Space of modular forms of level 5328, weight 2, and trivial character

• Label: 5328.2.a
• Level: $5328$
• Weight: $2$
• Character orbit: 5328.a
• Rep. character: $\chi_{5328}(1,\cdot)$
• Character field: $\Q$
• Dimension: $90$
• Newform subspaces: $47$
• Sturm bound: $1824$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 5328 = 2^{4} \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5328.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 47 \)
Sturm bound:			\(1824\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5328))\).

	Total	New	Old
Modular forms	936	90	846
Cusp forms	889	90	799
Eisenstein series	47	0	47

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

\(2\)	\(3\)	\(37\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(8\)
\(+\)	\(+\)	\(-\)	\(-\)	\(10\)
\(+\)	\(-\)	\(+\)	\(-\)	\(14\)
\(+\)	\(-\)	\(-\)	\(+\)	\(13\)
\(-\)	\(+\)	\(+\)	\(-\)	\(10\)
\(-\)	\(+\)	\(-\)	\(+\)	\(8\)
\(-\)	\(-\)	\(+\)	\(+\)	\(13\)
\(-\)	\(-\)	\(-\)	\(-\)	\(14\)
Plus space			\(+\)	\(42\)
Minus space			\(-\)	\(48\)

Trace form

90 * q + 4 * q^17 + 14 * q^19 + 18 * q^23 + 98 * q^25 + 8 * q^29 + 2 * q^31 - 12 * q^35 - 4 * q^41 + 22 * q^43 + 98 * q^49 - 8 * q^53 - 4 * q^55 - 10 * q^59 - 24 * q^61 + 16 * q^65 - 36 * q^67 - 40 * q^71 - 4 * q^73 + 8 * q^77 + 10 * q^79 - 8 * q^83 - 16 * q^85 - 12 * q^89 + 20 * q^91 - 44 * q^95 - 28 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5328))\) 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	37
5328.2.a.a	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				888.2.a.d	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+2q^{13}-6q^{23}+11q^{25}+\cdots\)
5328.2.a.b	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				222.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+q^{7}-q^{11}-3q^{13}-3q^{17}+\cdots\)
5328.2.a.c	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				2664.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}+5q^{11}+3q^{13}-q^{17}+\cdots\)
5328.2.a.d	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				1332.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-4q^{11}-6q^{13}+6q^{17}+4q^{19}+\cdots\)
5328.2.a.e	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				222.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-4q^{11}+6q^{13}-6q^{17}-8q^{19}+\cdots\)
5328.2.a.f	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				666.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+3q^{7}+5q^{11}-3q^{13}-3q^{17}+\cdots\)
5328.2.a.g	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				333.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{7}-4q^{11}-2q^{13}-6q^{17}+\cdots\)
5328.2.a.h	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				222.2.a.d	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{7}+q^{11}+q^{13}+3q^{17}-3q^{19}+\cdots\)
5328.2.a.i	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				888.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-6q^{13}+4q^{17}-4q^{19}+6q^{23}+\cdots\)
5328.2.a.j	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				444.2.a.a	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{11}-2q^{13}-6q^{19}+8q^{23}+\cdots\)
5328.2.a.k	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				37.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}+3q^{11}-4q^{13}-6q^{17}-2q^{19}+\cdots\)
5328.2.a.l	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				222.2.a.e	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}+3q^{11}-q^{13}+3q^{17}+7q^{19}+\cdots\)
5328.2.a.m	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				296.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{7}-3q^{11}-2q^{17}+2q^{19}-6q^{23}+\cdots\)
5328.2.a.n	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				2664.2.a.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{7}-5q^{11}+3q^{13}+q^{17}+\cdots\)
