Space of modular forms of level 8967, weight 2, and trivial character

• Label: 8967.2.a
• Level: $8967$
• Weight: $2$
• Character orbit: 8967.a
• Rep. character: $\chi_{8967}(1,\cdot)$
• Character field: $\Q$
• Dimension: $410$
• Newform subspaces: $44$
• Sturm bound: $2314$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 8967 = 3 \cdot 7^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8967.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 44 \)
Sturm bound:			\(2314\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8967))\).

	Total	New	Old
Modular forms	1172	410	762
Cusp forms	1141	410	731
Eisenstein series	31	0	31

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

\(3\)	\(7\)	\(61\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(45\)
\(+\)	\(+\)	\(-\)	\(-\)	\(55\)
\(+\)	\(-\)	\(+\)	\(-\)	\(54\)
\(+\)	\(-\)	\(-\)	\(+\)	\(51\)
\(-\)	\(+\)	\(+\)	\(-\)	\(61\)
\(-\)	\(+\)	\(-\)	\(+\)	\(39\)
\(-\)	\(-\)	\(+\)	\(+\)	\(42\)
\(-\)	\(-\)	\(-\)	\(-\)	\(63\)
Plus space			\(+\)	\(177\)
Minus space			\(-\)	\(233\)

Trace form

410 * q + 4 * q^2 + 414 * q^4 + 2 * q^6 + 24 * q^8 + 410 * q^9 + 20 * q^10 + 12 * q^11 - 8 * q^13 + 438 * q^16 - 8 * q^17 + 4 * q^18 + 8 * q^20 + 12 * q^22 + 8 * q^23 + 18 * q^24 + 434 * q^25 + 4 * q^26 + 28 * q^29 + 20 * q^30 + 12 * q^31 + 32 * q^32 + 12 * q^33 + 44 * q^34 + 414 * q^36 + 36 * q^37 - 24 * q^38 - 8 * q^39 + 36 * q^40 + 32 * q^41 + 4 * q^43 + 44 * q^44 + 44 * q^46 + 16 * q^47 + 8 * q^48 - 8 * q^50 - 8 * q^51 - 8 * q^52 + 2 * q^54 - 4 * q^55 + 8 * q^57 + 28 * q^58 + 16 * q^59 + 16 * q^60 + 6 * q^61 + 12 * q^62 + 542 * q^64 + 44 * q^65 + 8 * q^66 - 32 * q^68 + 8 * q^69 + 32 * q^71 + 24 * q^72 + 8 * q^74 - 24 * q^76 + 4 * q^78 - 24 * q^79 - 32 * q^80 + 410 * q^81 + 20 * q^82 - 56 * q^83 + 32 * q^85 - 92 * q^86 - 12 * q^87 - 124 * q^88 + 20 * q^89 + 20 * q^90 - 136 * q^92 + 20 * q^93 - 24 * q^94 + 48 * q^95 + 38 * q^96 + 44 * q^97 + 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8967))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	7	61
8967.2.a.a	$8967$	$2$	8967.a	1.a	$1$	$1$	$1$	$71.602$	\(\Q\)	None	✓	✓			8967.2.a.a	$1$	$1$	\(-2\)	\(-1\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+2q^{4}+2q^{5}+2q^{6}+\cdots\)
8967.2.a.b	$8967$	$2$	8967.a	1.a	$1$	$1$	$1$	$71.602$	\(\Q\)	None	✓				1281.2.j.c	$1$	$0$	\(-2\)	\(-1\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+2q^{4}+4q^{5}+2q^{6}+\cdots\)
8967.2.a.c	$8967$	$2$	8967.a	1.a	$1$	$1$	$1$	$71.602$	\(\Q\)	None	✓				1281.2.j.c	$1$	$1$	\(-2\)	\(1\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+2q^{4}-4q^{5}-2q^{6}+\cdots\)
8967.2.a.d	$8967$	$2$	8967.a	1.a	$1$	$1$	$1$	$71.602$	\(\Q\)	None	✓	✓			8967.2.a.a	$1$	$1$	\(-2\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+2q^{4}-2q^{5}-2q^{6}+\cdots\)
8967.2.a.e	$8967$	$2$	8967.a	1.a	$1$	$1$	$1$	$71.602$	\(\Q\)	None	✓				1281.2.a.a	$1$	$1$	\(-1\)	\(-1\)	\(-3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}-3q^{5}+q^{6}+3q^{8}+\cdots\)
8967.2.a.f	$8967$	$2$	8967.a	1.a	$1$	$1$	$1$	$71.602$	\(\Q\)	None	✓				1281.2.j.b	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-2q^{5}+q^{9}+2q^{12}+\cdots\)
8967.2.a.g	$8967$	$2$	8967.a	1.a	$1$	$1$	$1$	$71.602$	\(\Q\)	None	✓				1281.2.j.a	$1$	$1$	\(0\)	\(-1\)	\(4\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}+4q^{5}+q^{9}-2q^{11}+\cdots\)
8967.2.a.h	$8967$	$2$	8967.a	1.a	$1$	$1$	$1$	$71.602$	\(\Q\)	None	✓				1281.2.j.a	$1$	$0$	\(0\)	\(1\)	\(-4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}-4q^{5}+q^{9}-2q^{11}+\cdots\)
