Space of modular forms of level 8954, weight 2, and trivial character

• Label: 8954.2.a
• Level: $8954$
• Weight: $2$
• Character orbit: 8954.a
• Rep. character: $\chi_{8954}(1,\cdot)$
• Character field: $\Q$
• Dimension: $327$
• Newform subspaces: $48$
• Sturm bound: $2508$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 8954 = 2 \cdot 11^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8954.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 48 \)
Sturm bound:			\(2508\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8954))\).

	Total	New	Old
Modular forms	1278	327	951
Cusp forms	1231	327	904
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.

\(2\)	\(11\)	\(37\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(150\)	\(38\)	\(112\)		\(145\)	\(38\)	\(107\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)		\(168\)	\(45\)	\(123\)		\(162\)	\(45\)	\(117\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(167\)	\(45\)	\(122\)		\(161\)	\(45\)	\(116\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(154\)	\(35\)	\(119\)		\(148\)	\(35\)	\(113\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(165\)	\(46\)	\(119\)		\(159\)	\(46\)	\(113\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(153\)	\(33\)	\(120\)		\(147\)	\(33\)	\(114\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(157\)	\(35\)	\(122\)		\(151\)	\(35\)	\(116\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(164\)	\(50\)	\(114\)		\(158\)	\(50\)	\(108\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(614\)	\(141\)	\(473\)		\(591\)	\(141\)	\(450\)		\(23\)	\(0\)	\(23\)
Minus space			\(-\)		\(664\)	\(186\)	\(478\)		\(640\)	\(186\)	\(454\)		\(24\)	\(0\)	\(24\)

Trace form

327 * q + q^2 + 2 * q^3 + 327 * q^4 + 2 * q^5 + 8 * q^7 + q^8 + 333 * q^9 + 4 * q^10 + 2 * q^12 + 14 * q^13 - 4 * q^14 + 327 * q^16 + 6 * q^17 + 5 * q^18 + 16 * q^19 + 2 * q^20 - 4 * q^21 - 4 * q^23 + 335 * q^25 + 12 * q^26 - 4 * q^27 + 8 * q^28 + 6 * q^29 + 12 * q^31 + q^32 + 6 * q^34 + 12 * q^35 + 333 * q^36 - q^37 + 20 * q^38 + 28 * q^39 + 4 * q^40 - 4 * q^41 + 8 * q^42 + 16 * q^43 + 10 * q^45 - 22 * q^46 - 4 * q^47 + 2 * q^48 + 351 * q^49 - q^50 - 8 * q^51 + 14 * q^52 + 14 * q^53 + 24 * q^54 - 4 * q^56 - 28 * q^57 + 20 * q^58 + 32 * q^59 - 2 * q^61 + 14 * q^62 + 12 * q^63 + 327 * q^64 - 32 * q^65 + 34 * q^67 + 6 * q^68 - 16 * q^69 + 20 * q^70 - 8 * q^71 + 5 * q^72 + 8 * q^73 + 5 * q^74 - 16 * q^75 + 16 * q^76 - 10 * q^78 + 4 * q^79 + 2 * q^80 + 335 * q^81 + 26 * q^82 - 20 * q^83 - 4 * q^84 - 4 * q^85 + 16 * q^86 - 12 * q^87 + 2 * q^89 + 2 * q^90 - 8 * q^91 - 4 * q^92 - 40 * q^93 - 24 * q^94 - 36 * q^95 - 2 * q^97 - 7 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8954))\) 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	11	37
8954.2.a.a	$8954$	$2$	8954.a	1.a	$1$	$1$	$1$	$71.498$	\(\Q\)	None	✓	✓			8954.2.a.a	$1$	$1$	\(-1\)	\(-2\)	\(-1\)	\(4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}+q^{4}-q^{5}+2q^{6}+4q^{7}+\cdots\)
8954.2.a.b	$8954$	$2$	8954.a	1.a	$1$	$1$	$1$	$71.498$	\(\Q\)	None	✓	✓			8954.2.a.b	$1$	$1$	\(-1\)	\(-2\)	\(0\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}+q^{4}+2q^{6}-4q^{7}-q^{8}+\cdots\)
8954.2.a.c	$8954$	$2$	8954.a	1.a	$1$	$1$	$1$	$71.498$	\(\Q\)	None	✓				814.2.a.b	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+4q^{7}-q^{8}-3q^{9}+\cdots\)