5328.2.a.o	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				296.2.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{7}+q^{11}-6q^{13}+4q^{17}+\cdots\)
5328.2.a.p	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				888.2.a.c	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-4q^{11}-2q^{13}+6q^{17}-4q^{23}+\cdots\)
5328.2.a.q	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				1332.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+4q^{11}-6q^{13}-6q^{17}+4q^{19}+\cdots\)
5328.2.a.r	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				37.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{7}-5q^{11}-2q^{13}+2q^{23}+\cdots\)
5328.2.a.s	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				666.2.a.c	$1$	$1$	\(0\)	\(0\)	\(2\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+3q^{7}-5q^{11}-3q^{13}+3q^{17}+\cdots\)
5328.2.a.t	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				444.2.a.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+4q^{7}-4q^{11}-6q^{13}-6q^{17}+\cdots\)
5328.2.a.u	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				333.2.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+4q^{7}+4q^{11}-2q^{13}+6q^{17}+\cdots\)
5328.2.a.v	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				222.2.a.a	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-3q^{7}+5q^{11}+3q^{13}-3q^{17}+\cdots\)
5328.2.a.w	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				888.2.a.a	$1$	$1$	\(0\)	\(0\)	\(4\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+q^{7}-3q^{11}-5q^{13}-7q^{17}+\cdots\)
5328.2.a.x	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	\(\Q\)	None	✓				148.2.a.a	$1$	$0$	\(0\)	\(0\)	\(4\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+3q^{7}+5q^{11}+6q^{17}-2q^{19}+\cdots\)
5328.2.a.y	$5328$	$2$	5328.a	1.a	$1$	$2$	$2$	$42.544$	\(\Q(\sqrt{17}) \)	None	✓				666.2.a.h	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+(-1+\beta )q^{7}+(1-\beta )q^{11}+\cdots\)
5328.2.a.z	$5328$	$2$	5328.a	1.a	$1$	$2$	$2$	$42.544$	\(\Q(\sqrt{17}) \)	None	✓				148.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+(-1+\beta )q^{7}+(1-\beta )q^{11}+\cdots\)
5328.2.a.ba	$5328$	$2$	5328.a	1.a	$1$	$2$	$2$	$42.544$	\(\Q(\sqrt{5}) \)	None	✓				888.2.a.f	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-8\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}-4q^{7}+(2+2\beta )q^{11}+\cdots\)
5328.2.a.bb	$5328$	$2$	5328.a	1.a	$1$	$2$	$2$	$42.544$	\(\Q(\sqrt{3}) \)	None	✓				888.2.a.e	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{5}+2q^{7}+(-2+2\beta )q^{11}+\cdots\)
5328.2.a.bc	$5328$	$2$	5328.a	1.a	$1$	$2$	$2$	$42.544$	\(\Q(\sqrt{5}) \)	None	✓				74.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-3\beta )q^{5}+2\beta q^{7}+(-3+\beta )q^{11}+\cdots\)
5328.2.a.bd	$5328$	$2$	5328.a	1.a	$1$	$2$	$2$	$42.544$	\(\Q(\sqrt{6}) \)	None	✓				444.2.a.d	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-2q^{7}+(2+2\beta )q^{13}-\beta q^{17}+\cdots\)
5328.2.a.be	$5328$	$2$	5328.a	1.a	$1$	$2$	$2$	$42.544$	\(\Q(\sqrt{41}) \)	None	✓				888.2.a.h	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{7}+(1+\beta )q^{11}+(1-\beta )q^{13}+\cdots\)
5328.2.a.bf	$5328$	$2$	5328.a	1.a	$1$	$2$	$2$	$42.544$	\(\Q(\sqrt{13}) \)	None	✓				74.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(-2+2\beta )q^{7}-\beta q^{11}+(-1+\cdots)q^{13}+\cdots\)
5328.2.a.bg	$5328$	$2$	5328.a	1.a	$1$	$2$	$2$	$42.544$	\(\Q(\sqrt{3}) \)	None	✓				444.2.a.c	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}-2\beta q^{7}-4q^{11}-2\beta q^{13}+\cdots\)
5328.2.a.bh	$5328$	$2$	5328.a	1.a	$1$	$2$	$2$	$42.544$	\(\Q(\sqrt{17}) \)	None	✓				666.2.a.h	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+(-1+\beta )q^{7}+(-1+\beta )q^{11}+\cdots\)
