Space of modular forms of level 9675, weight 2, and trivial character

• Label: 9675.2.a
• Level: $9675$
• Weight: $2$
• Character orbit: 9675.a
• Rep. character: $\chi_{9675}(1,\cdot)$
• Character field: $\Q$
• Dimension: $332$
• Newform subspaces: $80$
• Sturm bound: $2640$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 9675 = 3^{2} \cdot 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9675.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 80 \)
Sturm bound:			\(2640\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(2\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9675))\).

	Total	New	Old
Modular forms	1344	332	1012
Cusp forms	1297	332	965
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.

\(3\)	\(5\)	\(43\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(162\)	\(26\)	\(136\)		\(157\)	\(26\)	\(131\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)		\(174\)	\(38\)	\(136\)		\(168\)	\(38\)	\(130\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(174\)	\(38\)	\(136\)		\(168\)	\(38\)	\(130\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(162\)	\(30\)	\(132\)		\(156\)	\(30\)	\(126\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(174\)	\(50\)	\(124\)		\(168\)	\(50\)	\(118\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(162\)	\(44\)	\(118\)		\(156\)	\(44\)	\(112\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(162\)	\(51\)	\(111\)		\(156\)	\(51\)	\(105\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(174\)	\(55\)	\(119\)		\(168\)	\(55\)	\(113\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(648\)	\(151\)	\(497\)		\(625\)	\(151\)	\(474\)		\(23\)	\(0\)	\(23\)
Minus space			\(-\)		\(696\)	\(181\)	\(515\)		\(672\)	\(181\)	\(491\)		\(24\)	\(0\)	\(24\)

Trace form

332 * q - q^2 + 335 * q^4 + 4 * q^7 - 15 * q^8 + 5 * q^11 - q^13 - 12 * q^14 + 341 * q^16 + q^17 + 6 * q^19 - 6 * q^22 + q^23 + 12 * q^26 + 20 * q^28 + 16 * q^29 + q^31 - 31 * q^32 + 24 * q^34 - 6 * q^37 - 8 * q^38 - 7 * q^41 + 2 * q^43 + 22 * q^44 - 6 * q^46 - 28 * q^47 + 344 * q^49 + 3 * q^53 - 16 * q^56 + 18 * q^58 + 12 * q^59 + 48 * q^61 - 2 * q^62 + 389 * q^64 + 7 * q^67 - 4 * q^68 - 10 * q^71 - 8 * q^73 + 6 * q^74 + 20 * q^77 - 16 * q^79 + 8 * q^82 + q^83 + 5 * q^86 - 50 * q^89 - 16 * q^91 + 34 * q^92 - 8 * q^94 + 23 * q^97 - 21 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9675))\) 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	5	43
9675.2.a.a	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				645.2.a.a	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-4q^{7}-q^{11}-5q^{13}+\cdots\)
9675.2.a.b	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				43.2.a.a	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-3q^{11}+5q^{13}-4q^{16}+\cdots\)
9675.2.a.c	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				1075.2.a.a	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+2q^{7}-4q^{11}-2q^{13}+\cdots\)
9675.2.a.d	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				645.2.a.b	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+4q^{7}+3q^{11}-5q^{13}+\cdots\)
9675.2.a.e	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				1075.2.a.b	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-4q^{7}+3q^{8}-3q^{11}+\cdots\)
9675.2.a.f	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				1935.2.a.c	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-4q^{7}+3q^{8}+4q^{11}+\cdots\)
9675.2.a.g	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				387.2.a.b	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+3q^{7}+3q^{8}-3q^{11}+\cdots\)
9675.2.a.h	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				1935.2.a.b	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+4q^{7}+3q^{8}-2q^{13}+\cdots\)
