Space of modular forms of level 33120, weight 2, and trivial character

• Label: 33120.2.a
• Level: $33120$
• Weight: $2$
• Character orbit: 33120.a
• Rep. character: $\chi_{33120}(1,\cdot)$
• Character field: $\Q$
• Dimension: $440$
• Newform subspaces: $110$
• Sturm bound: $13824$

Defining parameters

Level:	\( N \)	\(=\)	\( 33120 = 2^{5} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	33120.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 110 \)
Sturm bound:			\(13824\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(33120))\).

	Total	New	Old
Modular forms	6976	440	6536
Cusp forms	6849	440	6409
Eisenstein series	127	0	127

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		Total				Cusp				Eisenstein
						All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)		\(420\)	\(22\)	\(398\)		\(413\)	\(22\)	\(391\)		\(7\)	\(0\)	\(7\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)		\(448\)	\(22\)	\(426\)		\(440\)	\(22\)	\(418\)		\(8\)	\(0\)	\(8\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)		\(444\)	\(22\)	\(422\)		\(436\)	\(22\)	\(414\)		\(8\)	\(0\)	\(8\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)		\(432\)	\(22\)	\(410\)		\(424\)	\(22\)	\(402\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)		\(442\)	\(36\)	\(406\)		\(434\)	\(36\)	\(398\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)		\(434\)	\(31\)	\(403\)		\(426\)	\(31\)	\(395\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)		\(438\)	\(31\)	\(407\)		\(430\)	\(31\)	\(399\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)		\(430\)	\(36\)	\(394\)		\(422\)	\(36\)	\(386\)		\(8\)	\(0\)	\(8\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)		\(452\)	\(22\)	\(430\)		\(444\)	\(22\)	\(422\)		\(8\)	\(0\)	\(8\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)		\(424\)	\(22\)	\(402\)		\(416\)	\(22\)	\(394\)		\(8\)	\(0\)	\(8\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)		\(428\)	\(22\)	\(406\)		\(420\)	\(22\)	\(398\)		\(8\)	\(0\)	\(8\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)		\(440\)	\(22\)	\(418\)		\(432\)	\(22\)	\(410\)		\(8\)	\(0\)	\(8\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)		\(430\)	\(30\)	\(400\)		\(422\)	\(30\)	\(392\)		\(8\)	\(0\)	\(8\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)		\(438\)	\(35\)	\(403\)		\(430\)	\(35\)	\(395\)		\(8\)	\(0\)	\(8\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)		\(434\)	\(35\)	\(399\)		\(426\)	\(35\)	\(391\)		\(8\)	\(0\)	\(8\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)		\(442\)	\(30\)	\(412\)		\(434\)	\(30\)	\(404\)		\(8\)	\(0\)	\(8\)
Plus space				\(+\)		\(3448\)	\(210\)	\(3238\)		\(3385\)	\(210\)	\(3175\)		\(63\)	\(0\)	\(63\)
Minus space				\(-\)		\(3528\)	\(230\)	\(3298\)		\(3464\)	\(230\)	\(3234\)		\(64\)	\(0\)	\(64\)

Trace form

\( 440 q - 32 q^{13} + 16 q^{17} + 440 q^{25} - 32 q^{37} - 48 q^{41} + 408 q^{49} - 32 q^{53} - 64 q^{61} - 80 q^{73} - 32 q^{77} + 16 q^{89} - 80 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(33120))\) 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
33120.2.a.a	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(-4\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
33120.2.a.b	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(-4\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}+2q^{11}-4q^{13}-6q^{17}+\cdots\)
33120.2.a.c	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(-4\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}+4q^{11}-4q^{13}+8q^{19}+\cdots\)
33120.2.a.d	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-6q^{11}+2q^{13}+4q^{17}+\cdots\)
33120.2.a.e	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-2q^{11}-4q^{13}-6q^{17}+\cdots\)
33120.2.a.f	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}+4q^{11}-2q^{13}+6q^{17}+\cdots\)
33120.2.a.g	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}+2q^{11}-4q^{13}+3q^{17}+\cdots\)
33120.2.a.h	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-6q^{11}+4q^{13}-2q^{17}-4q^{19}+\cdots\)
33120.2.a.i	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-6q^{13}-6q^{17}-8q^{19}+q^{23}+\cdots\)
33120.2.a.j	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-6q^{13}-6q^{17}+8q^{19}-q^{23}+\cdots\)
33120.2.a.k	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+6q^{11}+4q^{13}-2q^{17}+4q^{19}+\cdots\)
