$2$	8280.a	1.a	$1$	$3$	$3$	$66.116$	3.3.229.1	None	✓		✓		2760.2.a.t	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(1\)		$-$	$-$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{5}-\beta _{1}q^{7}+(1-\beta _{2})q^{13}+(-2+\cdots)q^{17}+\cdots\)
8280.2.a.bi	$8280$	$2$	8280.a	1.a	$1$	$3$	$3$	$66.116$	3.3.568.1	None	✓		✓		2760.2.a.u	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(1-2\beta _{1}-\beta _{2})q^{7}+(-2-\beta _{1}+\cdots)q^{11}+\cdots\)
8280.2.a.bj	$8280$	$2$	8280.a	1.a	$1$	$3$	$3$	$66.116$	3.3.2597.1	None	✓		✓		920.2.a.h	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(1-\beta _{1})q^{7}+(-2-\beta _{1})q^{11}+\cdots\)
8280.2.a.bk	$8280$	$2$	8280.a	1.a	$1$	$3$	$3$	$66.116$	3.3.568.1	None	✓	✓	✓		8280.2.a.bk	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(4\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(1+\beta _{1})q^{7}+(-2-\beta _{1}-\beta _{2})q^{11}+\cdots\)
8280.2.a.bl	$8280$	$2$	8280.a	1.a	$1$	$3$	$3$	$66.116$	3.3.229.1	None	✓				920.2.a.i	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(7\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(2-\beta _{2})q^{7}+(-1-\beta _{1})q^{11}+\cdots\)
8280.2.a.bm	$8280$	$2$	8280.a	1.a	$1$	$3$	$3$	$66.116$	3.3.316.1	None	✓				2760.2.a.r	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-6\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(-2+\beta _{2})q^{7}+(-1+\beta _{1}+\beta _{2})q^{11}+\cdots\)
8280.2.a.bn	$8280$	$2$	8280.a	1.a	$1$	$3$	$3$	$66.116$	3.3.1436.1	None	✓				2760.2.a.s	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(-1+\beta _{2})q^{7}+(-1-\beta _{1}-\beta _{2})q^{11}+\cdots\)
8280.2.a.bo	$8280$	$2$	8280.a	1.a	$1$	$3$	$3$	$66.116$	3.3.621.1	None	✓				920.2.a.g	$1$	$0$	\(0\)	\(0\)	\(3\)	\(3\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(1+\beta _{1})q^{7}+(-1+\beta _{1}-\beta _{2})q^{11}+\cdots\)
8280.2.a.bp	$8280$	$2$	8280.a	1.a	$1$	$3$	$3$	$66.116$	3.3.568.1	None	✓	✓	✓		8280.2.a.bk	$1$	$0$	\(0\)	\(0\)	\(3\)	\(4\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(1+\beta _{1})q^{7}+(2+\beta _{1}+\beta _{2})q^{11}+\cdots\)
8280.2.a.bq	$8280$	$2$	8280.a	1.a	$1$	$4$	$4$	$66.116$	4.4.54764.1	None	✓		✓		2760.2.a.v	$1$	$1$	\(0\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}-\beta _{1}q^{7}+\beta _{3}q^{11}+(-1+\beta _{1}+\cdots)q^{13}+\cdots\)
8280.2.a.br	$8280$	$2$	8280.a	1.a	$1$	$5$	$5$	$66.116$	5.5.20087896.1	None	✓		✓		2760.2.a.w	$1$	$0$	\(0\)	\(0\)	\(-5\)	\(-4\)		$-$	$-$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{5}+(-1+\beta _{1})q^{7}+(1-\beta _{2})q^{11}+\cdots\)
8280.2.a.bs	$8280$	$2$	8280.a	1.a	$1$	$5$	$5$	$66.116$	5.5.13955077.1	None	✓		✓		920.2.a.j	$1$	$0$	\(0\)	\(0\)	\(5\)	\(-2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(-\beta _{3}-\beta _{4})q^{7}+(-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
8280.2.a.bt	$8280$	$2$	8280.a	1.a	$1$	$6$	$6$	$66.116$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓	✓		8280.2.a.bt	$1$	$1$	\(0\)	\(0\)	\(-6\)	\(-2\)		$+$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{5}-\beta _{2}q^{7}+(1+\beta _{3})q^{11}+\beta _{4}q^{13}+\cdots\)
8280.2.a.bu	$8280$	$2$	8280.a	1.a	$1$	$6$	$6$	$66.116$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓	✓		8280.2.a.bt	$1$	$0$	\(0\)	\(0\)	\(6\)	\(-2\)		$-$	$+$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{5}-\beta _{2}q^{7}+(-1-\beta _{3})q^{11}+\beta _{4}q^{13}+\cdots\)
8280.2.a.bv	$8280$	$2$	8280.a	1.a	$1$	$7$	$7$	$66.116$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓	✓	8280.2.a.bv	$1$	$0$	\(0\)	\(0\)	\(-7\)	\(-6\)		$-$	$+$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-q^{5}+(-1+\beta _{4})q^{7}+\beta _{3}q^{11}+(-2+\cdots)q^{13}+\cdots\)
8280.2.a.bw	$8280$	$2$	8280.a	1.a	$1$	$7$	$7$	$66.116$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓	✓	8280.2.a.bv	$1$	$1$	\(0\)	\(0\)	\(7\)	\(-6\)		$+$	$+$	$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+q^{5}+(-1+\beta _{4})q^{7}-\beta _{3}q^{11}+(-2+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8280))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8280)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(345))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(414))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(552))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(690))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(828))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(920))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1035))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1380))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1656))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2070))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2760))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4140))\)\(^{\oplus 2}\)