Space of modular forms of level 7280, weight 2, and trivial character

• Label: 7280.2.a
• Level: $7280$
• Weight: $2$
• Character orbit: 7280.a
• Rep. character: $\chi_{7280}(1,\cdot)$
• Character field: $\Q$
• Dimension: $144$
• Newform subspaces: $59$
• Sturm bound: $2688$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 7280 = 2^{4} \cdot 5 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7280.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 59 \)
Sturm bound:			\(2688\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(3\), \(11\), \(17\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7280))\).

	Total	New	Old
Modular forms	1368	144	1224
Cusp forms	1321	144	1177
Eisenstein series	47	0	47

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

\(2\)	\(5\)	\(7\)	\(13\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(10\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(8\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(10\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(8\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(8\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(10\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(8\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(10\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(11\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(8\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(5\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(12\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(8\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(11\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(12\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(5\)
Plus space				\(+\)	\(62\)
Minus space				\(-\)	\(82\)

Trace form

\( 144 q - 4 q^{7} + 128 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7280))\) 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	5	7	13
7280.2.a.a	$7280$	$2$	7280.a	1.a	$1$	$1$	$1$	$58.131$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}-q^{7}+q^{9}-6q^{11}-q^{13}+\cdots\)
7280.2.a.b	$7280$	$2$	7280.a	1.a	$1$	$1$	$1$	$58.131$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}+q^{13}+\cdots\)
7280.2.a.c	$7280$	$2$	7280.a	1.a	$1$	$1$	$1$	$58.131$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+q^{7}+q^{9}+2q^{11}-q^{13}+\cdots\)
7280.2.a.d	$7280$	$2$	7280.a	1.a	$1$	$1$	$1$	$58.131$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+q^{7}+q^{9}-q^{13}-2q^{15}+\cdots\)
7280.2.a.e	$7280$	$2$	7280.a	1.a	$1$	$1$	$1$	$58.131$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
7280.2.a.f	$7280$	$2$	7280.a	1.a	$1$	$1$	$1$	$58.131$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}-2q^{9}+3q^{11}+q^{13}+\cdots\)
7280.2.a.g	$7280$	$2$	7280.a	1.a	$1$	$1$	$1$	$58.131$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}-2q^{9}+3q^{11}+q^{13}+\cdots\)
7280.2.a.h	$7280$	$2$	7280.a	1.a	$1$	$1$	$1$	$58.131$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-3q^{9}-4q^{11}-q^{13}+\cdots\)
7280.2.a.i	$7280$	$2$	7280.a	1.a	$1$	$1$	$1$	$58.131$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-3q^{9}-q^{13}+6q^{17}+\cdots\)
7280.2.a.j	$7280$	$2$	7280.a	1.a	$1$	$1$	$1$	$58.131$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-3q^{9}-2q^{11}+q^{13}+\cdots\)
7280.2.a.k	$7280$	$2$	7280.a	1.a	$1$	$1$	$1$	$58.131$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-3q^{9}-q^{13}-2q^{17}+\cdots\)
7280.2.a.l	$7280$	$2$	7280.a	1.a	$1$	$1$	$1$	$58.131$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-3q^{9}+6q^{11}+q^{13}+\cdots\)
7280.2.a.m	$7280$	$2$	7280.a	1.a	$1$	$1$	$1$	$58.131$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-3q^{9}+2q^{11}-q^{13}+\cdots\)
7280.2.a.n	$7280$	$2$	7280.a	1.a	$1$	$1$	$1$	$58.131$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-3q^{9}+2q^{11}-q^{13}+\cdots\)
7280.2.a.o	$7280$	$2$	7280.a	1.a	$1$	$1$	$1$	$58.131$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-3q^{9}+q^{13}-6q^{17}+\cdots\)
7280.2.a.p	$7280$	$2$	7280.a	1.a	$1$	$1$	$1$	$58.131$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}-2q^{9}+5q^{11}-q^{13}+\cdots\)
7280.2.a.q	$7280$	$2$	7280.a	1.a	$1$	$1$	$1$	$58.131$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}-2q^{9}-5q^{11}-q^{13}+\cdots\)
7280.2.a.r	$7280$	$2$	7280.a	1.a	$1$	$1$	$1$	$58.131$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}-2q^{9}+3q^{11}-q^{13}+\cdots\)
