Space of modular forms of level 9075, weight 2, and trivial character

• Label: 9075.2.a
• Level: $9075$
• Weight: $2$
• Character orbit: 9075.a
• Rep. character: $\chi_{9075}(1,\cdot)$
• Character field: $\Q$
• Dimension: $345$
• Newform subspaces: $105$
• Sturm bound: $2640$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9075.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 105 \)
Sturm bound:			\(2640\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(2\), \(7\), \(13\), \(17\), \(19\), \(23\), \(37\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9075))\).

	Total	New	Old
Modular forms	1392	345	1047
Cusp forms	1249	345	904
Eisenstein series	143	0	143

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

\(3\)	\(5\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(36\)
\(+\)	\(+\)	\(-\)	\(-\)	\(45\)
\(+\)	\(-\)	\(+\)	\(-\)	\(46\)
\(+\)	\(-\)	\(-\)	\(+\)	\(45\)
\(-\)	\(+\)	\(+\)	\(-\)	\(48\)
\(-\)	\(+\)	\(-\)	\(+\)	\(35\)
\(-\)	\(-\)	\(+\)	\(+\)	\(38\)
\(-\)	\(-\)	\(-\)	\(-\)	\(52\)
Plus space			\(+\)	\(154\)
Minus space			\(-\)	\(191\)

Trace form

345 * q - 3 * q^2 + q^3 + 341 * q^4 - q^6 + 4 * q^7 - 15 * q^8 + 345 * q^9 + 7 * q^12 - 2 * q^13 + 345 * q^16 - 10 * q^17 - 3 * q^18 + 14 * q^19 + 10 * q^21 - 4 * q^23 - 9 * q^24 + 42 * q^26 + q^27 + 4 * q^28 - 6 * q^29 - 10 * q^31 - 23 * q^32 - 10 * q^34 + 341 * q^36 + 2 * q^37 - 4 * q^38 + 16 * q^39 + 26 * q^41 - 16 * q^42 - 16 * q^46 - 8 * q^47 - q^48 + 363 * q^49 + 6 * q^51 - 54 * q^52 - 30 * q^53 - q^54 - 12 * q^56 + 16 * q^57 + 6 * q^58 + 4 * q^59 + 8 * q^61 + 32 * q^62 + 4 * q^63 + 341 * q^64 + 24 * q^67 + 50 * q^68 - 8 * q^69 + 12 * q^71 - 15 * q^72 - 14 * q^73 - 22 * q^74 + 44 * q^76 - 6 * q^78 + 4 * q^79 + 345 * q^81 + 14 * q^82 + 28 * q^83 + 24 * q^84 + 4 * q^86 + 2 * q^87 - 26 * q^89 + 70 * q^91 + 8 * q^92 + 44 * q^93 + 64 * q^94 - 9 * q^96 + 38 * q^97 + 77 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9075))\) 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	11
9075.2.a.a	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	\(\Q\)	None	✓				75.2.a.a	$1$	$1$	\(-2\)	\(-1\)	\(0\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+3q^{7}+\cdots\)
9075.2.a.b	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	\(\Q\)	None	✓				363.2.a.a	$1$	$1$	\(-2\)	\(1\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+2q^{4}-2q^{6}+q^{7}+q^{9}+\cdots\)
9075.2.a.c	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	\(\Q\)	None	✓				1815.2.c.a	$1$	$2$	\(-1\)	\(-1\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+q^{6}-4q^{7}+3q^{8}+\cdots\)
9075.2.a.d	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	\(\Q\)	None	✓				1815.2.a.a	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+q^{6}-2q^{7}+3q^{8}+\cdots\)
9075.2.a.e	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	\(\Q\)	None	✓	✓			9075.2.a.e	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+q^{6}+q^{7}+3q^{8}+\cdots\)
9075.2.a.f	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	\(\Q\)	None	✓				1815.2.c.a	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-q^{6}-4q^{7}+3q^{8}+\cdots\)
9075.2.a.g	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	\(\Q\)	None	✓				15.2.a.a	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-q^{6}+3q^{8}+q^{9}+\cdots\)
9075.2.a.h	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	\(\Q\)	None	✓	✓			9075.2.a.e	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-q^{6}+q^{7}+3q^{8}+\cdots\)
9075.2.a.i	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	\(\Q\)	None	✓				825.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-q^{7}+q^{9}+2q^{12}-q^{13}+\cdots\)
9075.2.a.j	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	\(\Q\)	None	✓				1815.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-q^{7}+q^{9}+2q^{12}+2q^{13}+\cdots\)
