Space of modular forms of level 9225, weight 2, and trivial character

• Label: 9225.2.a
• Level: $9225$
• Weight: $2$
• Character orbit: 9225.a
• Rep. character: $\chi_{9225}(1,\cdot)$
• Character field: $\Q$
• Dimension: $316$
• Newform subspaces: $83$
• Sturm bound: $2520$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 9225 = 3^{2} \cdot 5^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9225.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 83 \)
Sturm bound:			\(2520\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(2\), \(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9225))\).

	Total	New	Old
Modular forms	1284	316	968
Cusp forms	1237	316	921
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.

\(3\)	\(5\)	\(41\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(30\)
\(+\)	\(+\)	\(-\)	$-$	\(30\)
\(+\)	\(-\)	\(+\)	$-$	\(33\)
\(+\)	\(-\)	\(-\)	$+$	\(33\)
\(-\)	\(+\)	\(+\)	$-$	\(47\)
\(-\)	\(+\)	\(-\)	$+$	\(43\)
\(-\)	\(-\)	\(+\)	$+$	\(46\)
\(-\)	\(-\)	\(-\)	$-$	\(54\)
Plus space			\(+\)	\(152\)
Minus space			\(-\)	\(164\)

Trace form

\( 316 q + 2 q^{2} + 320 q^{4} + 2 q^{7} + 6 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9225))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	41
9225.2.a.a	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$2$	\(-2\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-q^{7}-6q^{11}-5q^{13}+\cdots\)
9225.2.a.b	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+q^{7}+6q^{11}+5q^{13}+\cdots\)
9225.2.a.c	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+2q^{7}+3q^{11}-4q^{13}+\cdots\)
9225.2.a.d	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+2q^{7}+3q^{11}+6q^{13}+\cdots\)
9225.2.a.e	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+4q^{7}-2q^{13}-8q^{14}+\cdots\)
9225.2.a.f	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-4q^{7}+3q^{8}+3q^{11}+\cdots\)
9225.2.a.g	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$2$	\(-1\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{7}+3q^{8}-6q^{11}+\cdots\)
9225.2.a.h	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$2$	\(-1\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{7}+3q^{8}-3q^{11}+\cdots\)
9225.2.a.i	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+3q^{8}-2q^{11}-q^{16}+\cdots\)
9225.2.a.j	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+4q^{7}+3q^{8}-3q^{11}+\cdots\)
9225.2.a.k	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+4q^{7}+3q^{8}+2q^{13}+\cdots\)
9225.2.a.l	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-2q^{7}-2q^{13}+4q^{16}-7q^{17}+\cdots\)
9225.2.a.m	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-2q^{7}-2q^{13}+4q^{16}+7q^{17}+\cdots\)
9225.2.a.n	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-2q^{7}+3q^{11}-2q^{13}+4q^{16}+\cdots\)
9225.2.a.o	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-q^{7}-q^{13}+4q^{16}-7q^{19}+\cdots\)
9225.2.a.p	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{11}+4q^{13}+4q^{16}-3q^{17}+\cdots\)
9225.2.a.q	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{7}+q^{13}+4q^{16}-7q^{19}+\cdots\)
9225.2.a.r	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+2q^{7}-3q^{11}-4q^{13}+4q^{16}+\cdots\)
9225.2.a.s	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+2q^{7}+2q^{13}+4q^{16}-7q^{17}+\cdots\)
9225.2.a.t	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+2q^{7}+2q^{13}+4q^{16}+7q^{17}+\cdots\)
9225.2.a.u	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+2q^{7}+3q^{11}-4q^{13}+4q^{16}+\cdots\)
9225.2.a.v	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+2q^{7}+3q^{11}+2q^{13}+4q^{16}+\cdots\)
9225.2.a.w	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+4q^{7}-5q^{11}+4q^{13}+4q^{16}+\cdots\)
