Space of modular forms of level 4080, weight 2, and trivial character

• Label: 4080.2.a
• Level: $4080$
• Weight: $2$
• Character orbit: 4080.a
• Rep. character: $\chi_{4080}(1,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $46$
• Sturm bound: $1728$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 4080 = 2^{4} \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4080.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 46 \)
Sturm bound:			\(1728\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4080))\).

	Total	New	Old
Modular forms	888	64	824
Cusp forms	841	64	777
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.

\(2\)	\(3\)	\(5\)	\(17\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(4\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(3\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(4\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(5\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(4\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(5\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(5\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(5\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(2\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(6\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(2\)
Plus space				\(+\)	\(26\)
Minus space				\(-\)	\(38\)

Trace form

\( 64 q + 4 q^{3} + 64 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4080))\) 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	5	17
4080.2.a.a	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-5\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-5q^{7}+q^{9}-3q^{11}+2q^{13}+\cdots\)
4080.2.a.b	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}-5q^{11}+2q^{13}+\cdots\)
4080.2.a.c	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
4080.2.a.d	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+2q^{11}+2q^{13}+\cdots\)
4080.2.a.e	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
4080.2.a.f	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}+3q^{11}-4q^{13}+\cdots\)
4080.2.a.g	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}+5q^{11}+4q^{13}+\cdots\)
4080.2.a.h	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(3\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+3q^{7}+q^{9}-5q^{11}-2q^{13}+\cdots\)
4080.2.a.i	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(4\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+4q^{7}+q^{9}+2q^{13}+q^{15}+\cdots\)
4080.2.a.j	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-3\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-3q^{7}+q^{9}-5q^{11}-q^{15}+\cdots\)
4080.2.a.k	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-2\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots\)
4080.2.a.l	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{7}+q^{9}-4q^{13}-q^{15}+\cdots\)
4080.2.a.m	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+3q^{11}-4q^{13}+\cdots\)
4080.2.a.n	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}+q^{9}-4q^{11}-q^{15}+\cdots\)
4080.2.a.o	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}+q^{9}-q^{15}-q^{17}+\cdots\)
4080.2.a.p	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(3\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+3q^{7}+q^{9}+q^{11}-6q^{13}+\cdots\)
4080.2.a.q	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(5\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+5q^{7}+q^{9}+5q^{11}-q^{15}+\cdots\)
4080.2.a.r	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{7}+q^{9}+4q^{13}-q^{15}+\cdots\)
4080.2.a.s	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots\)
4080.2.a.t	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-2q^{13}-q^{15}-q^{17}+\cdots\)
4080.2.a.u	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\)
4080.2.a.v	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}-3q^{11}-2q^{13}+\cdots\)
4080.2.a.w	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(3\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+3q^{7}+q^{9}-3q^{11}+4q^{13}+\cdots\)
4080.2.a.x	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(4\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+4q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
4080.2.a.y	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-3\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-3q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
4080.2.a.z	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-3\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-3q^{7}+q^{9}+q^{11}-6q^{13}+\cdots\)
4080.2.a.ba	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
4080.2.a.bb	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}-2q^{13}+q^{15}+q^{17}+\cdots\)
4080.2.a.bc	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+6q^{11}+2q^{13}+\cdots\)
4080.2.a.bd	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(3\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+3q^{7}+q^{9}-3q^{11}-4q^{13}+\cdots\)
4080.2.a.be	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(3\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+3q^{7}+q^{9}+3q^{11}+4q^{13}+\cdots\)
4080.2.a.bf	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(4\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
4080.2.a.bg	$4080$	$2$	4080.a	1.a	$1$	$2$	$2$	$32.579$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
4080.2.a.bh	$4080$	$2$	4080.a	1.a	$1$	$2$	$2$	$32.579$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-\beta q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
4080.2.a.bi	$4080$	$2$	4080.a	1.a	$1$	$2$	$2$	$32.579$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-\beta q^{7}+q^{9}+\beta q^{11}-2q^{13}+\cdots\)
4080.2.a.bj	$4080$	$2$	4080.a	1.a	$1$	$2$	$2$	$32.579$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-5\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(-2-\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
4080.2.a.bk	$4080$	$2$	4080.a	1.a	$1$	$2$	$2$	$32.579$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-\beta q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
4080.2.a.bl	$4080$	$2$	4080.a	1.a	$1$	$2$	$2$	$32.579$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-\beta q^{7}+q^{9}-5q^{11}+(-3+\cdots)q^{13}+\cdots\)
4080.2.a.bm	$4080$	$2$	4080.a	1.a	$1$	$2$	$2$	$32.579$	\(\Q(\sqrt{73}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+\beta q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
4080.2.a.bn	$4080$	$2$	4080.a	1.a	$1$	$2$	$2$	$32.579$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+\beta q^{7}+q^{9}-\beta q^{11}-2q^{13}+\cdots\)
4080.2.a.bo	$4080$	$2$	4080.a	1.a	$1$	$2$	$2$	$32.579$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(-1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-\beta q^{7}+q^{9}+(4-\beta )q^{11}+\cdots\)
4080.2.a.bp	$4080$	$2$	4080.a	1.a	$1$	$2$	$2$	$32.579$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-\beta q^{7}+q^{9}+(-1-2\beta )q^{11}+\cdots\)
4080.2.a.bq	$4080$	$2$	4080.a	1.a	$1$	$2$	$2$	$32.579$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+\beta q^{7}+q^{9}+(2+\beta )q^{13}+\cdots\)
4080.2.a.br	$4080$	$2$	4080.a	1.a	$1$	$3$	$3$	$32.579$	3.3.229.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(-4\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(-1+\beta _{2})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
4080.2.a.bs	$4080$	$2$	4080.a	1.a	$1$	$3$	$3$	$32.579$	3.3.316.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(3\)	\(-3\)		$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(-1-\beta _{1})q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
4080.2.a.bt	$4080$	$2$	4080.a	1.a	$1$	$4$	$4$	$32.579$	4.4.13768.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(-4\)	\(-4\)		$-$	$+$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(-1-\beta _{1})q^{7}+q^{9}-\beta _{3}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4080))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4080)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(170))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(204))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(255))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(340))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(408))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(510))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(680))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(816))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1020))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2040))\)\(^{\oplus 2}\)