9075.2.a.k	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	\(\Q\)	None	✓				1815.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}+q^{7}+q^{9}+2q^{12}-2q^{13}+\cdots\)
9075.2.a.l	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	\(\Q\)	None	✓				825.2.a.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+q^{7}+q^{9}-2q^{12}+q^{13}+\cdots\)
9075.2.a.m	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	\(\Q\)	None	✓	✓			9075.2.a.e	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}-q^{6}-q^{7}-3q^{8}+\cdots\)
9075.2.a.n	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	\(\Q\)	None	✓				1815.2.a.a	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}-q^{6}+2q^{7}-3q^{8}+\cdots\)
9075.2.a.o	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	\(\Q\)	None	✓				1815.2.c.a	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}-q^{6}+4q^{7}-3q^{8}+\cdots\)
9075.2.a.p	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	\(\Q\)	None	✓	✓			9075.2.a.e	$1$	$1$	\(1\)	\(1\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}+q^{6}-q^{7}-3q^{8}+\cdots\)
9075.2.a.q	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	\(\Q\)	None	✓				33.2.a.a	$1$	$1$	\(1\)	\(1\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}+q^{6}+4q^{7}-3q^{8}+\cdots\)
9075.2.a.r	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	\(\Q\)	None	✓				1815.2.c.a	$1$	$1$	\(1\)	\(1\)	\(0\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}+q^{6}+4q^{7}-3q^{8}+\cdots\)
9075.2.a.s	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	\(\Q\)	None	✓				75.2.a.a	$1$	$1$	\(2\)	\(1\)	\(0\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}+2q^{6}-3q^{7}+\cdots\)
9075.2.a.t	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	\(\Q\)	None	✓				363.2.a.a	$1$	$1$	\(2\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}+2q^{6}-q^{7}+q^{9}+\cdots\)
9075.2.a.u	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{5}) \)	None	✓				33.2.e.b	$1$	$1$	\(-3\)	\(2\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+(-1+\cdots)q^{6}+\cdots\)
9075.2.a.v	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{2}) \)	None	✓				165.2.a.a	$1$	$1$	\(-2\)	\(2\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
9075.2.a.w	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{2}) \)	None	✓				825.2.a.d	$1$	$1$	\(-2\)	\(2\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
9075.2.a.x	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{5}) \)	None	✓				33.2.e.a	$1$	$1$	\(-1\)	\(-2\)	\(0\)	\(-6\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
9075.2.a.y	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{5}) \)	None	✓				825.2.n.a	$1$	$2$	\(-1\)	\(-2\)	\(0\)	\(-6\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
9075.2.a.z	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{5}) \)	None	✓				825.2.n.b	$1$	$0$	\(-1\)	\(-2\)	\(0\)	\(-6\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
9075.2.a.ba	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{5}) \)	None	✓	✓			9075.2.a.ba	$1$	$1$	\(-1\)	\(-2\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
9075.2.a.bb	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{5}) \)	None	✓				825.2.n.a	$1$	$1$	\(-1\)	\(2\)	\(0\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
9075.2.a.bc	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{5}) \)	None	✓				825.2.n.b	$1$	$1$	\(-1\)	\(2\)	\(0\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
9075.2.a.bd	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{5}) \)	None	✓				1815.2.a.f	$1$	$1$	\(-1\)	\(2\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
9075.2.a.be	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{5}) \)	None	✓	✓			9075.2.a.ba	$1$	$1$	\(-1\)	\(2\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