9675.2.a.i	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				1075.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-4q^{7}-q^{11}+5q^{13}+4q^{16}+\cdots\)
9675.2.a.j	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				3225.2.a.e	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-2q^{7}-2q^{13}+4q^{16}+3q^{17}+\cdots\)
9675.2.a.k	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				3225.2.a.e	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+2q^{7}+2q^{13}+4q^{16}-3q^{17}+\cdots\)
9675.2.a.l	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				215.2.a.a	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+2q^{7}+q^{11}+q^{13}+4q^{16}+\cdots\)
9675.2.a.m	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				129.2.a.a	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+2q^{7}+5q^{11}-3q^{13}+4q^{16}+\cdots\)
9675.2.a.n	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				645.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+2q^{7}+5q^{11}+5q^{13}+4q^{16}+\cdots\)
9675.2.a.o	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				1075.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+4q^{7}-q^{11}-5q^{13}+4q^{16}+\cdots\)
9675.2.a.p	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				1935.2.a.c	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-4q^{7}-3q^{8}-4q^{11}+\cdots\)
9675.2.a.q	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				645.2.a.e	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-4q^{7}-3q^{8}+2q^{11}+\cdots\)
9675.2.a.r	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				645.2.a.d	$1$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-3q^{8}-4q^{11}-6q^{13}+\cdots\)
9675.2.a.s	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				129.2.a.b	$1$	$1$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-3q^{8}+2q^{13}-q^{16}+\cdots\)
9675.2.a.t	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				387.2.a.b	$1$	$0$	\(1\)	\(0\)	\(0\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+3q^{7}-3q^{8}+3q^{11}+\cdots\)
9675.2.a.u	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				1075.2.a.b	$1$	$1$	\(1\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+4q^{7}-3q^{8}-3q^{11}+\cdots\)
9675.2.a.v	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				1935.2.a.b	$1$	$0$	\(1\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+4q^{7}-3q^{8}-2q^{13}+\cdots\)
9675.2.a.w	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				1075.2.a.a	$1$	$1$	\(2\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-2q^{7}-4q^{11}+2q^{13}+\cdots\)
9675.2.a.x	$9675$	$2$	9675.a	1.a	$1$	$1$	$1$	$77.255$	\(\Q\)	None	✓				645.2.a.f	$1$	$1$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-5q^{11}-q^{13}-4q^{16}+\cdots\)
9675.2.a.y	$9675$	$2$	9675.a	1.a	$1$	$2$	$2$	$77.255$	\(\Q(\sqrt{2}) \)	None	✓				645.2.b.a	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-2\beta q^{7}+\cdots\)
9675.2.a.z	$9675$	$2$	9675.a	1.a	$1$	$2$	$2$	$77.255$	\(\Q(\sqrt{3}) \)	None	✓				387.2.a.g	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-2q^{7}-3\beta q^{11}-5q^{13}+4q^{16}+\cdots\)
9675.2.a.ba	$9675$	$2$	9675.a	1.a	$1$	$2$	$2$	$77.255$	\(\Q(\sqrt{7}) \)	None	✓	✓			9675.2.a.ba	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-2q^{7}+2\beta q^{11}-2q^{13}+4q^{16}+\cdots\)
9675.2.a.bb	$9675$	$2$	9675.a	1.a	$1$	$2$	$2$	$77.255$	\(\Q(\sqrt{7}) \)	None	✓	✓			9675.2.a.bb	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-2q^{7}+\beta q^{11}+5q^{13}+4q^{16}+\cdots\)
9675.2.a.bc	$9675$	$2$	9675.a	1.a	$1$	$2$	$2$	$77.255$	\(\Q(\sqrt{7}) \)	None	✓	✓			9675.2.a.bb	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+2q^{7}-\beta q^{11}-5q^{13}+4q^{16}+\cdots\)