8967.2.a.i	$8967$	$2$	8967.a	1.a	$1$	$1$	$1$	$71.602$	\(\Q\)	None	✓				1281.2.j.b	$1$	$0$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+2q^{5}+q^{9}-2q^{12}+\cdots\)
8967.2.a.j	$8967$	$2$	8967.a	1.a	$1$	$1$	$1$	$71.602$	\(\Q\)	None	✓				1281.2.a.c	$1$	$0$	\(1\)	\(-1\)	\(1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-3q^{8}+\cdots\)
8967.2.a.k	$8967$	$2$	8967.a	1.a	$1$	$1$	$1$	$71.602$	\(\Q\)	None	✓				1281.2.a.b	$1$	$1$	\(1\)	\(1\)	\(-3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}-3q^{5}+q^{6}-3q^{8}+\cdots\)
8967.2.a.l	$8967$	$2$	8967.a	1.a	$1$	$1$	$1$	$71.602$	\(\Q\)	None	✓				1281.2.a.e	$1$	$1$	\(2\)	\(-1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}-2q^{6}+q^{9}+4q^{11}+\cdots\)
8967.2.a.m	$8967$	$2$	8967.a	1.a	$1$	$1$	$1$	$71.602$	\(\Q\)	None	✓				1281.2.a.d	$1$	$0$	\(2\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}+2q^{6}+q^{9}-4q^{11}+\cdots\)
8967.2.a.n	$8967$	$2$	8967.a	1.a	$1$	$2$	$2$	$71.602$	\(\Q(\sqrt{5}) \)	None	✓				1281.2.j.e	$1$	$1$	\(-3\)	\(-2\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}-2\beta q^{5}+\cdots\)
8967.2.a.o	$8967$	$2$	8967.a	1.a	$1$	$2$	$2$	$71.602$	\(\Q(\sqrt{5}) \)	None	✓				1281.2.j.e	$1$	$0$	\(-3\)	\(2\)	\(2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+2\beta q^{5}+\cdots\)
8967.2.a.p	$8967$	$2$	8967.a	1.a	$1$	$2$	$2$	$71.602$	\(\Q(\sqrt{2}) \)	None	✓				183.2.a.a	$1$	$0$	\(-2\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+q^{5}+\cdots\)
8967.2.a.q	$8967$	$2$	8967.a	1.a	$1$	$2$	$2$	$71.602$	\(\Q(\sqrt{5}) \)	None	✓				1281.2.j.d	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}+(1+\beta )q^{5}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
8967.2.a.r	$8967$	$2$	8967.a	1.a	$1$	$2$	$2$	$71.602$	\(\Q(\sqrt{5}) \)	None	✓				1281.2.j.d	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+(-1-\beta )q^{5}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
8967.2.a.s	$8967$	$2$	8967.a	1.a	$1$	$3$	$3$	$71.602$	3.3.148.1	None	✓				183.2.a.b	$1$	$1$	\(1\)	\(3\)	\(-6\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-2q^{5}+\cdots\)
8967.2.a.t	$8967$	$2$	8967.a	1.a	$1$	$4$	$4$	$71.602$	4.4.725.1	None	✓				1281.2.a.f	$1$	$1$	\(-2\)	\(-4\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}-q^{3}+(\beta _{2}-\beta _{3})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
8967.2.a.u	$8967$	$2$	8967.a	1.a	$1$	$5$	$5$	$71.602$	5.5.216637.1	None	✓				1281.2.a.g	$1$	$1$	\(-2\)	\(5\)	\(5\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots\)
8967.2.a.v	$8967$	$2$	8967.a	1.a	$1$	$5$	$5$	$71.602$	5.5.2027733.1	None	✓				1281.2.a.i	$1$	$1$	\(-1\)	\(-5\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots\)
8967.2.a.w	$8967$	$2$	8967.a	1.a	$1$	$5$	$5$	$71.602$	5.5.594077.1	None	✓				1281.2.a.h	$1$	$1$	\(-1\)	\(5\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{2}q^{5}+\cdots\)
8967.2.a.x	$8967$	$2$	8967.a	1.a	$1$	$6$	$6$	$71.602$	6.6.1767625.1	None	✓				1281.2.a.j	$1$	$0$	\(0\)	\(-6\)	\(5\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(1-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
8967.2.a.y	$8967$	$2$	8967.a	1.a	$1$	$6$	$6$	$71.602$	6.6.91407488.1	None	✓				183.2.a.c	$1$	$1$	\(0\)	\(-6\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-1-\beta _{3}+\cdots)q^{5}+\cdots\)
8967.2.a.z	$8967$	$2$	8967.a	1.a	$1$	$8$	$8$	$71.602$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				1281.2.a.k	$1$	$0$	\(-2\)	\(8\)	\(5\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
8967.2.a.ba	$8967$	$2$	8967.a	1.a	$1$	$10$	$10$	$71.602$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓			8967.2.a.ba	$1$	$1$	\(0\)	\(-10\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{9}q^{5}+\cdots\)