9225.2.a.x	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$2$	\(1\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-4q^{7}-3q^{8}-3q^{11}+\cdots\)
9225.2.a.y	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-2q^{7}-3q^{8}+4q^{13}+\cdots\)
9225.2.a.z	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+2q^{7}-3q^{8}-3q^{11}+\cdots\)
9225.2.a.ba	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+4q^{7}-3q^{8}+3q^{11}+\cdots\)
9225.2.a.bb	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-4q^{7}+2q^{13}-8q^{14}+\cdots\)
9225.2.a.bc	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-2q^{7}+3q^{11}+4q^{13}+\cdots\)
9225.2.a.bd	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{7}+6q^{11}-5q^{13}+\cdots\)
9225.2.a.be	$9225$	$2$	9225.a	1.a	$1$	$1$	$1$	$73.662$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+q^{7}-6q^{11}+5q^{13}+\cdots\)
9225.2.a.bf	$9225$	$2$	9225.a	1.a	$1$	$2$	$2$	$73.662$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+2\beta q^{7}+\cdots\)
9225.2.a.bg	$9225$	$2$	9225.a	1.a	$1$	$2$	$2$	$73.662$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-2\beta q^{7}+\cdots\)
9225.2.a.bh	$9225$	$2$	9225.a	1.a	$1$	$2$	$2$	$73.662$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}-3\beta q^{7}+(-1+\cdots)q^{8}+\cdots\)
9225.2.a.bi	$9225$	$2$	9225.a	1.a	$1$	$2$	$2$	$73.662$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+(1-\beta )q^{7}+(-1+\cdots)q^{8}+\cdots\)
9225.2.a.bj	$9225$	$2$	9225.a	1.a	$1$	$2$	$2$	$73.662$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1+\beta )q^{4}+(2-\beta )q^{7}-3q^{8}+\cdots\)
9225.2.a.bk	$9225$	$2$	9225.a	1.a	$1$	$2$	$2$	$73.662$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1+\beta )q^{4}+(2-\beta )q^{7}-3q^{8}+\cdots\)
9225.2.a.bl	$9225$	$2$	9225.a	1.a	$1$	$2$	$2$	$73.662$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(2+\beta )q^{4}+(-4-\beta )q^{8}+(3+\cdots)q^{11}+\cdots\)
9225.2.a.bm	$9225$	$2$	9225.a	1.a	$1$	$2$	$2$	$73.662$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(2-\beta )q^{7}-2\beta q^{8}+(-1+\beta )q^{11}+\cdots\)
9225.2.a.bn	$9225$	$2$	9225.a	1.a	$1$	$2$	$2$	$73.662$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+(-1+\beta )q^{7}+\cdots\)
9225.2.a.bo	$9225$	$2$	9225.a	1.a	$1$	$2$	$2$	$73.662$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1+\beta )q^{4}+(-2+\beta )q^{7}+3q^{8}+\cdots\)
9225.2.a.bp	$9225$	$2$	9225.a	1.a	$1$	$2$	$2$	$73.662$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+2\beta q^{7}+(3+\cdots)q^{8}+\cdots\)
9225.2.a.bq	$9225$	$2$	9225.a	1.a	$1$	$2$	$2$	$73.662$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(2\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-2\beta q^{7}+(3+\cdots)q^{8}+\cdots\)
9225.2.a.br	$9225$	$2$	9225.a	1.a	$1$	$3$	$3$	$73.662$	3.3.148.1	None	✓	$1$	$1$	\(-3\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
9225.2.a.bs	$9225$	$2$	9225.a	1.a	$1$	$3$	$3$	$73.662$	3.3.148.1	None	✓	$1$	$1$	\(-3\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
9225.2.a.bt	$9225$	$2$	9225.a	1.a	$1$	$3$	$3$	$73.662$	3.3.148.1	None	✓	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
9225.2.a.bu	$9225$	$2$	9225.a	1.a	$1$	$3$	$3$	$73.662$	3.3.229.1	None	✓	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(2+\beta _{1})q^{4}-\beta _{2}q^{7}+\cdots\)
9225.2.a.bv	$9225$	$2$	9225.a	1.a	$1$	$3$	$3$	$73.662$	3.3.148.1	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{2}+(1+2\beta _{1})q^{4}+(-2+\cdots)q^{7}+\cdots\)
9225.2.a.bw	$9225$	$2$	9225.a	1.a	$1$	$3$	$3$	$73.662$	3.3.229.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{2}q^{7}+q^{8}+\cdots\)
9225.2.a.bx	$9225$	$2$	9225.a	1.a	$1$	$3$	$3$	$73.662$	3.3.316.1	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
9225.2.a.by	$9225$	$2$	9225.a	1.a	$1$	$3$	$3$	$73.662$	3.3.148.1	None	✓	$1$	$1$	\(2\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\beta _{2}q^{7}+\cdots\)