9675.2.a.bd	$9675$	$2$	9675.a	1.a	$1$	$2$	$2$	$77.255$	\(\Q(\sqrt{7}) \)	None	✓	✓			9675.2.a.ba	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+2q^{7}-2\beta q^{11}+2q^{13}+4q^{16}+\cdots\)
9675.2.a.be	$9675$	$2$	9675.a	1.a	$1$	$2$	$2$	$77.255$	\(\Q(\sqrt{2}) \)	None	✓				645.2.a.g	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-\beta q^{7}-2\beta q^{8}+(1+\beta )q^{11}+\cdots\)
9675.2.a.bf	$9675$	$2$	9675.a	1.a	$1$	$2$	$2$	$77.255$	\(\Q(\sqrt{2}) \)	None	✓				43.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(2-\beta )q^{7}-2\beta q^{8}+(1-2\beta )q^{11}+\cdots\)
9675.2.a.bg	$9675$	$2$	9675.a	1.a	$1$	$2$	$2$	$77.255$	\(\Q(\sqrt{3}) \)	None	✓				645.2.b.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+(-1+2\beta )q^{7}-\beta q^{8}+\cdots\)
9675.2.a.bh	$9675$	$2$	9675.a	1.a	$1$	$2$	$2$	$77.255$	\(\Q(\sqrt{3}) \)	None	✓				645.2.b.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+(1+2\beta )q^{7}-\beta q^{8}-\beta q^{11}+\cdots\)
9675.2.a.bi	$9675$	$2$	9675.a	1.a	$1$	$2$	$2$	$77.255$	\(\Q(\sqrt{6}) \)	None	✓				1935.2.a.m	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+4q^{4}+(2-\beta )q^{7}+2\beta q^{8}+\cdots\)
9675.2.a.bj	$9675$	$2$	9675.a	1.a	$1$	$2$	$2$	$77.255$	\(\Q(\sqrt{6}) \)	None	✓				1935.2.a.m	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+4q^{4}+(2+\beta )q^{7}+2\beta q^{8}+\cdots\)
9675.2.a.bk	$9675$	$2$	9675.a	1.a	$1$	$2$	$2$	$77.255$	\(\Q(\sqrt{7}) \)	None	✓	✓			9675.2.a.bk	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+5q^{4}-2q^{7}+3\beta q^{8}+\beta q^{11}+\cdots\)
9675.2.a.bl	$9675$	$2$	9675.a	1.a	$1$	$2$	$2$	$77.255$	\(\Q(\sqrt{7}) \)	None	✓	✓			9675.2.a.bk	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+5q^{4}+2q^{7}+3\beta q^{8}-\beta q^{11}+\cdots\)
9675.2.a.bm	$9675$	$2$	9675.a	1.a	$1$	$2$	$2$	$77.255$	\(\Q(\sqrt{2}) \)	None	✓				129.2.a.c	$1$	$0$	\(2\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(-1+2\beta )q^{7}+\cdots\)
9675.2.a.bn	$9675$	$2$	9675.a	1.a	$1$	$2$	$2$	$77.255$	\(\Q(\sqrt{2}) \)	None	✓				645.2.b.a	$1$	$1$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-2\beta q^{7}+(3+\cdots)q^{8}+\cdots\)
9675.2.a.bo	$9675$	$2$	9675.a	1.a	$1$	$3$	$3$	$77.255$	3.3.148.1	None	✓				645.2.a.h	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
9675.2.a.bp	$9675$	$2$	9675.a	1.a	$1$	$3$	$3$	$77.255$	3.3.321.1	None	✓				215.2.a.b	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
9675.2.a.bq	$9675$	$2$	9675.a	1.a	$1$	$3$	$3$	$77.255$	3.3.568.1	None	✓				129.2.a.d	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(3+\beta _{2})q^{4}+(-1+\cdots)q^{7}+\cdots\)
9675.2.a.br	$9675$	$2$	9675.a	1.a	$1$	$3$	$3$	$77.255$	3.3.169.1	None	✓				215.2.b.a	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{7}+\cdots\)
9675.2.a.bs	$9675$	$2$	9675.a	1.a	$1$	$3$	$3$	$77.255$	3.3.148.1	None	✓				645.2.a.i	$1$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2})q^{4}+(3-\beta _{1}+\cdots)q^{7}+\cdots\)
9675.2.a.bt	$9675$	$2$	9675.a	1.a	$1$	$3$	$3$	$77.255$	3.3.169.1	None	✓				215.2.b.a	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}+\beta _{2})q^{2}+(2-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
9675.2.a.bu	$9675$	$2$	9675.a	1.a	$1$	$3$	$3$	$77.255$	3.3.316.1	None	✓				645.2.a.j	$1$	$1$	\(1\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
9675.2.a.bv	$9675$	$2$	9675.a	1.a	$1$	$4$	$4$	$77.255$	\(\Q(\sqrt{5}, \sqrt{13})\)	None	✓				387.2.a.j	$2$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{3})q^{2}+3q^{4}-\beta _{2}q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots\)
9675.2.a.bw	$9675$	$2$	9675.a	1.a	$1$	$5$	$5$	$77.255$	5.5.135076.1	None	✓				645.2.a.k	$1$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{3})q^{2}+(3-\beta _{1}+\beta _{2}+\beta _{4})q^{4}+\cdots\)