9075.2.a.bf	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{15}) \)	None	✓	✓			9075.2.a.bf	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}+\beta q^{7}+q^{9}+2q^{12}+\cdots\)
9075.2.a.bg	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{3}) \)	None	✓	✓			9075.2.a.bg	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+q^{4}-\beta q^{6}-2\beta q^{7}+\cdots\)
9075.2.a.bh	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{3}) \)	None	✓				165.2.a.b	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+q^{4}-\beta q^{6}+2q^{7}-\beta q^{8}+\cdots\)
9075.2.a.bi	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{5}) \)	None	✓				363.2.a.g	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+3q^{4}+\beta q^{6}+2\beta q^{7}+\cdots\)
9075.2.a.bj	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{5}) \)	None	✓				1815.2.c.c	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+3q^{4}+\beta q^{6}-\beta q^{8}+\cdots\)
9075.2.a.bk	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{5}) \)	None	✓	✓			9075.2.a.bk	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+3q^{4}+\beta q^{6}-\beta q^{7}+\cdots\)
9075.2.a.bl	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{3}) \)	None	✓				1815.2.a.g	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+\beta q^{7}+q^{9}-2q^{12}+\cdots\)
9075.2.a.bm	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{15}) \)	None	✓	✓			9075.2.a.bf	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+\beta q^{7}+q^{9}-2q^{12}+\cdots\)
9075.2.a.bn	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{3}) \)	None	✓	✓			9075.2.a.bg	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+q^{4}+\beta q^{6}-2\beta q^{7}+\cdots\)
9075.2.a.bo	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{3}) \)	None	✓				363.2.a.f	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+q^{4}+\beta q^{6}-2\beta q^{7}+\cdots\)
9075.2.a.bp	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{3}) \)	None	✓				1815.2.a.h	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+q^{4}+\beta q^{6}-\beta q^{8}+q^{9}+\cdots\)
9075.2.a.bq	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{5}) \)	None	✓				1815.2.c.c	$2$	$1$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+3q^{4}-\beta q^{6}-\beta q^{8}+\cdots\)
9075.2.a.br	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{5}) \)	None	✓	✓			9075.2.a.bk	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+3q^{4}-\beta q^{6}-\beta q^{7}+\cdots\)
9075.2.a.bs	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{5}) \)	None	✓	✓			9075.2.a.ba	$1$	$1$	\(1\)	\(-2\)	\(0\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
9075.2.a.bt	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{5}) \)	None	✓				825.2.n.b	$1$	$1$	\(1\)	\(-2\)	\(0\)	\(6\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
9075.2.a.bu	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{5}) \)	None	✓				825.2.n.a	$1$	$1$	\(1\)	\(-2\)	\(0\)	\(6\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
9075.2.a.bv	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{5}) \)	None	✓				33.2.e.a	$1$	$0$	\(1\)	\(-2\)	\(0\)	\(6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
9075.2.a.bw	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{5}) \)	None	✓	✓			9075.2.a.ba	$1$	$1$	\(1\)	\(2\)	\(0\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
9075.2.a.bx	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{5}) \)	None	✓				1815.2.a.f	$1$	$1$	\(1\)	\(2\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
9075.2.a.by	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{5}) \)	None	✓				825.2.n.b	$1$	$0$	\(1\)	\(2\)	\(0\)	\(6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
