Space of modular forms of level 6048, weight 2, and trivial character

• Label: 6048.2.a
• Level: $6048$
• Weight: $2$
• Character orbit: 6048.a
• Rep. character: $\chi_{6048}(1,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $48$
• Sturm bound: $2304$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6048.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 48 \)
Sturm bound:			\(2304\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6048))\).

	Total	New	Old
Modular forms	1200	96	1104
Cusp forms	1105	96	1009
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.

\(2\)	\(3\)	\(7\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(11\)
\(+\)	\(+\)	\(-\)	$-$	\(13\)
\(+\)	\(-\)	\(+\)	$-$	\(13\)
\(+\)	\(-\)	\(-\)	$+$	\(11\)
\(-\)	\(+\)	\(+\)	$-$	\(13\)
\(-\)	\(+\)	\(-\)	$+$	\(11\)
\(-\)	\(-\)	\(+\)	$+$	\(11\)
\(-\)	\(-\)	\(-\)	$-$	\(13\)
Plus space			\(+\)	\(44\)
Minus space			\(-\)	\(52\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6048))\) 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	7
6048.2.a.a	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-q^{7}-2q^{11}-4q^{13}+5q^{17}+\cdots\)
6048.2.a.b	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-q^{7}-q^{11}+2q^{13}-2q^{17}+\cdots\)
6048.2.a.c	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+q^{7}+q^{11}+2q^{13}-2q^{17}+\cdots\)
6048.2.a.d	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+q^{7}+2q^{11}-4q^{13}+5q^{17}+\cdots\)
6048.2.a.e	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-3q^{11}+2q^{13}+2q^{17}+\cdots\)
6048.2.a.f	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-2q^{11}-q^{17}+4q^{19}+\cdots\)
6048.2.a.g	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}+2q^{11}+4q^{13}+3q^{17}+\cdots\)
6048.2.a.h	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-2q^{11}+4q^{13}+3q^{17}+\cdots\)
6048.2.a.i	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+2q^{11}-q^{17}-4q^{19}+\cdots\)
6048.2.a.j	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+3q^{11}+2q^{13}+2q^{17}+\cdots\)
6048.2.a.k	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-4q^{11}+q^{13}+5q^{17}+2q^{19}+\cdots\)
6048.2.a.l	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}+4q^{11}+q^{13}-5q^{17}+2q^{19}+\cdots\)
6048.2.a.m	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-4q^{11}+q^{13}-5q^{17}-2q^{19}+\cdots\)
6048.2.a.n	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}+4q^{11}+q^{13}+5q^{17}-2q^{19}+\cdots\)
6048.2.a.o	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-2q^{11}+4q^{13}-3q^{17}+\cdots\)
6048.2.a.p	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+2q^{11}+q^{17}+4q^{19}+\cdots\)
6048.2.a.q	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+3q^{11}+2q^{13}-2q^{17}+\cdots\)
6048.2.a.r	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-3q^{11}+2q^{13}-2q^{17}+\cdots\)
6048.2.a.s	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-2q^{11}+q^{17}-4q^{19}+\cdots\)
6048.2.a.t	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+2q^{11}+4q^{13}-3q^{17}+\cdots\)
6048.2.a.u	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-q^{7}+q^{11}+2q^{13}+2q^{17}+\cdots\)
6048.2.a.v	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-q^{7}+2q^{11}-4q^{13}-5q^{17}+\cdots\)
6048.2.a.w	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+q^{7}-2q^{11}-4q^{13}-5q^{17}+\cdots\)
6048.2.a.x	$6048$	$2$	6048.a	1.a	$1$	$1$	$1$	$48.294$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+q^{7}-q^{11}+2q^{13}+2q^{17}+\cdots\)
6048.2.a.y	$6048$	$2$	6048.a	1.a	$1$	$2$	$2$	$48.294$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{5}-q^{7}+(-2-\beta )q^{11}+\cdots\)
6048.2.a.z	$6048$	$2$	6048.a	1.a	$1$	$2$	$2$	$48.294$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{5}-q^{7}+(1-\beta )q^{11}-2\beta q^{13}+\cdots\)
6048.2.a.ba	$6048$	$2$	6048.a	1.a	$1$	$2$	$2$	$48.294$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{5}+q^{7}+(-1+\beta )q^{11}+\cdots\)
6048.2.a.bb	$6048$	$2$	6048.a	1.a	$1$	$2$	$2$	$48.294$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{5}+q^{7}+(2+\beta )q^{11}+\beta q^{13}+\cdots\)