9675.2.a.bx	$9675$	$2$	9675.a	1.a	$1$	$5$	$5$	$77.255$	5.5.230224.1	None	✓				1935.2.a.s	$1$	$1$	\(-3\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
9675.2.a.by	$9675$	$2$	9675.a	1.a	$1$	$5$	$5$	$77.255$	5.5.205225.1	None	✓				3225.2.a.w	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(8\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+(2+\cdots)q^{7}+\cdots\)
9675.2.a.bz	$9675$	$2$	9675.a	1.a	$1$	$5$	$5$	$77.255$	5.5.161121.1	None	✓				3225.2.a.v	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(8\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2}-\beta _{3})q^{4}+(2+\beta _{2}+\cdots)q^{7}+\cdots\)
9675.2.a.ca	$9675$	$2$	9675.a	1.a	$1$	$5$	$5$	$77.255$	5.5.1240016.1	None	✓				1935.2.a.v	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-1+\beta _{2}+\cdots)q^{7}+\cdots\)
9675.2.a.cb	$9675$	$2$	9675.a	1.a	$1$	$5$	$5$	$77.255$	5.5.24217.1	None	✓				1075.2.a.n	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{2}+(-\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
9675.2.a.cc	$9675$	$2$	9675.a	1.a	$1$	$5$	$5$	$77.255$	5.5.24217.1	None	✓				1075.2.a.n	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{2})q^{2}+(-\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
9675.2.a.cd	$9675$	$2$	9675.a	1.a	$1$	$5$	$5$	$77.255$	5.5.161121.1	None	✓				3225.2.a.v	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-8\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2}-\beta _{3})q^{4}+(-2-\beta _{2}+\cdots)q^{7}+\cdots\)
9675.2.a.ce	$9675$	$2$	9675.a	1.a	$1$	$5$	$5$	$77.255$	5.5.205225.1	None	✓				3225.2.a.w	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-8\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+(-2+\cdots)q^{7}+\cdots\)
9675.2.a.cf	$9675$	$2$	9675.a	1.a	$1$	$5$	$5$	$77.255$	5.5.1240016.1	None	✓				1935.2.a.v	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-1+\beta _{2}+\cdots)q^{7}+\cdots\)
9675.2.a.cg	$9675$	$2$	9675.a	1.a	$1$	$5$	$5$	$77.255$	5.5.220036.1	None	✓				645.2.a.l	$1$	$0$	\(2\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}+(\beta _{1}-\beta _{3})q^{4}-\beta _{2}q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots\)
9675.2.a.ch	$9675$	$2$	9675.a	1.a	$1$	$5$	$5$	$77.255$	5.5.1933097.1	None	✓				215.2.a.c	$1$	$1$	\(2\)	\(0\)	\(0\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1+\beta _{3}-\beta _{4})q^{7}+\cdots\)
9675.2.a.ci	$9675$	$2$	9675.a	1.a	$1$	$5$	$5$	$77.255$	5.5.230224.1	None	✓				1935.2.a.s	$1$	$1$	\(3\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}-\beta _{2}q^{7}+\cdots\)
9675.2.a.cj	$9675$	$2$	9675.a	1.a	$1$	$6$	$6$	$77.255$	6.6.282109865.1	None	✓				1075.2.a.q	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
9675.2.a.ck	$9675$	$2$	9675.a	1.a	$1$	$6$	$6$	$77.255$	6.6.282109865.1	None	✓		✓		1075.2.a.q	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
9675.2.a.cl	$9675$	$2$	9675.a	1.a	$1$	$6$	$6$	$77.255$	6.6.32503921.1	None	✓				215.2.a.d	$1$	$0$	\(3\)	\(0\)	\(0\)	\(-8\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{7}+\cdots\)
9675.2.a.cm	$9675$	$2$	9675.a	1.a	$1$	$7$	$7$	$77.255$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				215.2.b.b	$1$	$1$	\(-4\)	\(0\)	\(0\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(1-\beta _{5}+\beta _{6})q^{4}+\cdots\)
9675.2.a.cn	$9675$	$2$	9675.a	1.a	$1$	$7$	$7$	$77.255$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				215.2.b.b	$1$	$0$	\(4\)	\(0\)	\(0\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-\beta _{5}+\beta _{6})q^{4}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
9675.2.a.co	$9675$	$2$	9675.a	1.a	$1$	$8$	$8$	$77.255$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				3225.2.a.ba	$1$	$0$	\(-3\)	\(0\)	\(0\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1-\beta _{7})q^{7}+\cdots\)
