Space of modular forms of level 5472, weight 2, and trivial character

• Label: 5472.2.a
• Level: $5472$
• Weight: $2$
• Character orbit: 5472.a
• Rep. character: $\chi_{5472}(1,\cdot)$
• Character field: $\Q$
• Dimension: $90$
• Newform subspaces: $48$
• Sturm bound: $1920$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 5472 = 2^{5} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5472.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 48 \)
Sturm bound:			\(1920\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(13\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5472))\).

	Total	New	Old
Modular forms	992	90	902
Cusp forms	929	90	839
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.

\(2\)	\(3\)	\(19\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(9\)
\(+\)	\(+\)	\(-\)	$-$	\(9\)
\(+\)	\(-\)	\(+\)	$-$	\(15\)
\(+\)	\(-\)	\(-\)	$+$	\(12\)
\(-\)	\(+\)	\(+\)	$-$	\(9\)
\(-\)	\(+\)	\(-\)	$+$	\(9\)
\(-\)	\(-\)	\(+\)	$+$	\(12\)
\(-\)	\(-\)	\(-\)	$-$	\(15\)
Plus space			\(+\)	\(42\)
Minus space			\(-\)	\(48\)

Trace form

\( 90 q + 4 q^{5} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5472))\) 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	19
5472.2.a.a	$5472$	$2$	5472.a	1.a	$1$	$1$	$1$	$43.694$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-5\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-5q^{7}+5q^{11}-4q^{13}+3q^{17}+\cdots\)
5472.2.a.b	$5472$	$2$	5472.a	1.a	$1$	$1$	$1$	$43.694$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-3q^{7}+3q^{11}-q^{17}-q^{19}+\cdots\)
5472.2.a.c	$5472$	$2$	5472.a	1.a	$1$	$1$	$1$	$43.694$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+3q^{7}-3q^{11}-q^{17}+q^{19}+\cdots\)
5472.2.a.d	$5472$	$2$	5472.a	1.a	$1$	$1$	$1$	$43.694$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+5q^{7}-5q^{11}-4q^{13}+3q^{17}+\cdots\)
5472.2.a.e	$5472$	$2$	5472.a	1.a	$1$	$1$	$1$	$43.694$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(0\)	\(-2\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-4q^{7}-6q^{11}-4q^{13}+q^{19}+\cdots\)
5472.2.a.f	$5472$	$2$	5472.a	1.a	$1$	$1$	$1$	$43.694$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(0\)	\(-2\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-4q^{7}-6q^{11}-2q^{13}-6q^{17}+\cdots\)
5472.2.a.g	$5472$	$2$	5472.a	1.a	$1$	$1$	$1$	$43.694$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{7}+6q^{11}-4q^{13}-q^{19}+\cdots\)
5472.2.a.h	$5472$	$2$	5472.a	1.a	$1$	$1$	$1$	$43.694$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{7}+6q^{11}-2q^{13}-6q^{17}+\cdots\)
5472.2.a.i	$5472$	$2$	5472.a	1.a	$1$	$1$	$1$	$43.694$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-2q^{11}-q^{13}-3q^{17}-q^{19}+\cdots\)
5472.2.a.j	$5472$	$2$	5472.a	1.a	$1$	$1$	$1$	$43.694$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{17}-q^{19}+6q^{23}-5q^{25}-10q^{29}+\cdots\)
5472.2.a.k	$5472$	$2$	5472.a	1.a	$1$	$1$	$1$	$43.694$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{17}+q^{19}-6q^{23}-5q^{25}-10q^{29}+\cdots\)
5472.2.a.l	$5472$	$2$	5472.a	1.a	$1$	$1$	$1$	$43.694$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}+2q^{11}-q^{13}-3q^{17}+q^{19}+\cdots\)
5472.2.a.m	$5472$	$2$	5472.a	1.a	$1$	$1$	$1$	$43.694$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-3q^{11}-4q^{13}+3q^{17}+\cdots\)
5472.2.a.n	$5472$	$2$	5472.a	1.a	$1$	$1$	$1$	$43.694$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-3q^{11}+7q^{17}+q^{19}+\cdots\)
5472.2.a.o	$5472$	$2$	5472.a	1.a	$1$	$1$	$1$	$43.694$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+5q^{11}+4q^{13}+3q^{17}+\cdots\)
5472.2.a.p	$5472$	$2$	5472.a	1.a	$1$	$1$	$1$	$43.694$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-5q^{11}+4q^{13}+3q^{17}+\cdots\)
5472.2.a.q	$5472$	$2$	5472.a	1.a	$1$	$1$	$1$	$43.694$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+3q^{11}-4q^{13}+3q^{17}+\cdots\)
5472.2.a.r	$5472$	$2$	5472.a	1.a	$1$	$1$	$1$	$43.694$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+3q^{11}+7q^{17}-q^{19}+\cdots\)
5472.2.a.s	$5472$	$2$	5472.a	1.a	$1$	$1$	$1$	$43.694$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-4q^{7}-4q^{11}+2q^{13}-2q^{17}+\cdots\)
5472.2.a.t	$5472$	$2$	5472.a	1.a	$1$	$1$	$1$	$43.694$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-4q^{7}+6q^{11}-4q^{13}+q^{19}+\cdots\)
5472.2.a.u	$5472$	$2$	5472.a	1.a	$1$	$1$	$1$	$43.694$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+4q^{7}-6q^{11}-4q^{13}-q^{19}+\cdots\)
5472.2.a.v	$5472$	$2$	5472.a	1.a	$1$	$1$	$1$	$43.694$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+4q^{7}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
5472.2.a.w	$5472$	$2$	5472.a	1.a	$1$	$2$	$2$	$43.694$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}+2\beta q^{11}+(-1+\beta )q^{13}+\cdots\)
5472.2.a.x	$5472$	$2$	5472.a	1.a	$1$	$2$	$2$	$43.694$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}-2\beta q^{11}+(-1+\beta )q^{13}+\cdots\)