6048.2.a.bc	$6048$	$2$	6048.a	1.a	$1$	$2$	$2$	$48.294$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{5}-q^{7}-2\beta q^{11}+(-5+\beta )q^{13}+\cdots\)
6048.2.a.bd	$6048$	$2$	6048.a	1.a	$1$	$2$	$2$	$48.294$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{5}+q^{7}+2\beta q^{11}+(-5+\beta )q^{13}+\cdots\)
6048.2.a.be	$6048$	$2$	6048.a	1.a	$1$	$2$	$2$	$48.294$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-q^{7}+2\beta q^{11}+(-5+\beta )q^{13}+\cdots\)
6048.2.a.bf	$6048$	$2$	6048.a	1.a	$1$	$2$	$2$	$48.294$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+q^{7}-2\beta q^{11}+(-5+\beta )q^{13}+\cdots\)
6048.2.a.bg	$6048$	$2$	6048.a	1.a	$1$	$2$	$2$	$48.294$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}-q^{7}+(-1-\beta )q^{11}+2\beta q^{13}+\cdots\)
6048.2.a.bh	$6048$	$2$	6048.a	1.a	$1$	$2$	$2$	$48.294$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}-q^{7}+(2-\beta )q^{11}-\beta q^{13}+\cdots\)
6048.2.a.bi	$6048$	$2$	6048.a	1.a	$1$	$2$	$2$	$48.294$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+q^{7}+(-2+\beta )q^{11}-\beta q^{13}+\cdots\)
6048.2.a.bj	$6048$	$2$	6048.a	1.a	$1$	$2$	$2$	$48.294$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+q^{7}+(1+\beta )q^{11}+2\beta q^{13}+\cdots\)
6048.2.a.bk	$6048$	$2$	6048.a	1.a	$1$	$4$	$4$	$48.294$	4.4.39528.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{5}-q^{7}-\beta _{1}q^{11}+(2+\cdots)q^{13}+\cdots\)
6048.2.a.bl	$6048$	$2$	6048.a	1.a	$1$	$4$	$4$	$48.294$	4.4.25808.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{5}-q^{7}+(1+\beta _{1})q^{11}+\cdots\)
6048.2.a.bm	$6048$	$2$	6048.a	1.a	$1$	$4$	$4$	$48.294$	4.4.22896.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{5}-q^{7}-\beta _{1}q^{11}+(\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots\)
6048.2.a.bn	$6048$	$2$	6048.a	1.a	$1$	$4$	$4$	$48.294$	4.4.25808.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(4\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{5}+q^{7}+(-1-\beta _{1})q^{11}+\cdots\)
6048.2.a.bo	$6048$	$2$	6048.a	1.a	$1$	$4$	$4$	$48.294$	4.4.22896.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(4\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{5}+q^{7}+\beta _{1}q^{11}+(\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots\)
6048.2.a.bp	$6048$	$2$	6048.a	1.a	$1$	$4$	$4$	$48.294$	4.4.39528.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{5}+q^{7}+\beta _{1}q^{11}+(2+\cdots)q^{13}+\cdots\)
6048.2.a.bq	$6048$	$2$	6048.a	1.a	$1$	$4$	$4$	$48.294$	4.4.25808.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{5}-q^{7}+(-1-\beta _{1})q^{11}+\cdots\)
6048.2.a.br	$6048$	$2$	6048.a	1.a	$1$	$4$	$4$	$48.294$	4.4.22896.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{5}-q^{7}+\beta _{1}q^{11}+(\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots\)
6048.2.a.bs	$6048$	$2$	6048.a	1.a	$1$	$4$	$4$	$48.294$	4.4.39528.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{5}-q^{7}+\beta _{1}q^{11}+(2+\beta _{1}+\cdots)q^{13}+\cdots\)
6048.2.a.bt	$6048$	$2$	6048.a	1.a	$1$	$4$	$4$	$48.294$	4.4.39528.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{5}+q^{7}-\beta _{1}q^{11}+(2+\beta _{1}+\cdots)q^{13}+\cdots\)
6048.2.a.bu	$6048$	$2$	6048.a	1.a	$1$	$4$	$4$	$48.294$	4.4.25808.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{5}+q^{7}+(1+\beta _{1})q^{11}+(-1+\cdots)q^{13}+\cdots\)
6048.2.a.bv	$6048$	$2$	6048.a	1.a	$1$	$4$	$4$	$48.294$	4.4.22896.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{5}+q^{7}-\beta _{1}q^{11}+(\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6048))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6048)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(378))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(432))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(504))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(672))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(756))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(864))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1008))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1512))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2016))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3024))\)\(^{\oplus 2}\)