7280.2.a.s	$7280$	$2$	7280.a	1.a	$1$	$1$	$1$	$58.131$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}-q^{7}+q^{9}+q^{13}-2q^{15}+\cdots\)
7280.2.a.t	$7280$	$2$	7280.a	1.a	$1$	$1$	$1$	$58.131$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}-q^{7}+q^{9}+q^{13}-2q^{15}+\cdots\)
7280.2.a.u	$7280$	$2$	7280.a	1.a	$1$	$1$	$1$	$58.131$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(1\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}-q^{7}+q^{9}+2q^{11}+q^{13}+\cdots\)
7280.2.a.v	$7280$	$2$	7280.a	1.a	$1$	$1$	$1$	$58.131$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(1\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
7280.2.a.w	$7280$	$2$	7280.a	1.a	$1$	$1$	$1$	$58.131$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-1\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{5}+q^{7}+6q^{9}-3q^{11}+\cdots\)
7280.2.a.x	$7280$	$2$	7280.a	1.a	$1$	$2$	$2$	$58.131$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}-q^{5}-q^{7}+(1-2\beta )q^{9}+\cdots\)
7280.2.a.y	$7280$	$2$	7280.a	1.a	$1$	$2$	$2$	$58.131$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}-q^{5}+q^{7}+(3+2\beta )q^{9}+\cdots\)
7280.2.a.z	$7280$	$2$	7280.a	1.a	$1$	$2$	$2$	$58.131$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{5}-q^{7}+(-2+\beta )q^{9}+4\beta q^{11}+\cdots\)
7280.2.a.ba	$7280$	$2$	7280.a	1.a	$1$	$2$	$2$	$58.131$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{5}+q^{7}+(-2+\beta )q^{9}-2\beta q^{11}+\cdots\)
7280.2.a.bb	$7280$	$2$	7280.a	1.a	$1$	$2$	$2$	$58.131$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{5}+q^{7}+(1+\beta )q^{9}+\beta q^{11}+\cdots\)
7280.2.a.bc	$7280$	$2$	7280.a	1.a	$1$	$2$	$2$	$58.131$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}-q^{7}+5q^{9}-4q^{11}+\cdots\)
7280.2.a.bd	$7280$	$2$	7280.a	1.a	$1$	$2$	$2$	$58.131$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-3q^{9}+\beta q^{11}+q^{13}+\cdots\)
7280.2.a.be	$7280$	$2$	7280.a	1.a	$1$	$2$	$2$	$58.131$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}-q^{7}+\beta q^{9}+2q^{11}+\cdots\)
7280.2.a.bf	$7280$	$2$	7280.a	1.a	$1$	$2$	$2$	$58.131$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+q^{7}+(-2+\beta )q^{9}+2\beta q^{11}+\cdots\)
7280.2.a.bg	$7280$	$2$	7280.a	1.a	$1$	$2$	$2$	$58.131$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+q^{7}+(1+\beta )q^{9}-\beta q^{11}+\cdots\)
7280.2.a.bh	$7280$	$2$	7280.a	1.a	$1$	$2$	$2$	$58.131$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}-q^{7}+\beta q^{9}+(2-2\beta )q^{11}+\cdots\)
7280.2.a.bi	$7280$	$2$	7280.a	1.a	$1$	$2$	$2$	$58.131$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(2\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}+q^{7}+(-2+\beta )q^{9}-q^{13}+\cdots\)
7280.2.a.bj	$7280$	$2$	7280.a	1.a	$1$	$2$	$2$	$58.131$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-q^{5}-q^{7}+(1+3\beta )q^{9}+\cdots\)
7280.2.a.bk	$7280$	$2$	7280.a	1.a	$1$	$2$	$2$	$58.131$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(3\)	\(2\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+q^{5}-q^{7}+(-1+3\beta )q^{9}+\cdots\)
7280.2.a.bl	$7280$	$2$	7280.a	1.a	$1$	$3$	$3$	$58.131$	3.3.229.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(-3\)		$-$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+q^{5}-q^{7}+(1-\beta _{1})q^{9}+(-2+\cdots)q^{11}+\cdots\)
7280.2.a.bm	$7280$	$2$	7280.a	1.a	$1$	$3$	$3$	$58.131$	3.3.1573.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(3\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+q^{7}+(2+\beta _{1}+\beta _{2})q^{9}+\cdots\)
7280.2.a.bn	$7280$	$2$	7280.a	1.a	$1$	$3$	$3$	$58.131$	3.3.1101.1	None	✓	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-3\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}-q^{7}+(4-\beta _{1}+\beta _{2})q^{9}+\cdots\)
7280.2.a.bo	$7280$	$2$	7280.a	1.a	$1$	$3$	$3$	$58.131$	3.3.568.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(3\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+q^{5}+q^{7}+(3-\beta _{1})q^{9}+(-2+\cdots)q^{11}+\cdots\)
7280.2.a.bp	$7280$	$2$	7280.a	1.a	$1$	$3$	$3$	$58.131$	3.3.229.1	None	✓	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(3\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}-q^{5}+q^{7}+(1+\beta _{1})q^{9}+\cdots\)
7280.2.a.bq	$7280$	$2$	7280.a	1.a	$1$	$4$	$4$	$58.131$	4.4.1957.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(4\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2})q^{3}+q^{5}+q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots\)