33120.2.a.l	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-2q^{11}-4q^{13}+3q^{17}+\cdots\)
33120.2.a.m	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-4q^{11}-2q^{13}+6q^{17}+\cdots\)
33120.2.a.n	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}+2q^{11}-4q^{13}-6q^{17}+\cdots\)
33120.2.a.o	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}+6q^{11}+2q^{13}+4q^{17}+\cdots\)
33120.2.a.p	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}-4q^{11}-4q^{13}-8q^{19}+\cdots\)
33120.2.a.q	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(4\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}-2q^{11}-4q^{13}-6q^{17}+\cdots\)
33120.2.a.r	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(4\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
33120.2.a.s	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(-5\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-5q^{7}+2q^{11}+4q^{13}-3q^{17}+\cdots\)
33120.2.a.t	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(-4\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{7}-4q^{11}-4q^{13}+8q^{19}+\cdots\)
33120.2.a.u	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(-3\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{7}+6q^{11}+4q^{13}-7q^{17}+\cdots\)
33120.2.a.v	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-4q^{11}-2q^{13}-6q^{17}+\cdots\)
33120.2.a.w	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+2q^{11}-4q^{13}+6q^{17}+\cdots\)
33120.2.a.x	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+2q^{11}+q^{17}+4q^{19}+\cdots\)
33120.2.a.y	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{11}-6q^{13}-6q^{17}-4q^{19}+\cdots\)
33120.2.a.z	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{11}-2q^{13}-6q^{17}-2q^{19}+\cdots\)
33120.2.a.ba	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{11}-2q^{13}-2q^{17}-4q^{19}+\cdots\)
33120.2.a.bb	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{13}+2q^{17}-4q^{19}-q^{23}+\cdots\)
33120.2.a.bc	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{13}+2q^{17}+4q^{19}+q^{23}+\cdots\)
33120.2.a.bd	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{11}-6q^{13}-6q^{17}+4q^{19}+\cdots\)
33120.2.a.be	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{11}-2q^{13}-6q^{17}+2q^{19}+\cdots\)
33120.2.a.bf	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{11}-2q^{13}-2q^{17}+4q^{19}+\cdots\)
33120.2.a.bg	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-2q^{11}+q^{17}-4q^{19}+\cdots\)
33120.2.a.bh	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(2\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-2q^{11}-4q^{13}+6q^{17}+\cdots\)
33120.2.a.bi	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(2\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}+4q^{11}-2q^{13}-6q^{17}+\cdots\)
33120.2.a.bj	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(3\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+3q^{7}-6q^{11}+4q^{13}-7q^{17}+\cdots\)
33120.2.a.bk	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(4\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}+4q^{11}-4q^{13}-8q^{19}+\cdots\)
33120.2.a.bl	$33120$	$2$	33120.a	1.a	$1$	$1$	$1$	$264.465$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(5\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+5q^{7}-2q^{11}+4q^{13}-3q^{17}+\cdots\)
33120.2.a.bm	$33120$	$2$	33120.a	1.a	$1$	$2$	$2$	$264.465$	\(\Q(\sqrt{7}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
33120.2.a.bn	$33120$	$2$	33120.a	1.a	$1$	$2$	$2$	$264.465$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
33120.2.a.bo	$33120$	$2$	33120.a	1.a	$1$	$2$	$2$	$264.465$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
33120.2.a.bp	$33120$	$2$	33120.a	1.a	$1$	$2$	$2$	$264.465$	\(\Q(\sqrt{7}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
33120.2.a.bq	$33120$	$2$	33120.a	1.a	$1$	$2$	$2$	$264.465$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(-3\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
33120.2.a.br	$33120$	$2$	33120.a	1.a	$1$	$2$	$2$	$264.465$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
33120.2.a.bs	$33120$	$2$	33120.a	1.a	$1$	$2$	$2$	$264.465$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