9075.2.a.bz	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{5}) \)	None	✓				825.2.n.a	$1$	$0$	\(1\)	\(2\)	\(0\)	\(6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
9075.2.a.ca	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{2}) \)	None	✓				825.2.a.d	$1$	$1$	\(2\)	\(-2\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
9075.2.a.cb	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	\(\Q(\sqrt{5}) \)	None	✓				33.2.e.b	$1$	$0$	\(3\)	\(2\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+q^{3}+3\beta q^{4}+(1+\beta )q^{6}+\cdots\)
9075.2.a.cc	$9075$	$2$	9075.a	1.a	$1$	$3$	$3$	$72.464$	3.3.148.1	None	✓				165.2.c.a	$1$	$1$	\(-3\)	\(-3\)	\(0\)	\(-8\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
9075.2.a.cd	$9075$	$2$	9075.a	1.a	$1$	$3$	$3$	$72.464$	3.3.568.1	None	✓				825.2.a.i	$1$	$0$	\(-2\)	\(3\)	\(0\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+q^{3}+(3+\beta _{2})q^{4}+\cdots\)
9075.2.a.ce	$9075$	$2$	9075.a	1.a	$1$	$3$	$3$	$72.464$	3.3.469.1	None	✓				1815.2.a.l	$1$	$0$	\(-1\)	\(-3\)	\(0\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
9075.2.a.cf	$9075$	$2$	9075.a	1.a	$1$	$3$	$3$	$72.464$	3.3.148.1	None	✓				165.2.a.c	$1$	$0$	\(-1\)	\(-3\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
9075.2.a.cg	$9075$	$2$	9075.a	1.a	$1$	$3$	$3$	$72.464$	3.3.148.1	None	✓				165.2.c.b	$1$	$0$	\(-1\)	\(3\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.ch	$9075$	$2$	9075.a	1.a	$1$	$3$	$3$	$72.464$	3.3.148.1	None	✓				165.2.c.b	$1$	$1$	\(1\)	\(-3\)	\(0\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.ci	$9075$	$2$	9075.a	1.a	$1$	$3$	$3$	$72.464$	3.3.469.1	None	✓				1815.2.a.l	$1$	$0$	\(1\)	\(-3\)	\(0\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.cj	$9075$	$2$	9075.a	1.a	$1$	$3$	$3$	$72.464$	3.3.568.1	None	✓				825.2.a.i	$1$	$0$	\(2\)	\(-3\)	\(0\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}-q^{3}+(3+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
9075.2.a.ck	$9075$	$2$	9075.a	1.a	$1$	$3$	$3$	$72.464$	3.3.148.1	None	✓				165.2.c.a	$1$	$0$	\(3\)	\(3\)	\(0\)	\(8\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
9075.2.a.cl	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	4.4.725.1	None	✓				165.2.m.a	$1$	$1$	\(-5\)	\(-4\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1}+\beta _{2})q^{2}-q^{3}+(3-\beta _{1}+\cdots)q^{4}+\cdots\)
9075.2.a.cm	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	4.4.725.1	None	✓				165.2.m.d	$1$	$0$	\(-3\)	\(-4\)	\(0\)	\(-6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-q^{3}+(-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
9075.2.a.cn	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	4.4.5725.1	None	✓				825.2.n.h	$1$	$1$	\(-1\)	\(-4\)	\(0\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{2})q^{2}-q^{3}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots\)
9075.2.a.co	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	\(\Q(\zeta_{15})^+\)	None	✓				165.2.m.c	$1$	$0$	\(-1\)	\(4\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{2}+\beta _{3})q^{2}+q^{3}+\beta _{1}q^{4}+(\beta _{2}+\beta _{3})q^{6}+\cdots\)
9075.2.a.cp	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	4.4.5725.1	None	✓				825.2.n.h	$1$	$0$	\(-1\)	\(4\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{2})q^{2}+q^{3}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots\)
9075.2.a.cq	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	4.4.5725.1	None	✓				165.2.m.b	$1$	$0$	\(-1\)	\(4\)	\(0\)	\(8\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{2})q^{2}+q^{3}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots\)
9075.2.a.cr	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	\(\Q(\zeta_{24})^+\)	None	✓				1815.2.c.g	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}-q^{3}-\beta _{2}q^{6}-\beta _{1}q^{7}-2\beta _{2}q^{8}+\cdots\)
