Space of modular forms of level 28900, weight 2, and trivial character

• Label: 28900.2.a
• Level: $28900$
• Weight: $2$
• Character orbit: 28900.a
• Rep. character: $\chi_{28900}(1,\cdot)$
• Character field: $\Q$
• Dimension: $429$
• Newform subspaces: $64$
• Sturm bound: $9180$

Defining parameters

Level:	\( N \)	\(=\)	\( 28900 = 2^{2} \cdot 5^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	28900.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 64 \)
Sturm bound:			\(9180\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(28900))\).

	Total	New	Old
Modular forms	4752	429	4323
Cusp forms	4429	429	4000
Eisenstein series	323	0	323

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

\(2\)	\(5\)	\(17\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(594\)	\(0\)	\(594\)		\(541\)	\(0\)	\(541\)		\(53\)	\(0\)	\(53\)
\(+\)	\(+\)	\(-\)	\(-\)		\(606\)	\(0\)	\(606\)		\(552\)	\(0\)	\(552\)		\(54\)	\(0\)	\(54\)
\(+\)	\(-\)	\(+\)	\(-\)		\(603\)	\(0\)	\(603\)		\(549\)	\(0\)	\(549\)		\(54\)	\(0\)	\(54\)
\(+\)	\(-\)	\(-\)	\(+\)		\(599\)	\(0\)	\(599\)		\(545\)	\(0\)	\(545\)		\(54\)	\(0\)	\(54\)
\(-\)	\(+\)	\(+\)	\(-\)		\(594\)	\(103\)	\(491\)		\(567\)	\(103\)	\(464\)		\(27\)	\(0\)	\(27\)
\(-\)	\(+\)	\(-\)	\(+\)		\(582\)	\(100\)	\(482\)		\(555\)	\(100\)	\(455\)		\(27\)	\(0\)	\(27\)
\(-\)	\(-\)	\(+\)	\(+\)		\(585\)	\(109\)	\(476\)		\(558\)	\(109\)	\(449\)		\(27\)	\(0\)	\(27\)
\(-\)	\(-\)	\(-\)	\(-\)		\(589\)	\(117\)	\(472\)		\(562\)	\(117\)	\(445\)		\(27\)	\(0\)	\(27\)
Plus space			\(+\)		\(2360\)	\(209\)	\(2151\)		\(2199\)	\(209\)	\(1990\)		\(161\)	\(0\)	\(161\)
Minus space			\(-\)		\(2392\)	\(220\)	\(2172\)		\(2230\)	\(220\)	\(2010\)		\(162\)	\(0\)	\(162\)