8954.2.a.d	$8954$	$2$	8954.a	1.a	$1$	$1$	$1$	$71.498$	\(\Q\)	None	✓	✓			8954.2.a.d	$1$	$1$	\(-1\)	\(2\)	\(3\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}+3q^{5}-2q^{6}-q^{8}+\cdots\)
8954.2.a.e	$8954$	$2$	8954.a	1.a	$1$	$1$	$1$	$71.498$	\(\Q\)	None	✓				814.2.a.a	$1$	$2$	\(1\)	\(-2\)	\(-3\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}-3q^{5}-2q^{6}-2q^{7}+\cdots\)
8954.2.a.f	$8954$	$2$	8954.a	1.a	$1$	$1$	$1$	$71.498$	\(\Q\)	None	✓	✓			8954.2.a.a	$1$	$2$	\(1\)	\(-2\)	\(-1\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}-4q^{7}+\cdots\)
8954.2.a.g	$8954$	$2$	8954.a	1.a	$1$	$1$	$1$	$71.498$	\(\Q\)	None	✓	✓			8954.2.a.b	$1$	$0$	\(1\)	\(-2\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}-2q^{6}+4q^{7}+q^{8}+\cdots\)
8954.2.a.h	$8954$	$2$	8954.a	1.a	$1$	$1$	$1$	$71.498$	\(\Q\)	None	✓	✓			8954.2.a.d	$1$	$0$	\(1\)	\(2\)	\(3\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}+q^{4}+3q^{5}+2q^{6}+q^{8}+\cdots\)
8954.2.a.i	$8954$	$2$	8954.a	1.a	$1$	$2$	$2$	$71.498$	\(\Q(\sqrt{2}) \)	None	✓				814.2.a.d	$1$	$1$	\(-2\)	\(-4\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-2+\beta )q^{3}+q^{4}+(-1-\beta )q^{5}+\cdots\)
8954.2.a.j	$8954$	$2$	8954.a	1.a	$1$	$2$	$2$	$71.498$	\(\Q(\sqrt{5}) \)	None	✓				74.2.a.b	$1$	$0$	\(-2\)	\(-1\)	\(1\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta q^{3}+q^{4}+(-1+3\beta )q^{5}+\cdots\)
8954.2.a.k	$8954$	$2$	8954.a	1.a	$1$	$2$	$2$	$71.498$	\(\Q(\sqrt{2}) \)	None	✓	✓			8954.2.a.k	$1$	$0$	\(-2\)	\(0\)	\(-6\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}+q^{4}+(-3+\beta )q^{5}-\beta q^{6}+\cdots\)
8954.2.a.l	$8954$	$2$	8954.a	1.a	$1$	$2$	$2$	$71.498$	\(\Q(\sqrt{5}) \)	None	✓	✓			8954.2.a.l	$1$	$1$	\(-2\)	\(0\)	\(5\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-2\beta )q^{3}+q^{4}+(3-\beta )q^{5}+\cdots\)
8954.2.a.m	$8954$	$2$	8954.a	1.a	$1$	$2$	$2$	$71.498$	\(\Q(\sqrt{2}) \)	None	✓	✓			8954.2.a.k	$1$	$1$	\(2\)	\(0\)	\(-6\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta q^{3}+q^{4}+(-3+\beta )q^{5}+\beta q^{6}+\cdots\)
8954.2.a.n	$8954$	$2$	8954.a	1.a	$1$	$2$	$2$	$71.498$	\(\Q(\sqrt{2}) \)	None	✓				814.2.a.c	$1$	$0$	\(2\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta q^{3}+q^{4}+(1-\beta )q^{5}+\beta q^{6}+\cdots\)
8954.2.a.o	$8954$	$2$	8954.a	1.a	$1$	$2$	$2$	$71.498$	\(\Q(\sqrt{5}) \)	None	✓	✓			8954.2.a.l	$1$	$0$	\(2\)	\(0\)	\(5\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-2\beta )q^{3}+q^{4}+(3-\beta )q^{5}+\cdots\)
8954.2.a.p	$8954$	$2$	8954.a	1.a	$1$	$2$	$2$	$71.498$	\(\Q(\sqrt{13}) \)	None	✓				74.2.a.a	$1$	$0$	\(2\)	\(3\)	\(-1\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1+\beta )q^{3}+q^{4}-\beta q^{5}+(1+\beta )q^{6}+\cdots\)
8954.2.a.q	$8954$	$2$	8954.a	1.a	$1$	$3$	$3$	$71.498$	3.3.404.1	None	✓				814.2.a.f	$1$	$0$	\(-3\)	\(-2\)	\(-7\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-2-\beta _{2})q^{5}+\cdots\)
8954.2.a.r	$8954$	$2$	8954.a	1.a	$1$	$3$	$3$	$71.498$	3.3.229.1	None	✓	✓			8954.2.a.r	$1$	$1$	\(-3\)	\(-2\)	\(-1\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
8954.2.a.s	$8954$	$2$	8954.a	1.a	$1$	$3$	$3$	$71.498$	3.3.229.1	None	✓	✓			8954.2.a.r	$1$	$0$	\(3\)	\(-2\)	\(-1\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