9075.2.a.cs	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓				1815.2.c.f	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}-q^{3}-\beta _{2}q^{4}-\beta _{3}q^{6}-2\beta _{3}q^{7}+\cdots\)
9075.2.a.ct	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓	✓			9075.2.a.ct	$2$	$1$	\(0\)	\(-4\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}-q^{3}-\beta _{2}q^{4}-\beta _{3}q^{6}+\beta _{1}q^{7}+\cdots\)
9075.2.a.cu	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓				1815.2.a.t	$2$	$1$	\(0\)	\(-4\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}-q^{3}-\beta _{2}q^{4}-\beta _{3}q^{6}-2\beta _{1}q^{7}+\cdots\)
9075.2.a.cv	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	\(\Q(\sqrt{3}, \sqrt{11})\)	None	✓				363.2.a.j	$2$	$1$	\(0\)	\(-4\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{3})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.cw	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	\(\Q(\sqrt{3}, \sqrt{11})\)	None	✓	✓			9075.2.a.cw	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{3})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.cx	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	\(\Q(\sqrt{3}, \sqrt{5})\)	None	✓	✓			9075.2.a.cx	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{2})q^{2}-q^{3}+(2+\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
9075.2.a.cy	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	\(\Q(\zeta_{24})^+\)	None	✓				1815.2.c.g	$2$	$1$	\(0\)	\(4\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+q^{3}+\beta _{2}q^{6}-\beta _{1}q^{7}-2\beta _{2}q^{8}+\cdots\)
9075.2.a.cz	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓				1815.2.c.f	$2$	$1$	\(0\)	\(4\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+q^{3}-\beta _{2}q^{4}+\beta _{3}q^{6}-2\beta _{3}q^{7}+\cdots\)
9075.2.a.da	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓	✓			9075.2.a.ct	$2$	$1$	\(0\)	\(4\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+q^{3}-\beta _{2}q^{4}+\beta _{3}q^{6}+\beta _{1}q^{7}+\cdots\)
9075.2.a.db	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	\(\Q(\sqrt{3}, \sqrt{11})\)	None	✓	✓			9075.2.a.cw	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{3})q^{4}+\beta _{1}q^{6}+\cdots\)
9075.2.a.dc	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	4.4.8112.1	None	✓				1815.2.a.s	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+q^{3}+(2-\beta _{3})q^{4}-\beta _{2}q^{6}+\cdots\)
9075.2.a.dd	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	\(\Q(\sqrt{3}, \sqrt{5})\)	None	✓	✓			9075.2.a.cx	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{2})q^{2}+q^{3}+(2+\beta _{3})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
9075.2.a.de	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	4.4.5725.1	None	✓				825.2.n.h	$1$	$0$	\(1\)	\(-4\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{2})q^{2}-q^{3}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots\)
9075.2.a.df	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	\(\Q(\zeta_{15})^+\)	None	✓				165.2.m.c	$1$	$1$	\(1\)	\(4\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{2}-\beta _{3})q^{2}+q^{3}+\beta _{1}q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)
9075.2.a.dg	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	4.4.5725.1	None	✓				165.2.m.b	$1$	$1$	\(1\)	\(4\)	\(0\)	\(-8\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{2})q^{2}+q^{3}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots\)
9075.2.a.dh	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	4.4.5725.1	None	✓				825.2.n.h	$1$	$1$	\(1\)	\(4\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{2})q^{2}+q^{3}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots\)
