Space of modular forms of level 5544, weight 2, and trivial character

• Label: 5544.2.a
• Level: $5544$
• Weight: $2$
• Character orbit: 5544.a
• Rep. character: $\chi_{5544}(1,\cdot)$
• Character field: $\Q$
• Dimension: $74$
• Newform subspaces: $43$
• Sturm bound: $2304$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 5544 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5544.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 43 \)
Sturm bound:			\(2304\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5544))\).

	Total	New	Old
Modular forms	1184	74	1110
Cusp forms	1121	74	1047
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.

\(2\)	\(3\)	\(7\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(3\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(4\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(2\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(7\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(6\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(7\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(4\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(2\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(5\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(7\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(5\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(4\)
Plus space				\(+\)	\(31\)
Minus space				\(-\)	\(43\)

Trace form

\( 74 q + 4 q^{5} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5544))\) 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	11
5544.2.a.a	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-q^{7}+q^{11}-3q^{13}+6q^{17}+\cdots\)
5544.2.a.b	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}-q^{11}+6q^{13}-6q^{17}+\cdots\)
5544.2.a.c	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}-q^{11}-6q^{13}+2q^{17}+\cdots\)
5544.2.a.d	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}+q^{11}-4q^{17}+4q^{19}+\cdots\)
5544.2.a.e	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}+q^{11}+4q^{13}-4q^{19}+\cdots\)
5544.2.a.f	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}+q^{11}+4q^{13}+6q^{17}+\cdots\)
5544.2.a.g	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}+q^{11}-5q^{13}+4q^{17}+\cdots\)
5544.2.a.h	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}+q^{11}+3q^{13}+7q^{19}+\cdots\)
5544.2.a.i	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+q^{11}-q^{13}+2q^{17}+\cdots\)
5544.2.a.j	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+q^{11}+3q^{13}-2q^{17}+\cdots\)
5544.2.a.k	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}+q^{11}-6q^{13}-2q^{19}-4q^{23}+\cdots\)
5544.2.a.l	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}+q^{11}+2q^{13}+8q^{17}-6q^{19}+\cdots\)
5544.2.a.m	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-q^{11}+q^{13}+6q^{17}+\cdots\)
5544.2.a.n	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-q^{11}-q^{13}-2q^{17}+\cdots\)
5544.2.a.o	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-q^{11}+2q^{17}-2q^{19}+\cdots\)
5544.2.a.p	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-q^{11}+3q^{13}+2q^{17}+\cdots\)
5544.2.a.q	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+q^{11}-5q^{13}+6q^{17}+\cdots\)
5544.2.a.r	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+q^{11}-3q^{13}-4q^{17}+\cdots\)
5544.2.a.s	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{7}+q^{11}-2q^{13}-2q^{17}+\cdots\)
5544.2.a.t	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{7}-q^{11}+4q^{13}-6q^{17}+\cdots\)
5544.2.a.u	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{7}+q^{11}+2q^{13}+2q^{17}+\cdots\)
5544.2.a.v	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-q^{7}-q^{11}-3q^{13}-6q^{17}+\cdots\)
5544.2.a.w	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+q^{7}-q^{11}-3q^{13}-4q^{17}+\cdots\)
5544.2.a.x	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+q^{7}-q^{11}-q^{13}+2q^{17}+\cdots\)
5544.2.a.y	$5544$	$2$	5544.a	1.a	$1$	$1$	$1$	$44.269$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-q^{7}+q^{11}-2q^{13}+2q^{19}+\cdots\)
5544.2.a.z	$5544$	$2$	5544.a	1.a	$1$	$2$	$2$	$44.269$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}-q^{7}-q^{11}+(1-\beta )q^{13}+\cdots\)
5544.2.a.ba	$5544$	$2$	5544.a	1.a	$1$	$2$	$2$	$44.269$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}-q^{7}+q^{11}+(1+\beta )q^{13}+\cdots\)
5544.2.a.bb	$5544$	$2$	5544.a	1.a	$1$	$2$	$2$	$44.269$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}+q^{7}-q^{11}+(3-\beta )q^{13}+\cdots\)
5544.2.a.bc	$5544$	$2$	5544.a	1.a	$1$	$2$	$2$	$44.269$	\(\Q(\sqrt{41}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{5}-q^{7}-q^{11}-\beta q^{13}+2q^{17}+\cdots\)
5544.2.a.bd	$5544$	$2$	5544.a	1.a	$1$	$2$	$2$	$44.269$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{5}-q^{7}+q^{11}+(2-\beta )q^{13}+2\beta q^{17}+\cdots\)
5544.2.a.be	$5544$	$2$	5544.a	1.a	$1$	$2$	$2$	$44.269$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}-q^{7}-q^{11}+(-1-\beta )q^{13}+\cdots\)
5544.2.a.bf	$5544$	$2$	5544.a	1.a	$1$	$2$	$2$	$44.269$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}-q^{7}-q^{11}-2\beta q^{13}+\cdots\)
5544.2.a.bg	$5544$	$2$	5544.a	1.a	$1$	$2$	$2$	$44.269$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}-q^{7}-q^{11}+(-1+3\beta )q^{13}+\cdots\)
5544.2.a.bh	$5544$	$2$	5544.a	1.a	$1$	$2$	$2$	$44.269$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}-q^{7}+q^{11}+(1-\beta )q^{13}+\cdots\)
5544.2.a.bi	$5544$	$2$	5544.a	1.a	$1$	$2$	$2$	$44.269$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+q^{7}+q^{11}+(-3+\beta )q^{13}+\cdots\)
5544.2.a.bj	$5544$	$2$	5544.a	1.a	$1$	$3$	$3$	$44.269$	3.3.229.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(3\)		$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{5}+q^{7}-q^{11}+(-2+\beta _{1}-\beta _{2})q^{13}+\cdots\)
5544.2.a.bk	$5544$	$2$	5544.a	1.a	$1$	$3$	$3$	$44.269$	3.3.568.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(3\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{5}+q^{7}-q^{11}+\beta _{1}q^{13}+(-2+\cdots)q^{17}+\cdots\)
5544.2.a.bl	$5544$	$2$	5544.a	1.a	$1$	$3$	$3$	$44.269$	3.3.961.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(3\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}+q^{7}+q^{11}+(1+\beta _{2})q^{13}+\cdots\)
5544.2.a.bm	$5544$	$2$	5544.a	1.a	$1$	$4$	$4$	$44.269$	4.4.11348.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-5\)	\(-4\)		$-$	$-$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{5}-q^{7}-q^{11}+(1+\beta _{3})q^{13}+\cdots\)
5544.2.a.bn	$5544$	$2$	5544.a	1.a	$1$	$4$	$4$	$44.269$	4.4.22592.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}-q^{7}-q^{11}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots\)
5544.2.a.bo	$5544$	$2$	5544.a	1.a	$1$	$4$	$4$	$44.269$	4.4.123040.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{5}+q^{7}-q^{11}+(1-\beta _{3})q^{13}+\cdots\)
5544.2.a.bp	$5544$	$2$	5544.a	1.a	$1$	$4$	$4$	$44.269$	4.4.22592.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}-q^{7}+q^{11}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots\)
5544.2.a.bq	$5544$	$2$	5544.a	1.a	$1$	$4$	$4$	$44.269$	4.4.123040.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{5}+q^{7}+q^{11}+(1-\beta _{3})q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5544))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5544)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(308))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(396))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(504))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(616))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(693))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(792))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(924))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1386))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1848))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2772))\)\(^{\oplus 2}\)