Space of modular forms of level 3960, weight 2, and trivial character

• Label: 3960.2.a
• Level: $3960$
• Weight: $2$
• Character orbit: 3960.a
• Rep. character: $\chi_{3960}(1,\cdot)$
• Character field: $\Q$
• Dimension: $50$
• Newform subspaces: $34$
• Sturm bound: $1728$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 3960 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3960.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 34 \)
Sturm bound:			\(1728\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(7\), \(13\), \(17\), \(19\), \(23\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3960))\).

	Total	New	Old
Modular forms	896	50	846
Cusp forms	833	50	783
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.

\(2\)	\(3\)	\(5\)	\(11\)	Fricke		Total				Cusp				Eisenstein
						All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)		\(48\)	\(3\)	\(45\)		\(45\)	\(3\)	\(42\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)		\(62\)	\(2\)	\(60\)		\(58\)	\(2\)	\(56\)		\(4\)	\(0\)	\(4\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)		\(64\)	\(3\)	\(61\)		\(60\)	\(3\)	\(57\)		\(4\)	\(0\)	\(4\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)		\(50\)	\(2\)	\(48\)		\(46\)	\(2\)	\(44\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)		\(61\)	\(4\)	\(57\)		\(57\)	\(4\)	\(53\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)		\(53\)	\(3\)	\(50\)		\(49\)	\(3\)	\(46\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)		\(51\)	\(3\)	\(48\)		\(47\)	\(3\)	\(44\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)		\(59\)	\(5\)	\(54\)		\(55\)	\(5\)	\(50\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)		\(56\)	\(2\)	\(54\)		\(52\)	\(2\)	\(50\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)		\(58\)	\(3\)	\(55\)		\(54\)	\(3\)	\(51\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)		\(56\)	\(2\)	\(54\)		\(52\)	\(2\)	\(50\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)		\(54\)	\(3\)	\(51\)		\(50\)	\(3\)	\(47\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)		\(59\)	\(3\)	\(56\)		\(55\)	\(3\)	\(52\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)		\(51\)	\(4\)	\(47\)		\(47\)	\(4\)	\(43\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)		\(53\)	\(5\)	\(48\)		\(49\)	\(5\)	\(44\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)		\(61\)	\(3\)	\(58\)		\(57\)	\(3\)	\(54\)		\(4\)	\(0\)	\(4\)
Plus space				\(+\)		\(436\)	\(22\)	\(414\)		\(405\)	\(22\)	\(383\)		\(31\)	\(0\)	\(31\)
Minus space				\(-\)		\(460\)	\(28\)	\(432\)		\(428\)	\(28\)	\(400\)		\(32\)	\(0\)	\(32\)

