Space of modular forms of level 3840, weight 2, and trivial character

• Label: 3840.2.a
• Level: $3840$
• Weight: $2$
• Character orbit: 3840.a
• Rep. character: $\chi_{3840}(1,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $44$
• Sturm bound: $1536$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 3840 = 2^{8} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3840.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 44 \)
Sturm bound:			\(1536\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3840))\).

	Total	New	Old
Modular forms	816	64	752
Cusp forms	721	64	657
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.

\(2\)	\(3\)	\(5\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(95\)	\(8\)	\(87\)		\(84\)	\(8\)	\(76\)		\(11\)	\(0\)	\(11\)
\(+\)	\(+\)	\(-\)	\(-\)		\(109\)	\(10\)	\(99\)		\(97\)	\(10\)	\(87\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(+\)	\(-\)		\(101\)	\(8\)	\(93\)		\(89\)	\(8\)	\(81\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(-\)	\(+\)		\(103\)	\(6\)	\(97\)		\(91\)	\(6\)	\(85\)		\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(+\)	\(-\)		\(107\)	\(8\)	\(99\)		\(95\)	\(8\)	\(87\)		\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(-\)	\(+\)		\(97\)	\(6\)	\(91\)		\(85\)	\(6\)	\(79\)		\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(+\)	\(+\)		\(105\)	\(8\)	\(97\)		\(93\)	\(8\)	\(85\)		\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(-\)	\(-\)		\(99\)	\(10\)	\(89\)		\(87\)	\(10\)	\(77\)		\(12\)	\(0\)	\(12\)
Plus space			\(+\)		\(400\)	\(28\)	\(372\)		\(353\)	\(28\)	\(325\)		\(47\)	\(0\)	\(47\)
Minus space			\(-\)		\(416\)	\(36\)	\(380\)		\(368\)	\(36\)	\(332\)		\(48\)	\(0\)	\(48\)