9075.2.a.di	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	4.4.725.1	None	✓				165.2.m.d	$1$	$1$	\(3\)	\(-4\)	\(0\)	\(6\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}-q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots\)
9075.2.a.dj	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	4.4.725.1	None	✓				165.2.m.a	$1$	$0$	\(5\)	\(-4\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1}-\beta _{2})q^{2}-q^{3}+(3-\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots\)
9075.2.a.dk	$9075$	$2$	9075.a	1.a	$1$	$5$	$5$	$72.464$	5.5.9444552.1	None	✓	✓			9075.2.a.dk	$1$	$0$	\(-1\)	\(-5\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
9075.2.a.dl	$9075$	$2$	9075.a	1.a	$1$	$5$	$5$	$72.464$	5.5.9444552.1	None	✓	✓			9075.2.a.dk	$1$	$0$	\(-1\)	\(5\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.dm	$9075$	$2$	9075.a	1.a	$1$	$5$	$5$	$72.464$	5.5.9444552.1	None	✓	✓			9075.2.a.dk	$1$	$0$	\(1\)	\(-5\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.dn	$9075$	$2$	9075.a	1.a	$1$	$5$	$5$	$72.464$	5.5.9444552.1	None	✓	✓			9075.2.a.dk	$1$	$0$	\(1\)	\(5\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
9075.2.a.do	$9075$	$2$	9075.a	1.a	$1$	$6$	$6$	$72.464$	6.6.860280160.1	None	✓				1815.2.c.h	$1$	$1$	\(-1\)	\(-6\)	\(0\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
9075.2.a.dp	$9075$	$2$	9075.a	1.a	$1$	$6$	$6$	$72.464$	6.6.860280160.1	None	✓				1815.2.c.h	$1$	$0$	\(-1\)	\(6\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.dq	$9075$	$2$	9075.a	1.a	$1$	$6$	$6$	$72.464$	6.6.437199552.1	None	✓		✓		1815.2.a.y	$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
9075.2.a.dr	$9075$	$2$	9075.a	1.a	$1$	$6$	$6$	$72.464$	6.6.860280160.1	None	✓				1815.2.c.h	$1$	$1$	\(1\)	\(-6\)	\(0\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.ds	$9075$	$2$	9075.a	1.a	$1$	$6$	$6$	$72.464$	6.6.860280160.1	None	✓				1815.2.c.h	$1$	$0$	\(1\)	\(6\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
9075.2.a.dt	$9075$	$2$	9075.a	1.a	$1$	$8$	$8$	$72.464$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		825.2.n.m	$1$	$0$	\(-1\)	\(-8\)	\(0\)	\(-8\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
9075.2.a.du	$9075$	$2$	9075.a	1.a	$1$	$8$	$8$	$72.464$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				825.2.n.m	$1$	$1$	\(-1\)	\(8\)	\(0\)	\(-8\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.dv	$9075$	$2$	9075.a	1.a	$1$	$8$	$8$	$72.464$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		825.2.n.m	$1$	$1$	\(1\)	\(-8\)	\(0\)	\(8\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.dw	$9075$	$2$	9075.a	1.a	$1$	$8$	$8$	$72.464$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				825.2.n.m	$1$	$0$	\(1\)	\(8\)	\(0\)	\(8\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
9075.2.a.dx	$9075$	$2$	9075.a	1.a	$1$	$12$	$12$	$72.464$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		165.2.s.a	$1$	$1$	\(-4\)	\(-12\)	\(0\)	\(-8\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
9075.2.a.dy	$9075$	$2$	9075.a	1.a	$1$	$12$	$12$	$72.464$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		165.2.s.a	$1$	$1$	\(-4\)	\(12\)	\(0\)	\(-8\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.dz	$9075$	$2$	9075.a	1.a	$1$	$12$	$12$	$72.464$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		165.2.s.a	$1$	$0$	\(4\)	\(-12\)	\(0\)	\(8\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.ea	$9075$	$2$	9075.a	1.a	$1$	$12$	$12$	$72.464$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		165.2.s.a	$1$	$0$	\(4\)	\(12\)	\(0\)	\(8\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9075))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9075)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(605))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(825))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1815))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3025))\)\(^{\oplus 2}\)