Trace form

50 * q + 2 * q^5 - 8 * q^7 - 8 * q^13 - 8 * q^19 - 4 * q^23 + 50 * q^25 - 12 * q^29 + 12 * q^31 - 4 * q^37 - 4 * q^41 + 32 * q^43 + 20 * q^47 + 38 * q^49 + 4 * q^53 - 8 * q^59 - 20 * q^61 + 12 * q^67 + 12 * q^71 - 16 * q^73 + 8 * q^77 + 24 * q^89 + 8 * q^91 - 8 * q^95 + 20 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3960))\) 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	11
3960.2.a.a	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	\(\Q\)	None	✓				1320.2.a.m	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-4\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}-q^{11}-6q^{13}+2q^{17}+\cdots\)
3960.2.a.b	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	\(\Q\)	None	✓				1320.2.a.e	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-4\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}+q^{11}+2q^{13}-6q^{17}+\cdots\)
3960.2.a.c	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	\(\Q\)	None	✓				1320.2.a.g	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{11}-6q^{13}+6q^{17}+q^{25}+\cdots\)
3960.2.a.d	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	\(\Q\)	None	✓				1320.2.a.n	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{11}-2q^{13}-2q^{17}+4q^{19}+\cdots\)
3960.2.a.e	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	\(\Q\)	None	✓				1320.2.a.f	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{11}-2q^{13}+6q^{17}-4q^{19}+\cdots\)
3960.2.a.f	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	\(\Q\)	None	✓				440.2.a.d	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+q^{11}-6q^{13}-3q^{17}+\cdots\)
3960.2.a.g	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	\(\Q\)	None	✓				1320.2.a.h	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(4\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}-q^{11}+2q^{13}+2q^{17}+\cdots\)
3960.2.a.h	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	\(\Q\)	None	✓	✓			3960.2.a.h	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(4\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}+q^{11}-4q^{13}+2q^{17}+\cdots\)
3960.2.a.i	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	\(\Q\)	None	✓				440.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(4\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}+q^{11}+6q^{13}+6q^{17}+\cdots\)
3960.2.a.j	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	\(\Q\)	None	✓				440.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-q^{11}-4q^{13}+4q^{17}+\cdots\)
3960.2.a.k	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	\(\Q\)	None	✓				1320.2.a.k	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-q^{11}+8q^{17}-8q^{19}+\cdots\)
3960.2.a.l	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	\(\Q\)	None	✓				1320.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-q^{11}+4q^{13}-4q^{19}+\cdots\)
3960.2.a.m	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	\(\Q\)	None	✓				1320.2.a.i	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+q^{11}-4q^{13}-4q^{17}+\cdots\)
3960.2.a.n	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	\(\Q\)	None	✓				1320.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+q^{11}-4q^{13}+4q^{17}+\cdots\)
3960.2.a.o	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	\(\Q\)	None	✓				1320.2.a.j	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+q^{11}-4q^{17}+4q^{19}+\cdots\)
3960.2.a.p	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	\(\Q\)	None	✓				440.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+q^{11}-8q^{19}+8q^{23}+\cdots\)
3960.2.a.q	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	\(\Q\)	None	✓				1320.2.a.l	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-q^{11}-4q^{17}-4q^{19}+\cdots\)
3960.2.a.r	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	\(\Q\)	None	✓				1320.2.a.c	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}+q^{11}-4q^{13}-4q^{19}+\cdots\)
3960.2.a.s	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	\(\Q\)	None	✓	✓			3960.2.a.h	$1$	$0$	\(0\)	\(0\)	\(1\)	\(4\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}-q^{11}-4q^{13}-2q^{17}+\cdots\)
3960.2.a.t	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	\(\Q\)	None	✓				1320.2.a.d	$1$	$0$	\(0\)	\(0\)	\(1\)	\(4\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}+q^{11}+2q^{13}-2q^{17}+\cdots\)
3960.2.a.u	$3960$	$2$	3960.a	1.a	$1$	$2$	$2$	$31.621$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓	✓	3960.2.a.u	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(-2+\beta )q^{7}-q^{11}+\beta q^{13}+\cdots\)
3960.2.a.v	$3960$	$2$	3960.a	1.a	$1$	$2$	$2$	$31.621$	\(\Q(\sqrt{6}) \)	None	✓	✓	✓		3960.2.a.v	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(-2+\beta )q^{7}+q^{11}+\beta q^{13}+\cdots\)
3960.2.a.w	$3960$	$2$	3960.a	1.a	$1$	$2$	$2$	$31.621$	\(\Q(\sqrt{17}) \)	None	✓		✓		440.2.a.e	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-\beta q^{7}-q^{11}+2q^{13}+(-2+\cdots)q^{17}+\cdots\)
3960.2.a.x	$3960$	$2$	3960.a	1.a	$1$	$2$	$2$	$31.621$	\(\Q(\sqrt{2}) \)	None	✓		✓		1320.2.a.q	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta q^{7}-q^{11}+(2-\beta )q^{13}+(-2+\cdots)q^{17}+\cdots\)
3960.2.a.y	$3960$	$2$	3960.a	1.a	$1$	$2$	$2$	$31.621$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓	✓	3960.2.a.y	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta q^{7}+q^{11}+(-2+\beta )q^{13}+\cdots\)
3960.2.a.z	$3960$	$2$	3960.a	1.a	$1$	$2$	$2$	$31.621$	\(\Q(\sqrt{2}) \)	None	✓		✓		1320.2.a.p	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta q^{7}+q^{11}+(2-\beta )q^{13}+(-2+\cdots)q^{17}+\cdots\)
3960.2.a.ba	$3960$	$2$	3960.a	1.a	$1$	$2$	$2$	$31.621$	\(\Q(\sqrt{6}) \)	None	✓	✓	✓		3960.2.a.v	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(-2+\beta )q^{7}-q^{11}+\beta q^{13}+\cdots\)
3960.2.a.bb	$3960$	$2$	3960.a	1.a	$1$	$2$	$2$	$31.621$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓	✓	3960.2.a.u	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(-2+\beta )q^{7}+q^{11}+\beta q^{13}+\cdots\)
3960.2.a.bc	$3960$	$2$	3960.a	1.a	$1$	$2$	$2$	$31.621$	\(\Q(\sqrt{17}) \)	None	✓				1320.2.a.o	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}+(-1-\beta )q^{7}-q^{11}+(1-\beta )q^{13}+\cdots\)
3960.2.a.bd	$3960$	$2$	3960.a	1.a	$1$	$2$	$2$	$31.621$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓	✓	3960.2.a.y	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+\beta q^{7}-q^{11}+(-2+\beta )q^{13}+\cdots\)
3960.2.a.be	$3960$	$2$	3960.a	1.a	$1$	$2$	$2$	$31.621$	\(\Q(\sqrt{17}) \)	None	✓				440.2.a.f	$1$	$0$	\(0\)	\(0\)	\(2\)	\(3\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(1+\beta )q^{7}-q^{11}+(2-2\beta )q^{13}+\cdots\)
3960.2.a.bf	$3960$	$2$	3960.a	1.a	$1$	$2$	$2$	$31.621$	\(\Q(\sqrt{17}) \)	None	✓		✓		440.2.a.g	$1$	$0$	\(0\)	\(0\)	\(2\)	\(5\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(3-\beta )q^{7}+q^{11}+(2+2\beta )q^{13}+\cdots\)
3960.2.a.bg	$3960$	$2$	3960.a	1.a	$1$	$3$	$3$	$31.621$	3.3.1016.1	None	✓	✓	✓	✓	3960.2.a.bg	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta _{2}q^{7}-q^{11}+(1-\beta _{1}-\beta _{2})q^{13}+\cdots\)
3960.2.a.bh	$3960$	$2$	3960.a	1.a	$1$	$3$	$3$	$31.621$	3.3.1016.1	None	✓	✓	✓	✓	3960.2.a.bg	$1$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}+\beta _{2}q^{7}+q^{11}+(1-\beta _{1}-\beta _{2})q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3960))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3960)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(396))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(440))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(495))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(660))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(792))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(990))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1980))\)\(^{\oplus 2}\)