8967.2.a.bb	$8967$	$2$	8967.a	1.a	$1$	$10$	$10$	$71.602$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓			8967.2.a.ba	$1$	$1$	\(0\)	\(10\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{9}q^{5}+\cdots\)
8967.2.a.bc	$8967$	$2$	8967.a	1.a	$1$	$10$	$10$	$71.602$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				1281.2.a.l	$1$	$0$	\(4\)	\(10\)	\(-3\)	\(0\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots\)
8967.2.a.bd	$8967$	$2$	8967.a	1.a	$1$	$11$	$11$	$71.602$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓				1281.2.a.m	$1$	$0$	\(0\)	\(-11\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{9}q^{5}+\cdots\)
8967.2.a.be	$8967$	$2$	8967.a	1.a	$1$	$15$	$15$	$71.602$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓				1281.2.j.f	$1$	$0$	\(0\)	\(-15\)	\(5\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots\)
8967.2.a.bf	$8967$	$2$	8967.a	1.a	$1$	$15$	$15$	$71.602$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓		✓		1281.2.j.f	$1$	$1$	\(0\)	\(15\)	\(-5\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)
8967.2.a.bg	$8967$	$2$	8967.a	1.a	$1$	$16$	$16$	$71.602$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓				1281.2.j.g	$1$	$0$	\(0\)	\(-16\)	\(3\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots\)
8967.2.a.bh	$8967$	$2$	8967.a	1.a	$1$	$16$	$16$	$71.602$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓				1281.2.j.g	$1$	$1$	\(0\)	\(16\)	\(-3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
8967.2.a.bi	$8967$	$2$	8967.a	1.a	$1$	$19$	$19$	$71.602$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	✓	✓		8967.2.a.bi	$1$	$0$	\(4\)	\(-19\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}+\cdots\)
8967.2.a.bj	$8967$	$2$	8967.a	1.a	$1$	$19$	$19$	$71.602$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	✓			8967.2.a.bi	$1$	$0$	\(4\)	\(19\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots\)
8967.2.a.bk	$8967$	$2$	8967.a	1.a	$1$	$21$	$21$	$71.602$		None	✓				1281.2.j.i	$1$	$1$	\(0\)	\(-21\)	\(-11\)	\(0\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
8967.2.a.bl	$8967$	$2$	8967.a	1.a	$1$	$21$	$21$	$71.602$		None	✓		✓		1281.2.j.i	$1$	$0$	\(0\)	\(21\)	\(11\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
8967.2.a.bm	$8967$	$2$	8967.a	1.a	$1$	$21$	$21$	$71.602$		None	✓		✓		1281.2.j.h	$1$	$1$	\(1\)	\(-21\)	\(-7\)	\(0\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
8967.2.a.bn	$8967$	$2$	8967.a	1.a	$1$	$21$	$21$	$71.602$		None	✓				1281.2.j.h	$1$	$0$	\(1\)	\(21\)	\(7\)	\(0\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
8967.2.a.bo	$8967$	$2$	8967.a	1.a	$1$	$22$	$22$	$71.602$		None	✓	✓	✓		8967.2.a.bo	$1$	$1$	\(-4\)	\(-22\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
8967.2.a.bp	$8967$	$2$	8967.a	1.a	$1$	$22$	$22$	$71.602$		None	✓	✓	✓		8967.2.a.bo	$1$	$1$	\(-4\)	\(22\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
8967.2.a.bq	$8967$	$2$	8967.a	1.a	$1$	$38$	$38$	$71.602$		None	✓	✓	✓		8967.2.a.bq	$1$	$0$	\(8\)	\(-38\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
8967.2.a.br	$8967$	$2$	8967.a	1.a	$1$	$38$	$38$	$71.602$		None	✓	✓	✓		8967.2.a.bq	$1$	$0$	\(8\)	\(38\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8967))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8967)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(61))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(183))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(427))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1281))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2989))\)\(^{\oplus 2}\)