5472.2.a.y	$5472$	$2$	5472.a	1.a	$1$	$2$	$2$	$43.694$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(-1-2\beta )q^{7}+(-2+\beta )q^{11}+\cdots\)
5472.2.a.z	$5472$	$2$	5472.a	1.a	$1$	$2$	$2$	$43.694$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(-1+2\beta )q^{7}+(2+\beta )q^{11}+\cdots\)
5472.2.a.ba	$5472$	$2$	5472.a	1.a	$1$	$2$	$2$	$43.694$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(1-2\beta )q^{7}+(-2-\beta )q^{11}+\cdots\)
5472.2.a.bb	$5472$	$2$	5472.a	1.a	$1$	$2$	$2$	$43.694$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(1+2\beta )q^{7}+(2-\beta )q^{11}+(2+\cdots)q^{13}+\cdots\)
5472.2.a.bc	$5472$	$2$	5472.a	1.a	$1$	$2$	$2$	$43.694$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-6\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-3q^{7}+(-2+\beta )q^{11}+(1-\beta )q^{13}+\cdots\)
5472.2.a.bd	$5472$	$2$	5472.a	1.a	$1$	$2$	$2$	$43.694$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-\beta q^{7}+(-4+\beta )q^{11}-4q^{13}+\cdots\)
5472.2.a.be	$5472$	$2$	5472.a	1.a	$1$	$2$	$2$	$43.694$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+\beta q^{7}+(4-\beta )q^{11}-4q^{13}+\cdots\)
5472.2.a.bf	$5472$	$2$	5472.a	1.a	$1$	$2$	$2$	$43.694$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+3q^{7}+(2-\beta )q^{11}+(1-\beta )q^{13}+\cdots\)
5472.2.a.bg	$5472$	$2$	5472.a	1.a	$1$	$2$	$2$	$43.694$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}-2\beta q^{11}+(-1+\beta )q^{13}+\cdots\)
5472.2.a.bh	$5472$	$2$	5472.a	1.a	$1$	$2$	$2$	$43.694$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+2\beta q^{11}+(-1+\beta )q^{13}+\cdots\)
5472.2.a.bi	$5472$	$2$	5472.a	1.a	$1$	$2$	$2$	$43.694$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+(-1+\beta )q^{7}+(1-\beta )q^{11}+\cdots\)
5472.2.a.bj	$5472$	$2$	5472.a	1.a	$1$	$2$	$2$	$43.694$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+(-1+\beta )q^{7}+(1+\beta )q^{11}+\cdots\)
5472.2.a.bk	$5472$	$2$	5472.a	1.a	$1$	$2$	$2$	$43.694$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+(1-\beta )q^{7}+(-1-\beta )q^{11}+\cdots\)
5472.2.a.bl	$5472$	$2$	5472.a	1.a	$1$	$2$	$2$	$43.694$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+(1-\beta )q^{7}+(-1+\beta )q^{11}+\cdots\)
5472.2.a.bm	$5472$	$2$	5472.a	1.a	$1$	$3$	$3$	$43.694$	3.3.229.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-5\)	\(-1\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{2})q^{5}+\beta _{1}q^{7}-\beta _{1}q^{11}+\cdots\)
5472.2.a.bn	$5472$	$2$	5472.a	1.a	$1$	$3$	$3$	$43.694$	3.3.229.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-5\)	\(1\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{2})q^{5}-\beta _{1}q^{7}+\beta _{1}q^{11}+\cdots\)
5472.2.a.bo	$5472$	$2$	5472.a	1.a	$1$	$3$	$3$	$43.694$	3.3.469.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-5\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{5}+(-2+\beta _{2})q^{7}+(-2+\cdots)q^{11}+\cdots\)
5472.2.a.bp	$5472$	$2$	5472.a	1.a	$1$	$3$	$3$	$43.694$	3.3.469.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(5\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{5}+(2-\beta _{2})q^{7}+(2+\beta _{2})q^{11}+\cdots\)
5472.2.a.bq	$5472$	$2$	5472.a	1.a	$1$	$4$	$4$	$43.694$	4.4.19664.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-2\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{3})q^{5}+(-1-\beta _{2})q^{7}+(1+\cdots)q^{11}+\cdots\)
5472.2.a.br	$5472$	$2$	5472.a	1.a	$1$	$4$	$4$	$43.694$	4.4.19664.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(2\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{3})q^{5}+(1+\beta _{2})q^{7}+(-1+\cdots)q^{11}+\cdots\)
5472.2.a.bs	$5472$	$2$	5472.a	1.a	$1$	$4$	$4$	$43.694$	4.4.15317.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{7}+(-2+\beta _{1}+\cdots)q^{11}+\cdots\)
5472.2.a.bt	$5472$	$2$	5472.a	1.a	$1$	$4$	$4$	$43.694$	4.4.15317.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{2})q^{5}-\beta _{3}q^{7}+(2-\beta _{1}+\cdots)q^{11}+\cdots\)
5472.2.a.bu	$5472$	$2$	5472.a	1.a	$1$	$4$	$4$	$43.694$	4.4.19664.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-2\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{5}+(-1-\beta _{2})q^{7}+(-1+\cdots)q^{11}+\cdots\)
5472.2.a.bv	$5472$	$2$	5472.a	1.a	$1$	$4$	$4$	$43.694$	4.4.19664.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(2\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{5}+(1+\beta _{2})q^{7}+(1+\beta _{3})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5472))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5472)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(342))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(456))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(608))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(684))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(912))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1368))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1824))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2736))\)\(^{\oplus 2}\)