Trace form

429 * q - 4 * q^7 + 425 * q^9 - 6 * q^11 - 10 * q^19 - 12 * q^21 + 8 * q^23 - 18 * q^29 + 6 * q^31 - 10 * q^33 + 10 * q^37 - 12 * q^39 - 14 * q^41 - 8 * q^43 - 16 * q^47 + 399 * q^49 + 12 * q^53 - 32 * q^57 - 10 * q^59 - 26 * q^61 - 12 * q^63 - 4 * q^67 - 66 * q^69 - 10 * q^71 + 2 * q^73 - 14 * q^77 - 2 * q^79 + 385 * q^81 - 10 * q^83 - 16 * q^89 - 28 * q^91 - 4 * q^93 - 10 * q^97 - 86 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(28900))\) 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	5	17
28900.2.a.a	$28900$	$2$	28900.a	1.a	$1$	$1$	$1$	$230.768$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{7}+q^{9}+5q^{11}-6q^{13}+\cdots\)
28900.2.a.b	$28900$	$2$	28900.a	1.a	$1$	$1$	$1$	$230.768$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+2q^{7}+q^{9}-2q^{13}-4q^{19}+\cdots\)
28900.2.a.c	$28900$	$2$	28900.a	1.a	$1$	$1$	$1$	$230.768$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}-2q^{9}-q^{13}-4q^{19}+\cdots\)
28900.2.a.d	$28900$	$2$	28900.a	1.a	$1$	$1$	$1$	$230.768$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{7}-2q^{9}-6q^{11}-6q^{13}+\cdots\)
28900.2.a.e	$28900$	$2$	28900.a	1.a	$1$	$1$	$1$	$230.768$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{7}-2q^{9}+6q^{11}+6q^{13}+\cdots\)
28900.2.a.f	$28900$	$2$	28900.a	1.a	$1$	$1$	$1$	$230.768$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}-3q^{9}-2q^{11}+6q^{13}+6q^{29}+\cdots\)
28900.2.a.g	$28900$	$2$	28900.a	1.a	$1$	$1$	$1$	$230.768$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-3q^{9}-q^{11}+3q^{19}-3q^{29}+\cdots\)
28900.2.a.h	$28900$	$2$	28900.a	1.a	$1$	$1$	$1$	$230.768$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-3q^{9}+q^{11}+3q^{19}+3q^{29}+\cdots\)
28900.2.a.i	$28900$	$2$	28900.a	1.a	$1$	$1$	$1$	$230.768$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{7}-2q^{9}-6q^{11}+6q^{13}+\cdots\)
28900.2.a.j	$28900$	$2$	28900.a	1.a	$1$	$1$	$1$	$230.768$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{7}-2q^{9}+6q^{11}-6q^{13}+\cdots\)
28900.2.a.k	$28900$	$2$	28900.a	1.a	$1$	$1$	$1$	$230.768$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}-2q^{9}+q^{13}-4q^{19}+\cdots\)
28900.2.a.l	$28900$	$2$	28900.a	1.a	$1$	$1$	$1$	$230.768$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+2q^{7}+q^{9}-5q^{11}-6q^{13}+\cdots\)
28900.2.a.m	$28900$	$2$	28900.a	1.a	$1$	$2$	$2$	$230.768$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
28900.2.a.n	$28900$	$2$	28900.a	1.a	$1$	$2$	$2$	$230.768$	\(\Q(\sqrt{21}) \)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(-5\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
28900.2.a.o	$28900$	$2$	28900.a	1.a	$1$	$2$	$2$	$230.768$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
28900.2.a.p	$28900$	$2$	28900.a	1.a	$1$	$2$	$2$	$230.768$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
28900.2.a.q	$28900$	$2$	28900.a	1.a	$1$	$2$	$2$	$230.768$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
28900.2.a.r	$28900$	$2$	28900.a	1.a	$1$	$2$	$2$	$230.768$	\(\Q(\sqrt{21}) \)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(5\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
28900.2.a.s	$28900$	$2$	28900.a	1.a	$1$	$2$	$2$	$230.768$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
28900.2.a.t	$28900$	$2$	28900.a	1.a	$1$	$2$	$2$	$230.768$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
28900.2.a.u	$28900$	$2$	28900.a	1.a	$1$	$3$	$3$	$230.768$	3.3.785.1	None	✓	?				$-1$		\(0\)	\(-3\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
28900.2.a.v	$28900$	$2$	28900.a	1.a	$1$	$3$	$3$	$230.768$	3.3.785.1	None	✓	?				$-1$		\(0\)	\(-3\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
28900.2.a.w	$28900$	$2$	28900.a	1.a	$1$	$3$	$3$	$230.768$	\(\Q(\zeta_{18})^+\)	None	✓	?				$-1$		\(0\)	\(-3\)	\(0\)	\(6\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
28900.2.a.x	$28900$	$2$	28900.a	1.a	$1$	$3$	$3$	$230.768$	3.3.1524.1	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
28900.2.a.y	$28900$	$2$	28900.a	1.a	$1$	$3$	$3$	$230.768$	3.3.785.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
28900.2.a.z	$28900$	$2$	28900.a	1.a	$1$	$3$	$3$	$230.768$	3.3.785.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
28900.2.a.ba	$28900$	$2$	28900.a	1.a	$1$	$3$	$3$	$230.768$	3.3.404.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
28900.2.a.bb	$28900$	$2$	28900.a	1.a	$1$	$3$	$3$	$230.768$	3.3.785.1	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
28900.2.a.bc	$28900$	$2$	28900.a	1.a	$1$	$3$	$3$	$230.768$	3.3.785.1	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
28900.2.a.bd	$28900$	$2$	28900.a	1.a	$1$	$3$	$3$	$230.768$	3.3.1524.1	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(4\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
28900.2.a.be	$28900$	$2$	28900.a	1.a	$1$	$3$	$3$	$230.768$	\(\Q(\zeta_{18})^+\)	None	✓	?				$-1$		\(0\)	\(3\)	\(0\)	\(-6\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
28900.2.a.bf	$28900$	$2$	28900.a	1.a	$1$	$3$	$3$	$230.768$	3.3.785.1	None	✓	?				$-1$		\(0\)	\(3\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
28900.2.a.bg	$28900$	$2$	28900.a	1.a	$1$	$3$	$3$	$230.768$	3.3.785.1	None	✓	?				$-1$		\(0\)	\(3\)	\(0\)	\(-1\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