9675.2.a.cp	$9675$	$2$	9675.a	1.a	$1$	$8$	$8$	$77.255$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				645.2.b.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{5}-\beta _{7})q^{7}+\cdots\)
9675.2.a.cq	$9675$	$2$	9675.a	1.a	$1$	$8$	$8$	$77.255$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				645.2.b.c	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{5}+\beta _{7})q^{7}+\cdots\)
9675.2.a.cr	$9675$	$2$	9675.a	1.a	$1$	$8$	$8$	$77.255$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				3225.2.a.ba	$1$	$0$	\(3\)	\(0\)	\(0\)	\(-6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1+\beta _{7})q^{7}+\cdots\)
9675.2.a.cs	$9675$	$2$	9675.a	1.a	$1$	$9$	$9$	$77.255$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		3225.2.a.be	$1$	$0$	\(-3\)	\(0\)	\(0\)	\(8\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{5}-\beta _{8})q^{7}+\cdots\)
9675.2.a.ct	$9675$	$2$	9675.a	1.a	$1$	$9$	$9$	$77.255$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				3225.2.a.be	$1$	$0$	\(3\)	\(0\)	\(0\)	\(-8\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{5}+\beta _{8})q^{7}+\cdots\)
9675.2.a.cu	$9675$	$2$	9675.a	1.a	$1$	$10$	$10$	$77.255$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		645.2.b.d	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(-8\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2}-\beta _{3})q^{4}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
9675.2.a.cv	$9675$	$2$	9675.a	1.a	$1$	$10$	$10$	$77.255$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓			9675.2.a.cv	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{5}q^{7}+\beta _{3}q^{8}+\cdots\)
9675.2.a.cw	$9675$	$2$	9675.a	1.a	$1$	$10$	$10$	$77.255$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓	✓		9675.2.a.cv	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{5}q^{7}+\beta _{3}q^{8}+\cdots\)
9675.2.a.cx	$9675$	$2$	9675.a	1.a	$1$	$10$	$10$	$77.255$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		645.2.b.d	$1$	$0$	\(2\)	\(0\)	\(0\)	\(8\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2}-\beta _{3})q^{4}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
9675.2.a.cy	$9675$	$2$	9675.a	1.a	$1$	$12$	$12$	$77.255$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		9675.2.a.cy	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{5}+\beta _{9}+\cdots)q^{7}+\cdots\)
9675.2.a.cz	$9675$	$2$	9675.a	1.a	$1$	$12$	$12$	$77.255$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			9675.2.a.cy	$2$	$0$	\(0\)	\(0\)	\(0\)	\(12\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{5}-\beta _{9}+\cdots)q^{7}+\cdots\)
9675.2.a.da	$9675$	$2$	9675.a	1.a	$1$	$20$	$20$	$77.255$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓		✓		1935.2.b.g	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)		$+$	$-$	$-$	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{9}q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots\)
9675.2.a.db	$9675$	$2$	9675.a	1.a	$1$	$20$	$20$	$77.255$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓		✓		1935.2.b.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$+$	$-$	$+$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{9}q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9675))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9675)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(129))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(215))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(387))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(645))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1075))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1935))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3225))\)\(^{\oplus 2}\)