Trace form

\( 64 q + 64 q^{9} + 64 q^{25} - 64 q^{57} - 64 q^{73} + 64 q^{81} - 64 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3840))\) 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	5
3840.2.a.a	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				960.2.k.a	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-4q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
3840.2.a.b	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				1920.2.k.a	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
3840.2.a.c	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				1920.2.k.b	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
3840.2.a.d	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				120.2.k.a	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{7}+q^{9}+4q^{11}+q^{15}+\cdots\)
3840.2.a.e	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				960.2.k.b	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+6q^{13}+q^{15}+2q^{19}+\cdots\)
3840.2.a.f	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				1920.2.k.c	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
3840.2.a.g	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				1920.2.k.d	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+2q^{7}+q^{9}+6q^{11}+6q^{13}+\cdots\)
3840.2.a.h	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				1920.2.k.c	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
3840.2.a.i	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				1920.2.k.d	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{7}+q^{9}+6q^{11}-6q^{13}+\cdots\)
3840.2.a.j	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				960.2.k.b	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}-6q^{13}-q^{15}+2q^{19}+\cdots\)
3840.2.a.k	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				1920.2.k.a	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
3840.2.a.l	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				1920.2.k.b	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
3840.2.a.m	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				120.2.k.a	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}+q^{9}+4q^{11}-q^{15}+\cdots\)
3840.2.a.n	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				960.2.k.a	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
3840.2.a.o	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				1920.2.k.d	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{7}+q^{9}-6q^{11}+6q^{13}+\cdots\)
3840.2.a.p	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				1920.2.k.c	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
3840.2.a.q	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				960.2.k.b	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}+6q^{13}-q^{15}-2q^{19}+\cdots\)
3840.2.a.r	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				120.2.k.a	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}+q^{9}-4q^{11}-q^{15}+\cdots\)
3840.2.a.s	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				1920.2.k.a	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
3840.2.a.t	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				1920.2.k.b	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
3840.2.a.u	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				960.2.k.a	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+4q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
3840.2.a.v	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				960.2.k.a	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
3840.2.a.w	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				120.2.k.a	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{7}+q^{9}-4q^{11}+q^{15}+\cdots\)
3840.2.a.x	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				1920.2.k.a	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
3840.2.a.y	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				1920.2.k.b	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
3840.2.a.z	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				960.2.k.b	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}-6q^{13}+q^{15}-2q^{19}+\cdots\)
3840.2.a.ba	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				1920.2.k.d	$1$	$1$	\(0\)	\(1\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+2q^{7}+q^{9}-6q^{11}-6q^{13}+\cdots\)
3840.2.a.bb	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	\(\Q\)	None	✓				1920.2.k.c	$1$	$0$	\(0\)	\(1\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
3840.2.a.bc	$3840$	$2$	3840.a	1.a	$1$	$2$	$2$	$30.663$	\(\Q(\sqrt{2}) \)	None	✓				1920.2.k.i	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(-2+\beta )q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
3840.2.a.bd	$3840$	$2$	3840.a	1.a	$1$	$2$	$2$	$30.663$	\(\Q(\sqrt{2}) \)	None	✓				1920.2.k.j	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(4\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+2q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
3840.2.a.be	$3840$	$2$	3840.a	1.a	$1$	$2$	$2$	$30.663$	\(\Q(\sqrt{3}) \)	None	✓				960.2.k.e	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(4\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+2q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
3840.2.a.bf	$3840$	$2$	3840.a	1.a	$1$	$2$	$2$	$30.663$	\(\Q(\sqrt{3}) \)	None	✓				960.2.k.e	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(-4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
3840.2.a.bg	$3840$	$2$	3840.a	1.a	$1$	$2$	$2$	$30.663$	\(\Q(\sqrt{2}) \)	None	✓		✓		1920.2.k.j	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-4\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
3840.2.a.bh	$3840$	$2$	3840.a	1.a	$1$	$2$	$2$	$30.663$	\(\Q(\sqrt{2}) \)	None	✓				1920.2.k.i	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(2+\beta )q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
3840.2.a.bi	$3840$	$2$	3840.a	1.a	$1$	$2$	$2$	$30.663$	\(\Q(\sqrt{3}) \)	None	✓				960.2.k.e	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
3840.2.a.bj	$3840$	$2$	3840.a	1.a	$1$	$2$	$2$	$30.663$	\(\Q(\sqrt{2}) \)	None	✓				1920.2.k.j	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
3840.2.a.bk	$3840$	$2$	3840.a	1.a	$1$	$2$	$2$	$30.663$	\(\Q(\sqrt{2}) \)	None	✓				1920.2.k.i	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(4\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(2+\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
3840.2.a.bl	$3840$	$2$	3840.a	1.a	$1$	$2$	$2$	$30.663$	\(\Q(\sqrt{2}) \)	None	✓		✓		1920.2.k.i	$1$	$1$	\(0\)	\(2\)	\(2\)	\(-4\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(-2+\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
3840.2.a.bm	$3840$	$2$	3840.a	1.a	$1$	$2$	$2$	$30.663$	\(\Q(\sqrt{2}) \)	None	✓				1920.2.k.j	$1$	$0$	\(0\)	\(2\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+2q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
3840.2.a.bn	$3840$	$2$	3840.a	1.a	$1$	$2$	$2$	$30.663$	\(\Q(\sqrt{3}) \)	None	✓				960.2.k.e	$1$	$0$	\(0\)	\(2\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+2q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
3840.2.a.bo	$3840$	$2$	3840.a	1.a	$1$	$3$	$3$	$30.663$	3.3.316.1	None	✓		✓		120.2.k.b	$1$	$0$	\(0\)	\(-3\)	\(-3\)	\(2\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(1+\beta _{1})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
3840.2.a.bp	$3840$	$2$	3840.a	1.a	$1$	$3$	$3$	$30.663$	3.3.316.1	None	✓		✓		120.2.k.b	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(-2\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(-1-\beta _{1})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
3840.2.a.bq	$3840$	$2$	3840.a	1.a	$1$	$3$	$3$	$30.663$	3.3.316.1	None	✓		✓		120.2.k.b	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(-2\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(-1-\beta _{1})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
3840.2.a.br	$3840$	$2$	3840.a	1.a	$1$	$3$	$3$	$30.663$	3.3.316.1	None	✓		✓		120.2.k.b	$1$	$0$	\(0\)	\(3\)	\(3\)	\(2\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(1+\beta _{1})q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3840))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3840)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(256))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(384))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(640))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(768))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(960))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1280))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1920))\)\(^{\oplus 2}\)