33120.2.a.bt	$33120$	$2$	33120.a	1.a	$1$	$2$	$2$	$264.465$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33120.2.a.bu	$33120$	$2$	33120.a	1.a	$1$	$2$	$2$	$264.465$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
33120.2.a.bv	$33120$	$2$	33120.a	1.a	$1$	$2$	$2$	$264.465$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(3\)		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33120.2.a.bw	$33120$	$2$	33120.a	1.a	$1$	$3$	$3$	$264.465$	3.3.1573.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-3\)	\(-4\)		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
33120.2.a.bx	$33120$	$2$	33120.a	1.a	$1$	$3$	$3$	$264.465$	3.3.148.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-3\)	\(-3\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
33120.2.a.by	$33120$	$2$	33120.a	1.a	$1$	$3$	$3$	$264.465$	3.3.148.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-3\)	\(3\)		$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
33120.2.a.bz	$33120$	$2$	33120.a	1.a	$1$	$3$	$3$	$264.465$	3.3.1573.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-3\)	\(4\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
33120.2.a.ca	$33120$	$2$	33120.a	1.a	$1$	$4$	$4$	$264.465$	4.4.11348.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(-5\)		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
33120.2.a.cb	$33120$	$2$	33120.a	1.a	$1$	$4$	$4$	$264.465$	4.4.63796.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(-3\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
33120.2.a.cc	$33120$	$2$	33120.a	1.a	$1$	$4$	$4$	$264.465$	4.4.19796.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(-3\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
33120.2.a.cd	$33120$	$2$	33120.a	1.a	$1$	$4$	$4$	$264.465$	4.4.22676.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(-1\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
33120.2.a.ce	$33120$	$2$	33120.a	1.a	$1$	$4$	$4$	$264.465$	4.4.22676.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(1\)		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
33120.2.a.cf	$33120$	$2$	33120.a	1.a	$1$	$4$	$4$	$264.465$	4.4.63796.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(3\)		$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
33120.2.a.cg	$33120$	$2$	33120.a	1.a	$1$	$4$	$4$	$264.465$	4.4.19796.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(3\)		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
33120.2.a.ch	$33120$	$2$	33120.a	1.a	$1$	$4$	$4$	$264.465$	4.4.11348.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(5\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
33120.2.a.ci	$33120$	$2$	33120.a	1.a	$1$	$4$	$4$	$264.465$	4.4.21208.1	None	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(-5\)		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33120.2.a.cj	$33120$	$2$	33120.a	1.a	$1$	$4$	$4$	$264.465$	4.4.25492.1	None	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(-3\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
33120.2.a.ck	$33120$	$2$	33120.a	1.a	$1$	$4$	$4$	$264.465$	4.4.25492.1	None	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(3\)		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33120.2.a.cl	$33120$	$2$	33120.a	1.a	$1$	$4$	$4$	$264.465$	4.4.21208.1	None	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(5\)		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
33120.2.a.cm	$33120$	$2$	33120.a	1.a	$1$	$5$	$5$	$264.465$	5.5.406264.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-5\)	\(-8\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
33120.2.a.cn	$33120$	$2$	33120.a	1.a	$1$	$5$	$5$	$264.465$	5.5.876604.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-5\)	\(-1\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
33120.2.a.co	$33120$	$2$	33120.a	1.a	$1$	$5$	$5$	$264.465$	5.5.876604.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-5\)	\(1\)		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
33120.2.a.cp	$33120$	$2$	33120.a	1.a	$1$	$5$	$5$	$264.465$	5.5.406264.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-5\)	\(8\)		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
33120.2.a.cq	$33120$	$2$	33120.a	1.a	$1$	$5$	$5$	$264.465$	5.5.4276148.1	None	✓	?				$-1$		\(0\)	\(0\)	\(5\)	\(-5\)		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33120.2.a.cr	$33120$	$2$	33120.a	1.a	$1$	$5$	$5$	$264.465$	5.5.792644.1	None	✓	?				$-1$		\(0\)	\(0\)	\(5\)	\(-5\)		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