7280.2.a.br	$7280$	$2$	7280.a	1.a	$1$	$4$	$4$	$58.131$	4.4.4913.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-4\)	\(4\)		$+$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-q^{5}+q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
7280.2.a.bs	$7280$	$2$	7280.a	1.a	$1$	$4$	$4$	$58.131$	4.4.23724.1	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-4\)	\(-4\)		$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}-q^{7}+(1+\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots\)
7280.2.a.bt	$7280$	$2$	7280.a	1.a	$1$	$4$	$4$	$58.131$	4.4.2225.1	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-4\)	\(4\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
7280.2.a.bu	$7280$	$2$	7280.a	1.a	$1$	$4$	$4$	$58.131$	4.4.50908.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(4\)	\(-4\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+q^{5}-q^{7}+(2-\beta _{1}+\beta _{3})q^{9}+\cdots\)
7280.2.a.bv	$7280$	$2$	7280.a	1.a	$1$	$4$	$4$	$58.131$	4.4.24197.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(-4\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}-q^{7}+\beta _{2}q^{9}+(\beta _{2}-\beta _{3})q^{11}+\cdots\)
7280.2.a.bw	$7280$	$2$	7280.a	1.a	$1$	$4$	$4$	$58.131$	4.4.12197.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(4\)		$-$	$+$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+q^{7}+(2-\beta _{3})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
7280.2.a.bx	$7280$	$2$	7280.a	1.a	$1$	$4$	$4$	$58.131$	4.4.24197.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(4\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+q^{5}+q^{7}+(4+\beta _{1})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
7280.2.a.by	$7280$	$2$	7280.a	1.a	$1$	$4$	$4$	$58.131$	4.4.30972.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(-4\)	\(4\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7280.2.a.bz	$7280$	$2$	7280.a	1.a	$1$	$4$	$4$	$58.131$	4.4.13676.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(-4\)	\(4\)		$+$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+q^{7}+(3+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots\)
7280.2.a.ca	$7280$	$2$	7280.a	1.a	$1$	$4$	$4$	$58.131$	4.4.2225.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(4\)	\(4\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
7280.2.a.cb	$7280$	$2$	7280.a	1.a	$1$	$4$	$4$	$58.131$	4.4.27004.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(4\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+q^{5}+q^{7}+(1-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7280.2.a.cc	$7280$	$2$	7280.a	1.a	$1$	$5$	$5$	$58.131$	5.5.1194649.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-5\)	\(-5\)		$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}-q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
7280.2.a.cd	$7280$	$2$	7280.a	1.a	$1$	$5$	$5$	$58.131$	5.5.2112217.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(5\)	\(-5\)		$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}-q^{7}+(1+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
7280.2.a.ce	$7280$	$2$	7280.a	1.a	$1$	$6$	$6$	$58.131$	6.6.45853772.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(6\)	\(-6\)		$-$	$-$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{3}+q^{5}-q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7280.2.a.cf	$7280$	$2$	7280.a	1.a	$1$	$7$	$7$	$58.131$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-4\)	\(7\)	\(-7\)		$+$	$-$	$+$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+q^{5}-q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots\)
7280.2.a.cg	$7280$	$2$	7280.a	1.a	$1$	$7$	$7$	$58.131$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-7\)	\(-7\)		$-$	$+$	$+$	$+$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{3}-q^{5}-q^{7}+(3-\beta _{4})q^{9}+(-1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7280))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7280)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(260))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(455))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(520))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(560))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(728))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(910))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1040))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1456))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1820))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3640))\)\(^{\oplus 2}\)