8954.2.a.t	$8954$	$2$	8954.a	1.a	$1$	$3$	$3$	$71.498$	3.3.148.1	None	✓				814.2.a.e	$1$	$1$	\(3\)	\(0\)	\(-5\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{2}q^{3}+q^{4}+(-2+\beta _{1})q^{5}+\cdots\)
8954.2.a.u	$8954$	$2$	8954.a	1.a	$1$	$4$	$4$	$71.498$	4.4.11344.1	None	✓				814.2.a.h	$1$	$1$	\(-4\)	\(2\)	\(2\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}-\beta _{2}q^{5}+(-1+\cdots)q^{6}+\cdots\)
8954.2.a.v	$8954$	$2$	8954.a	1.a	$1$	$4$	$4$	$71.498$	4.4.4352.1	None	✓				814.2.a.i	$1$	$0$	\(-4\)	\(4\)	\(4\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta _{2}+\beta _{3})q^{3}+q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
8954.2.a.w	$8954$	$2$	8954.a	1.a	$1$	$4$	$4$	$71.498$	4.4.16448.1	None	✓				814.2.a.g	$1$	$1$	\(4\)	\(-2\)	\(2\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{3}q^{3}+q^{4}-\beta _{2}q^{5}+\beta _{3}q^{6}+\cdots\)
8954.2.a.x	$8954$	$2$	8954.a	1.a	$1$	$5$	$5$	$71.498$	5.5.303952.1	None	✓	✓			8954.2.a.x	$1$	$0$	\(-5\)	\(0\)	\(1\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{4}q^{3}+q^{4}+\beta _{1}q^{5}+\beta _{4}q^{6}+\cdots\)
8954.2.a.y	$8954$	$2$	8954.a	1.a	$1$	$5$	$5$	$71.498$	5.5.592041.1	None	✓	✓			8954.2.a.y	$1$	$1$	\(-5\)	\(1\)	\(6\)	\(-9\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{2}q^{3}+q^{4}+(1+\beta _{1})q^{5}+\beta _{2}q^{6}+\cdots\)
8954.2.a.z	$8954$	$2$	8954.a	1.a	$1$	$5$	$5$	$71.498$	5.5.702521.1	None	✓	✓			8954.2.a.z	$1$	$1$	\(-5\)	\(3\)	\(0\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta _{4})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
8954.2.a.ba	$8954$	$2$	8954.a	1.a	$1$	$5$	$5$	$71.498$	5.5.303952.1	None	✓	✓			8954.2.a.x	$1$	$1$	\(5\)	\(0\)	\(1\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{4}q^{3}+q^{4}+\beta _{1}q^{5}-\beta _{4}q^{6}+\cdots\)
8954.2.a.bb	$8954$	$2$	8954.a	1.a	$1$	$5$	$5$	$71.498$	5.5.2186192.1	None	✓				814.2.a.j	$1$	$0$	\(5\)	\(0\)	\(6\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
8954.2.a.bc	$8954$	$2$	8954.a	1.a	$1$	$5$	$5$	$71.498$	5.5.592041.1	None	✓	✓			8954.2.a.y	$1$	$0$	\(5\)	\(1\)	\(6\)	\(9\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{2}q^{3}+q^{4}+(1+\beta _{1})q^{5}-\beta _{2}q^{6}+\cdots\)
8954.2.a.bd	$8954$	$2$	8954.a	1.a	$1$	$5$	$5$	$71.498$	5.5.702521.1	None	✓	✓			8954.2.a.z	$1$	$0$	\(5\)	\(3\)	\(0\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{4})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
8954.2.a.be	$8954$	$2$	8954.a	1.a	$1$	$6$	$6$	$71.498$	6.6.249645904.1	None	✓	✓			8954.2.a.be	$1$	$1$	\(-6\)	\(0\)	\(1\)	\(-8\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-\beta _{1}-\beta _{4})q^{5}+\cdots\)
8954.2.a.bf	$8954$	$2$	8954.a	1.a	$1$	$6$	$6$	$71.498$	6.6.249645904.1	None	✓	✓			8954.2.a.be	$1$	$0$	\(6\)	\(0\)	\(1\)	\(8\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-\beta _{1}-\beta _{4})q^{5}+\cdots\)
8954.2.a.bg	$8954$	$2$	8954.a	1.a	$1$	$7$	$7$	$71.498$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			8954.2.a.bg	$1$	$0$	\(-7\)	\(-1\)	\(-3\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots\)
8954.2.a.bh	$8954$	$2$	8954.a	1.a	$1$	$7$	$7$	$71.498$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			8954.2.a.bh	$1$	$0$	\(-7\)	\(1\)	\(-3\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{5}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{5}q^{6}+\cdots\)