33120.2.a.cs	$33120$	$2$	33120.a	1.a	$1$	$5$	$5$	$264.465$	5.5.2255384.1	None	✓	?				$-1$		\(0\)	\(0\)	\(5\)	\(-4\)		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
33120.2.a.ct	$33120$	$2$	33120.a	1.a	$1$	$5$	$5$	$264.465$	5.5.998068.1	None	✓	?				$-1$		\(0\)	\(0\)	\(5\)	\(-3\)		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
33120.2.a.cu	$33120$	$2$	33120.a	1.a	$1$	$5$	$5$	$264.465$	5.5.1143052.1	None	✓	?				$-1$		\(0\)	\(0\)	\(5\)	\(-1\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
33120.2.a.cv	$33120$	$2$	33120.a	1.a	$1$	$5$	$5$	$264.465$	5.5.387268.1	None	✓	?				$-1$		\(0\)	\(0\)	\(5\)	\(-1\)		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
33120.2.a.cw	$33120$	$2$	33120.a	1.a	$1$	$5$	$5$	$264.465$	5.5.2147332.1	None	✓	?				$-1$		\(0\)	\(0\)	\(5\)	\(-1\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
33120.2.a.cx	$33120$	$2$	33120.a	1.a	$1$	$5$	$5$	$264.465$	5.5.2147332.1	None	✓	?				$-1$		\(0\)	\(0\)	\(5\)	\(1\)		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
33120.2.a.cy	$33120$	$2$	33120.a	1.a	$1$	$5$	$5$	$264.465$	5.5.387268.1	None	✓	?				$-1$		\(0\)	\(0\)	\(5\)	\(1\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
33120.2.a.cz	$33120$	$2$	33120.a	1.a	$1$	$5$	$5$	$264.465$	5.5.1143052.1	None	✓	?				$-1$		\(0\)	\(0\)	\(5\)	\(1\)		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33120.2.a.da	$33120$	$2$	33120.a	1.a	$1$	$5$	$5$	$264.465$	5.5.998068.1	None	✓	?				$-1$		\(0\)	\(0\)	\(5\)	\(3\)		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
33120.2.a.db	$33120$	$2$	33120.a	1.a	$1$	$5$	$5$	$264.465$	5.5.2255384.1	None	✓	?				$-1$		\(0\)	\(0\)	\(5\)	\(4\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
33120.2.a.dc	$33120$	$2$	33120.a	1.a	$1$	$5$	$5$	$264.465$	5.5.792644.1	None	✓	?				$-1$		\(0\)	\(0\)	\(5\)	\(5\)		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33120.2.a.dd	$33120$	$2$	33120.a	1.a	$1$	$5$	$5$	$264.465$	5.5.4276148.1	None	✓	?				$-1$		\(0\)	\(0\)	\(5\)	\(5\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
33120.2.a.de	$33120$	$2$	33120.a	1.a	$1$	$6$	$6$	$264.465$	6.6.255601784.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-6\)	\(-4\)		$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
33120.2.a.df	$33120$	$2$	33120.a	1.a	$1$	$6$	$6$	$264.465$	6.6.21692500.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-6\)	\(-1\)		$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
33120.2.a.dg	$33120$	$2$	33120.a	1.a	$1$	$6$	$6$	$264.465$	6.6.21692500.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-6\)	\(1\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
33120.2.a.dh	$33120$	$2$	33120.a	1.a	$1$	$6$	$6$	$264.465$	6.6.255601784.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-6\)	\(4\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
33120.2.a.di	$33120$	$2$	33120.a	1.a	$1$	$6$	$6$	$264.465$	6.6.1656120708.1	None	✓	?				$-1$		\(0\)	\(0\)	\(6\)	\(-3\)		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
33120.2.a.dj	$33120$	$2$	33120.a	1.a	$1$	$6$	$6$	$264.465$	6.6.180753348.1	None	✓	?	✓			$-1$		\(0\)	\(0\)	\(6\)	\(-3\)		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
33120.2.a.dk	$33120$	$2$	33120.a	1.a	$1$	$6$	$6$	$264.465$	6.6.180753348.1	None	✓	?				$-1$		\(0\)	\(0\)	\(6\)	\(3\)		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
33120.2.a.dl	$33120$	$2$	33120.a	1.a	$1$	$6$	$6$	$264.465$	6.6.1656120708.1	None	✓	?	✓			$-1$		\(0\)	\(0\)	\(6\)	\(3\)		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33120.2.a.dm	$33120$	$2$	33120.a	1.a	$1$	$7$	$7$	$264.465$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(0\)	\(-7\)	\(-7\)		$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
33120.2.a.dn	$33120$	$2$	33120.a	1.a	$1$	$7$	$7$	$264.465$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(0\)	\(-7\)	\(-3\)		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
33120.2.a.do	$33120$	$2$	33120.a	1.a	$1$	$7$	$7$	$264.465$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(0\)	\(-7\)	\(3\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
33120.2.a.dp	$33120$	$2$	33120.a	1.a	$1$	$7$	$7$	$264.465$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(0\)	\(-7\)	\(7\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
