Space of modular forms of level 6240, weight 2, and trivial character

• Label: 6240.2.a
• Level: $6240$
• Weight: $2$
• Character orbit: 6240.a
• Rep. character: $\chi_{6240}(1,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $58$
• Sturm bound: $2688$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 6240 = 2^{5} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6240.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 58 \)
Sturm bound:			\(2688\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(7\), \(11\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6240))\).

	Total	New	Old
Modular forms	1376	96	1280
Cusp forms	1313	96	1217
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.

\(2\)	\(3\)	\(5\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(6\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(6\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(7\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(5\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(7\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(5\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(4\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(8\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(5\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(7\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(5\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(7\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(8\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(4\)
Plus space				\(+\)	\(40\)
Minus space				\(-\)	\(56\)

Trace form

\( 96 q + 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6240))\) 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	13
6240.2.a.a	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-4\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-4q^{7}+q^{9}-4q^{11}-q^{13}+\cdots\)
6240.2.a.b	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{7}+q^{9}-q^{13}+q^{15}+\cdots\)
6240.2.a.c	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}-4q^{11}+q^{13}+q^{15}+\cdots\)
6240.2.a.d	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}-q^{13}+q^{15}+2q^{17}+\cdots\)
6240.2.a.e	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+4q^{11}+q^{13}+q^{15}+\cdots\)
6240.2.a.f	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
6240.2.a.g	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}+3q^{11}-q^{13}+\cdots\)
6240.2.a.h	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(5\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+5q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
6240.2.a.i	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
6240.2.a.j	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}+3q^{11}-q^{13}+\cdots\)
6240.2.a.k	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}+3q^{11}-q^{13}+\cdots\)
6240.2.a.l	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}+q^{9}-q^{13}-q^{15}+\cdots\)
6240.2.a.m	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}+q^{9}+2q^{11}-q^{13}+\cdots\)
6240.2.a.n	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(2\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
6240.2.a.o	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(3\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+3q^{7}+q^{9}-3q^{11}+q^{13}+\cdots\)
6240.2.a.p	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(4\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+4q^{7}+q^{9}+q^{13}-q^{15}+\cdots\)
6240.2.a.q	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-5\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-5q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
6240.2.a.r	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}-3q^{11}-q^{13}+\cdots\)
6240.2.a.s	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
6240.2.a.t	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-4q^{11}+q^{13}-q^{15}+\cdots\)
6240.2.a.u	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-q^{13}-q^{15}+2q^{17}+\cdots\)
6240.2.a.v	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}+4q^{11}+q^{13}-q^{15}+\cdots\)
6240.2.a.w	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}+q^{9}-q^{13}-q^{15}+\cdots\)
6240.2.a.x	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(4\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+4q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
6240.2.a.y	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-4\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-4q^{7}+q^{9}+q^{13}+q^{15}+\cdots\)
6240.2.a.z	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-3\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-3q^{7}+q^{9}+3q^{11}+q^{13}+\cdots\)
6240.2.a.ba	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{7}+q^{9}-4q^{11}+q^{13}+\cdots\)
6240.2.a.bb	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{7}+q^{9}-2q^{11}-q^{13}+\cdots\)
6240.2.a.bc	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{7}+q^{9}-q^{13}+q^{15}+\cdots\)
6240.2.a.bd	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}-3q^{11}-q^{13}+\cdots\)
6240.2.a.be	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}-3q^{11}-q^{13}+\cdots\)
6240.2.a.bf	$6240$	$2$	6240.a	1.a	$1$	$1$	$1$	$49.827$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
6240.2.a.bg	$6240$	$2$	6240.a	1.a	$1$	$2$	$2$	$49.827$	\(\Q(\sqrt{57}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-\beta q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
6240.2.a.bh	$6240$	$2$	6240.a	1.a	$1$	$2$	$2$	$49.827$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+\beta q^{11}+q^{13}+\cdots\)