28900.2.a.bh	$28900$	$2$	28900.a	1.a	$1$	$4$	$4$	$230.768$	4.4.11344.1	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
28900.2.a.bi	$28900$	$2$	28900.a	1.a	$1$	$4$	$4$	$230.768$	\(\Q(\zeta_{16})^+\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
28900.2.a.bj	$28900$	$2$	28900.a	1.a	$1$	$4$	$4$	$230.768$	\(\Q(\sqrt{2}, \sqrt{13})\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
28900.2.a.bk	$28900$	$2$	28900.a	1.a	$1$	$4$	$4$	$230.768$	4.4.11344.1	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
28900.2.a.bl	$28900$	$2$	28900.a	1.a	$1$	$5$	$5$	$230.768$	5.5.27977168.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
28900.2.a.bm	$28900$	$2$	28900.a	1.a	$1$	$5$	$5$	$230.768$	5.5.27977168.1	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(1\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
28900.2.a.bn	$28900$	$2$	28900.a	1.a	$1$	$6$	$6$	$230.768$	6.6.14414517.1	None	✓	?				$-1$		\(0\)	\(-3\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
28900.2.a.bo	$28900$	$2$	28900.a	1.a	$1$	$6$	$6$	$230.768$	6.6.9521152.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
28900.2.a.bp	$28900$	$2$	28900.a	1.a	$1$	$6$	$6$	$230.768$	6.6.336208896.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
28900.2.a.bq	$28900$	$2$	28900.a	1.a	$1$	$6$	$6$	$230.768$	6.6.336208896.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
28900.2.a.br	$28900$	$2$	28900.a	1.a	$1$	$6$	$6$	$230.768$	6.6.3031603600.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
28900.2.a.bs	$28900$	$2$	28900.a	1.a	$1$	$6$	$6$	$230.768$	6.6.3031603600.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
28900.2.a.bt	$28900$	$2$	28900.a	1.a	$1$	$6$	$6$	$230.768$	6.6.9521152.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
28900.2.a.bu	$28900$	$2$	28900.a	1.a	$1$	$6$	$6$	$230.768$	6.6.14414517.1	None	✓	?				$-1$		\(0\)	\(3\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
28900.2.a.bv	$28900$	$2$	28900.a	1.a	$1$	$8$	$8$	$230.768$	8.8.\(\cdots\).2	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
28900.2.a.bw	$28900$	$2$	28900.a	1.a	$1$	$12$	$12$	$230.768$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-3\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
28900.2.a.bx	$28900$	$2$	28900.a	1.a	$1$	$12$	$12$	$230.768$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-8\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
28900.2.a.by	$28900$	$2$	28900.a	1.a	$1$	$12$	$12$	$230.768$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
28900.2.a.bz	$28900$	$2$	28900.a	1.a	$1$	$12$	$12$	$230.768$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
28900.2.a.ca	$28900$	$2$	28900.a	1.a	$1$	$12$	$12$	$230.768$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
28900.2.a.cb	$28900$	$2$	28900.a	1.a	$1$	$12$	$12$	$230.768$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(8\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
28900.2.a.cc	$28900$	$2$	28900.a	1.a	$1$	$12$	$12$	$230.768$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(3\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
28900.2.a.cd	$28900$	$2$	28900.a	1.a	$1$	$15$	$15$	$230.768$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-3\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
28900.2.a.ce	$28900$	$2$	28900.a	1.a	$1$	$15$	$15$	$230.768$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-3\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
28900.2.a.cf	$28900$	$2$	28900.a	1.a	$1$	$15$	$15$	$230.768$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(3\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
28900.2.a.cg	$28900$	$2$	28900.a	1.a	$1$	$15$	$15$	$230.768$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(3\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
28900.2.a.ch	$28900$	$2$	28900.a	1.a	$1$	$24$	$24$	$230.768$		None	✓	?	✓			$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
28900.2.a.ci	$28900$	$2$	28900.a	1.a	$1$	$24$	$24$	$230.768$		None	✓	?	✓			$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
28900.2.a.cj	$28900$	$2$	28900.a	1.a	$1$	$24$	$24$	$230.768$		None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
28900.2.a.ck	$28900$	$2$	28900.a	1.a	$1$	$24$	$24$	$230.768$		None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
28900.2.a.cl	$28900$	$2$	28900.a	1.a	$1$	$40$	$40$	$230.768$		None	✓	?	✓			$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(28900))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(28900)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(170))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(340))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(425))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(578))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(850))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1156))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1445))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1700))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2890))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(5780))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(7225))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14450))\)\(^{\oplus 2}\)