33120.2.a.dq	$33120$	$2$	33120.a	1.a	$1$	$9$	$9$	$264.465$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-9\)	\(-4\)		$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
33120.2.a.dr	$33120$	$2$	33120.a	1.a	$1$	$9$	$9$	$264.465$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-9\)	\(0\)		$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
33120.2.a.ds	$33120$	$2$	33120.a	1.a	$1$	$9$	$9$	$264.465$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-9\)	\(0\)		$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
33120.2.a.dt	$33120$	$2$	33120.a	1.a	$1$	$9$	$9$	$264.465$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-9\)	\(4\)		$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
33120.2.a.du	$33120$	$2$	33120.a	1.a	$1$	$9$	$9$	$264.465$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(9\)	\(-4\)		$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
33120.2.a.dv	$33120$	$2$	33120.a	1.a	$1$	$9$	$9$	$264.465$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(9\)	\(0\)		$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33120.2.a.dw	$33120$	$2$	33120.a	1.a	$1$	$9$	$9$	$264.465$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(9\)	\(0\)		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
33120.2.a.dx	$33120$	$2$	33120.a	1.a	$1$	$9$	$9$	$264.465$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(9\)	\(4\)		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
33120.2.a.dy	$33120$	$2$	33120.a	1.a	$1$	$10$	$10$	$264.465$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(0\)	\(-10\)	\(-10\)		$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
33120.2.a.dz	$33120$	$2$	33120.a	1.a	$1$	$10$	$10$	$264.465$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-10\)	\(10\)		$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
33120.2.a.ea	$33120$	$2$	33120.a	1.a	$1$	$10$	$10$	$264.465$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(0\)	\(10\)	\(-10\)		$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
33120.2.a.eb	$33120$	$2$	33120.a	1.a	$1$	$10$	$10$	$264.465$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(10\)	\(10\)		$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
33120.2.a.ec	$33120$	$2$	33120.a	1.a	$1$	$11$	$11$	$264.465$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(0\)	\(-11\)	\(-6\)		$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
33120.2.a.ed	$33120$	$2$	33120.a	1.a	$1$	$11$	$11$	$264.465$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(0\)	\(-11\)	\(6\)		$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
33120.2.a.ee	$33120$	$2$	33120.a	1.a	$1$	$11$	$11$	$264.465$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(0\)	\(11\)	\(-6\)		$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
33120.2.a.ef	$33120$	$2$	33120.a	1.a	$1$	$11$	$11$	$264.465$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(0\)	\(11\)	\(6\)		$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(33120))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(33120)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(345))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(414))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(552))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(690))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(736))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(828))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(920))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1035))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1380))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1440))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1656))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1840))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2070))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2760))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3680))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(5520))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(6624))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(8280))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(11040))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(16560))\)\(^{\oplus 2}\)