Space of modular forms of level 5040, weight 2, and trivial character

• Label: 5040.2.a
• Level: $5040$
• Weight: $2$
• Character orbit: 5040.a
• Rep. character: $\chi_{5040}(1,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $51$
• Sturm bound: $2304$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5040.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 51 \)
Sturm bound:			\(2304\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(11\), \(13\), \(17\), \(19\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5040))\).

	Total	New	Old
Modular forms	1200	60	1140
Cusp forms	1105	60	1045
Eisenstein series	95	0	95

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

\(2\)	\(3\)	\(5\)	\(7\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(3\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(3\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(3\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(3\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(6\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(2\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(4\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(5\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(4\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(5\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(4\)
Plus space				\(+\)	\(27\)
Minus space				\(-\)	\(33\)

Trace form

\( 60 q + 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5040))\) 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	7
5040.2.a.a	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-5q^{11}-5q^{13}+7q^{17}+\cdots\)
5040.2.a.b	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-2q^{11}-2q^{13}-2q^{17}+\cdots\)
5040.2.a.c	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-2q^{11}+4q^{13}-2q^{17}+\cdots\)
5040.2.a.d	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-6q^{13}-2q^{17}+8q^{19}+\cdots\)
5040.2.a.e	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-4q^{13}-6q^{17}-2q^{19}+\cdots\)
5040.2.a.f	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}+2q^{13}-2q^{19}+q^{25}+\cdots\)
5040.2.a.g	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}+2q^{13}+6q^{17}-8q^{19}+\cdots\)
5040.2.a.h	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}+3q^{11}-q^{13}+3q^{17}+\cdots\)
5040.2.a.i	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
5040.2.a.j	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}+4q^{11}-2q^{13}+6q^{17}+\cdots\)
5040.2.a.k	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
5040.2.a.l	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
5040.2.a.m	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-4q^{11}+2q^{17}+6q^{19}+\cdots\)
5040.2.a.n	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-4q^{11}+6q^{13}-4q^{17}+\cdots\)
5040.2.a.o	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-2q^{11}-6q^{13}-2q^{17}+\cdots\)
5040.2.a.p	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+2q^{13}-2q^{17}+q^{25}+\cdots\)
5040.2.a.q	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+2q^{11}-2q^{13}+6q^{17}+\cdots\)
5040.2.a.r	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+2q^{11}+4q^{13}-2q^{17}+\cdots\)
5040.2.a.s	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
5040.2.a.t	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+4q^{11}+6q^{13}+4q^{17}+\cdots\)
5040.2.a.u	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-4q^{11}+2q^{13}+2q^{17}+\cdots\)
5040.2.a.v	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-3q^{11}+5q^{13}-3q^{17}+\cdots\)
5040.2.a.w	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-4q^{13}+6q^{17}-2q^{19}+\cdots\)
5040.2.a.x	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-2q^{13}-6q^{17}+4q^{19}+\cdots\)
5040.2.a.y	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+2q^{13}-2q^{17}-4q^{19}+\cdots\)
5040.2.a.z	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+2q^{13}-2q^{19}+q^{25}+\cdots\)
5040.2.a.ba	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+2q^{13}+6q^{17}+4q^{19}+\cdots\)
5040.2.a.bb	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+2q^{11}-2q^{13}+2q^{17}+\cdots\)
5040.2.a.bc	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+6q^{11}-4q^{13}-6q^{17}+\cdots\)
5040.2.a.bd	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-5q^{11}-3q^{13}+q^{17}+\cdots\)
5040.2.a.be	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-5q^{11}+q^{13}-3q^{17}+\cdots\)
5040.2.a.bf	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-4q^{11}-6q^{13}+2q^{17}+\cdots\)
5040.2.a.bg	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-4q^{11}-2q^{13}+6q^{17}+\cdots\)
5040.2.a.bh	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-4q^{11}+6q^{13}-4q^{17}+\cdots\)
5040.2.a.bi	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-2q^{11}-2q^{13}-6q^{17}+\cdots\)
5040.2.a.bj	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+6q^{13}+2q^{17}-4q^{19}+\cdots\)
5040.2.a.bk	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+2q^{11}-6q^{13}+2q^{17}+\cdots\)
5040.2.a.bl	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+2q^{11}+4q^{13}-6q^{17}+\cdots\)
5040.2.a.bm	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+4q^{11}-6q^{13}-2q^{17}+\cdots\)
5040.2.a.bn	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+4q^{11}-2q^{13}+6q^{17}+\cdots\)
5040.2.a.bo	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+4q^{11}-2q^{17}+6q^{19}+\cdots\)
5040.2.a.bp	$5040$	$2$	5040.a	1.a	$1$	$1$	$1$	$40.245$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+4q^{11}+6q^{13}+4q^{17}+\cdots\)
5040.2.a.bq	$5040$	$2$	5040.a	1.a	$1$	$2$	$2$	$40.245$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-\beta q^{11}+(2-3\beta )q^{13}+\cdots\)
5040.2.a.br	$5040$	$2$	5040.a	1.a	$1$	$2$	$2$	$40.245$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}+\beta q^{11}+2q^{13}+(-2+\cdots)q^{17}+\cdots\)
5040.2.a.bs	$5040$	$2$	5040.a	1.a	$1$	$2$	$2$	$40.245$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}+(1+\beta )q^{11}+2q^{13}+(-1+\cdots)q^{17}+\cdots\)
5040.2.a.bt	$5040$	$2$	5040.a	1.a	$1$	$2$	$2$	$40.245$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+\beta q^{11}+(2+\beta )q^{13}+(2+\cdots)q^{17}+\cdots\)
5040.2.a.bu	$5040$	$2$	5040.a	1.a	$1$	$2$	$2$	$40.245$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+(2+\beta )q^{11}+(-2+\beta )q^{13}+\cdots\)
5040.2.a.bv	$5040$	$2$	5040.a	1.a	$1$	$2$	$2$	$40.245$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+(-1-\beta )q^{11}+2q^{13}+\cdots\)
5040.2.a.bw	$5040$	$2$	5040.a	1.a	$1$	$2$	$2$	$40.245$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+(2+\beta )q^{11}+\beta q^{13}+2q^{17}+\cdots\)
5040.2.a.bx	$5040$	$2$	5040.a	1.a	$1$	$2$	$2$	$40.245$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+(-2+\beta )q^{11}+(-2-\beta )q^{13}+\cdots\)
5040.2.a.by	$5040$	$2$	5040.a	1.a	$1$	$2$	$2$	$40.245$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+(4-\beta )q^{11}+(2-\beta )q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5040))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5040)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(420))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(504))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(560))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(630))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(840))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1008))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1260))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1680))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2520))\)\(^{\oplus 2}\)