8954.2.a.bi	$8954$	$2$	8954.a	1.a	$1$	$7$	$7$	$71.498$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			8954.2.a.bg	$1$	$1$	\(7\)	\(-1\)	\(-3\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{6}q^{5}-\beta _{1}q^{6}+\cdots\)
8954.2.a.bj	$8954$	$2$	8954.a	1.a	$1$	$7$	$7$	$71.498$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			8954.2.a.bh	$1$	$1$	\(7\)	\(1\)	\(-3\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{5}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{5}q^{6}+\cdots\)
8954.2.a.bk	$8954$	$2$	8954.a	1.a	$1$	$12$	$12$	$71.498$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		814.2.h.a	$1$	$1$	\(-12\)	\(-7\)	\(-4\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+\beta _{5}q^{5}+\cdots\)
8954.2.a.bl	$8954$	$2$	8954.a	1.a	$1$	$12$	$12$	$71.498$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				814.2.h.a	$1$	$1$	\(12\)	\(-7\)	\(-4\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+\beta _{5}q^{5}+\cdots\)
8954.2.a.bm	$8954$	$2$	8954.a	1.a	$1$	$14$	$14$	$71.498$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓				814.2.h.b	$1$	$1$	\(-14\)	\(-4\)	\(-6\)	\(5\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{4}q^{5}+\beta _{1}q^{6}+\cdots\)
8954.2.a.bn	$8954$	$2$	8954.a	1.a	$1$	$14$	$14$	$71.498$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓			8954.2.a.bn	$1$	$0$	\(-14\)	\(0\)	\(-10\)	\(14\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{5})q^{5}+\cdots\)
8954.2.a.bo	$8954$	$2$	8954.a	1.a	$1$	$14$	$14$	$71.498$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓		✓		814.2.h.b	$1$	$1$	\(14\)	\(-4\)	\(-6\)	\(-5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots\)
8954.2.a.bp	$8954$	$2$	8954.a	1.a	$1$	$14$	$14$	$71.498$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓	✓		8954.2.a.bn	$1$	$1$	\(14\)	\(0\)	\(-10\)	\(-14\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{5})q^{5}+\cdots\)
8954.2.a.bq	$8954$	$2$	8954.a	1.a	$1$	$16$	$16$	$71.498$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓	✓		8954.2.a.bq	$1$	$1$	\(-16\)	\(0\)	\(6\)	\(-2\)		$+$	$+$	$+$	$+$	$3$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{10}q^{5}+\beta _{1}q^{6}+\cdots\)
8954.2.a.br	$8954$	$2$	8954.a	1.a	$1$	$16$	$16$	$71.498$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓			8954.2.a.bq	$1$	$0$	\(16\)	\(0\)	\(6\)	\(2\)		$-$	$+$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{10}q^{5}-\beta _{1}q^{6}+\cdots\)
8954.2.a.bs	$8954$	$2$	8954.a	1.a	$1$	$22$	$22$	$71.498$		None	✓		✓		814.2.h.c	$1$	$0$	\(-22\)	\(5\)	\(8\)	\(-7\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
8954.2.a.bt	$8954$	$2$	8954.a	1.a	$1$	$22$	$22$	$71.498$		None	✓		✓		814.2.h.c	$1$	$0$	\(22\)	\(5\)	\(8\)	\(7\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
8954.2.a.bu	$8954$	$2$	8954.a	1.a	$1$	$24$	$24$	$71.498$		None	✓		✓		814.2.h.d	$1$	$0$	\(-24\)	\(8\)	\(6\)	\(-3\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
8954.2.a.bv	$8954$	$2$	8954.a	1.a	$1$	$24$	$24$	$71.498$		None	✓		✓		814.2.h.d	$1$	$0$	\(24\)	\(8\)	\(6\)	\(3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8954))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8954)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(407))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(814))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4477))\)\(^{\oplus 2}\)