6240.2.a.bi	$6240$	$2$	6240.a	1.a	$1$	$2$	$2$	$49.827$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+\beta q^{11}+q^{13}+\cdots\)
6240.2.a.bj	$6240$	$2$	6240.a	1.a	$1$	$2$	$2$	$49.827$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+(4-\beta )q^{11}+\cdots\)
6240.2.a.bk	$6240$	$2$	6240.a	1.a	$1$	$2$	$2$	$49.827$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(3\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
6240.2.a.bl	$6240$	$2$	6240.a	1.a	$1$	$2$	$2$	$49.827$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(-6\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(-3-\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
6240.2.a.bm	$6240$	$2$	6240.a	1.a	$1$	$2$	$2$	$49.827$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(-1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-\beta q^{7}+q^{9}+(4+\beta )q^{11}+\cdots\)
6240.2.a.bn	$6240$	$2$	6240.a	1.a	$1$	$2$	$2$	$49.827$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+\beta q^{7}+q^{9}-4q^{11}-q^{13}+\cdots\)
6240.2.a.bo	$6240$	$2$	6240.a	1.a	$1$	$2$	$2$	$49.827$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-3\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(-1-\beta )q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
6240.2.a.bp	$6240$	$2$	6240.a	1.a	$1$	$2$	$2$	$49.827$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-\beta q^{7}+q^{9}+(-4+\beta )q^{11}+\cdots\)
6240.2.a.bq	$6240$	$2$	6240.a	1.a	$1$	$2$	$2$	$49.827$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-\beta q^{7}+q^{9}-\beta q^{11}+q^{13}+\cdots\)
6240.2.a.br	$6240$	$2$	6240.a	1.a	$1$	$2$	$2$	$49.827$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+\beta q^{7}+q^{9}+\beta q^{11}+q^{13}+\cdots\)
6240.2.a.bs	$6240$	$2$	6240.a	1.a	$1$	$2$	$2$	$49.827$	\(\Q(\sqrt{57}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+\beta q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
6240.2.a.bt	$6240$	$2$	6240.a	1.a	$1$	$2$	$2$	$49.827$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+\beta q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
6240.2.a.bu	$6240$	$2$	6240.a	1.a	$1$	$2$	$2$	$49.827$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+\beta q^{7}+q^{9}+(-4-\beta )q^{11}+\cdots\)
6240.2.a.bv	$6240$	$2$	6240.a	1.a	$1$	$2$	$2$	$49.827$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(6\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(3+\beta )q^{7}+q^{9}+(2-2\beta )q^{11}+\cdots\)
6240.2.a.bw	$6240$	$2$	6240.a	1.a	$1$	$3$	$3$	$49.827$	3.3.229.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-3\)	\(-5\)		$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(-2-\beta _{2})q^{7}+q^{9}-\beta _{1}q^{11}+\cdots\)
6240.2.a.bx	$6240$	$2$	6240.a	1.a	$1$	$3$	$3$	$49.827$	3.3.229.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-3\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-\beta _{1}q^{7}+q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\)
6240.2.a.by	$6240$	$2$	6240.a	1.a	$1$	$3$	$3$	$49.827$	3.3.568.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(3\)	\(-5\)		$+$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(-2-\beta _{2})q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
6240.2.a.bz	$6240$	$2$	6240.a	1.a	$1$	$3$	$3$	$49.827$	3.3.1849.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(5\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(2-\beta _{1})q^{7}+q^{9}+(2-\beta _{1}+\cdots)q^{11}+\cdots\)
6240.2.a.ca	$6240$	$2$	6240.a	1.a	$1$	$3$	$3$	$49.827$	3.3.229.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+\beta _{1}q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
6240.2.a.cb	$6240$	$2$	6240.a	1.a	$1$	$3$	$3$	$49.827$	3.3.229.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(5\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(2+\beta _{2})q^{7}+q^{9}+\beta _{1}q^{11}+\cdots\)
6240.2.a.cc	$6240$	$2$	6240.a	1.a	$1$	$3$	$3$	$49.827$	3.3.1849.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(3\)	\(-5\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(-2+\beta _{1})q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
6240.2.a.cd	$6240$	$2$	6240.a	1.a	$1$	$3$	$3$	$49.827$	3.3.568.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(3\)	\(5\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(2+\beta _{2})q^{7}+q^{9}+(2-\beta _{2})q^{11}+\cdots\)
6240.2.a.ce	$6240$	$2$	6240.a	1.a	$1$	$4$	$4$	$49.827$	4.4.15317.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(4\)	\(-3\)		$-$	$+$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(-1-\beta _{1})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
6240.2.a.cf	$6240$	$2$	6240.a	1.a	$1$	$4$	$4$	$49.827$	4.4.15317.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(4\)	\(3\)		$+$	$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(1-\beta _{3})q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6240))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6240)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(260))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(390))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(416))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(520))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(624))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(780))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1040))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1248))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1560))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2080))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3120))\)\(^{\oplus 2}\)