5328.2.a.bi	$5328$	$2$	5328.a	1.a	$1$	$2$	$2$	$42.544$	\(\Q(\sqrt{2}) \)	None	✓				888.2.a.g	$1$	$0$	\(0\)	\(0\)	\(4\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{5}+(2-2\beta )q^{7}-2\beta q^{11}+\cdots\)
5328.2.a.bj	$5328$	$2$	5328.a	1.a	$1$	$3$	$3$	$42.544$	3.3.148.1	None	✓		✓		111.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(4\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{5}+(2-\beta _{1}-\beta _{2})q^{7}+\cdots\)
5328.2.a.bk	$5328$	$2$	5328.a	1.a	$1$	$3$	$3$	$42.544$	3.3.148.1	None	✓				2664.2.a.n	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2})q^{5}+(-2+\beta _{1}+\beta _{2})q^{7}+\cdots\)
5328.2.a.bl	$5328$	$2$	5328.a	1.a	$1$	$3$	$3$	$42.544$	3.3.316.1	None	✓				888.2.a.i	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}+\beta _{2})q^{5}+(1+2\beta _{1}-\beta _{2})q^{7}+\cdots\)
5328.2.a.bm	$5328$	$2$	5328.a	1.a	$1$	$3$	$3$	$42.544$	3.3.568.1	None	✓				888.2.a.j	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+(2-\beta _{2})q^{11}+\cdots\)
5328.2.a.bn	$5328$	$2$	5328.a	1.a	$1$	$3$	$3$	$42.544$	3.3.229.1	None	✓				296.2.a.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-7\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{5}+(-2-\beta _{1}+\beta _{2})q^{7}-3\beta _{1}q^{11}+\cdots\)
5328.2.a.bo	$5328$	$2$	5328.a	1.a	$1$	$3$	$3$	$42.544$	3.3.148.1	None	✓				2664.2.a.n	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2})q^{5}+(-2+\beta _{1}+\beta _{2})q^{7}+\cdots\)
5328.2.a.bp	$5328$	$2$	5328.a	1.a	$1$	$4$	$4$	$42.544$	4.4.48389.1	None	✓		✓		296.2.a.d	$1$	$1$	\(0\)	\(0\)	\(-5\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{3})q^{5}+(\beta _{2}-\beta _{3})q^{7}+(1+\beta _{2}+\cdots)q^{11}+\cdots\)
5328.2.a.bq	$5328$	$2$	5328.a	1.a	$1$	$4$	$4$	$42.544$	4.4.27648.1	None	✓		✓		333.2.a.f	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{5}-2q^{7}+2q^{13}+\beta _{2}q^{17}+\cdots\)
5328.2.a.br	$5328$	$2$	5328.a	1.a	$1$	$4$	$4$	$42.544$	4.4.7168.1	None	✓		✓		1332.2.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$-$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}+(-2-\beta _{3})q^{7}-\beta _{2}q^{11}+\cdots\)
5328.2.a.bs	$5328$	$2$	5328.a	1.a	$1$	$4$	$4$	$42.544$	4.4.6224.1	None	✓		✓		111.2.a.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{5}+(-2+\beta _{2}+\beta _{3})q^{7}+\cdots\)
5328.2.a.bt	$5328$	$2$	5328.a	1.a	$1$	$5$	$5$	$42.544$	5.5.935504.1	None	✓				2664.2.a.s	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(7\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{5}+(1-\beta _{4})q^{7}+(1+\beta _{2}-\beta _{3}+\cdots)q^{11}+\cdots\)
5328.2.a.bu	$5328$	$2$	5328.a	1.a	$1$	$5$	$5$	$42.544$	5.5.935504.1	None	✓				2664.2.a.s	$1$	$0$	\(0\)	\(0\)	\(2\)	\(7\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{5}+(1-\beta _{4})q^{7}+(-1-\beta _{2}+\beta _{3}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5328))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5328)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(111))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(148))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(222))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(296))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(333))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(444))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(592))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(666))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(888))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1332))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1776))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2664))\)\(^{\oplus 2}\)