9225.2.a.bz	$9225$	$2$	9225.a	1.a	$1$	$3$	$3$	$73.662$	3.3.229.1	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}+(2+\beta _{1})q^{4}+\beta _{2}q^{7}+\cdots\)
9225.2.a.ca	$9225$	$2$	9225.a	1.a	$1$	$3$	$3$	$73.662$	3.3.229.1	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(9\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}+(2+\beta _{1})q^{4}+(3-\beta _{1}+\cdots)q^{7}+\cdots\)
9225.2.a.cb	$9225$	$2$	9225.a	1.a	$1$	$3$	$3$	$73.662$	3.3.148.1	None	✓	$1$	$0$	\(3\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{7}+\cdots\)
9225.2.a.cc	$9225$	$2$	9225.a	1.a	$1$	$3$	$3$	$73.662$	3.3.148.1	None	✓	$1$	$0$	\(3\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{7}+\cdots\)
9225.2.a.cd	$9225$	$2$	9225.a	1.a	$1$	$4$	$4$	$73.662$	4.4.3981.1	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+(1-\beta _{1})q^{4}+(1-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
9225.2.a.ce	$9225$	$2$	9225.a	1.a	$1$	$4$	$4$	$73.662$	4.4.3981.1	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}+(1-\beta _{1})q^{4}+(1-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
9225.2.a.cf	$9225$	$2$	9225.a	1.a	$1$	$4$	$4$	$73.662$	4.4.3981.1	None	✓	$1$	$0$	\(3\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{7}+\cdots\)
9225.2.a.cg	$9225$	$2$	9225.a	1.a	$1$	$5$	$5$	$73.662$	5.5.313905.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-11\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{4}q^{2}+(2\beta _{1}-\beta _{2}-\beta _{3}+\beta _{4})q^{4}+\cdots\)
9225.2.a.ch	$9225$	$2$	9225.a	1.a	$1$	$5$	$5$	$73.662$	5.5.313905.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(11\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{2}+(2\beta _{1}-\beta _{2}-\beta _{3}+\beta _{4})q^{4}+\cdots\)
9225.2.a.ci	$9225$	$2$	9225.a	1.a	$1$	$5$	$5$	$73.662$	5.5.1122797.1	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1-\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
9225.2.a.cj	$9225$	$2$	9225.a	1.a	$1$	$6$	$6$	$73.662$	6.6.3356224.1	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{4}q^{7}+(-\beta _{1}+\beta _{4}+\cdots)q^{8}+\cdots\)
9225.2.a.ck	$9225$	$2$	9225.a	1.a	$1$	$6$	$6$	$73.662$	6.6.69796620.1	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-8\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1+\beta _{5})q^{7}+\cdots\)
9225.2.a.cl	$9225$	$2$	9225.a	1.a	$1$	$7$	$7$	$73.662$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(-3\)	\(0\)	\(0\)	\(14\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(2+\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
9225.2.a.cm	$9225$	$2$	9225.a	1.a	$1$	$7$	$7$	$73.662$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(-7\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{4})q^{7}+\cdots\)
9225.2.a.cn	$9225$	$2$	9225.a	1.a	$1$	$7$	$7$	$73.662$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{5})q^{7}+\cdots\)
9225.2.a.co	$9225$	$2$	9225.a	1.a	$1$	$7$	$7$	$73.662$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{5})q^{7}+\cdots\)
9225.2.a.cp	$9225$	$2$	9225.a	1.a	$1$	$7$	$7$	$73.662$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(7\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{4})q^{7}+\cdots\)
9225.2.a.cq	$9225$	$2$	9225.a	1.a	$1$	$7$	$7$	$73.662$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{5})q^{7}+\cdots\)
9225.2.a.cr	$9225$	$2$	9225.a	1.a	$1$	$7$	$7$	$73.662$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{5})q^{7}+\cdots\)
9225.2.a.cs	$9225$	$2$	9225.a	1.a	$1$	$7$	$7$	$73.662$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(3\)	\(0\)	\(0\)	\(-14\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-2-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
9225.2.a.ct	$9225$	$2$	9225.a	1.a	$1$	$8$	$8$	$73.662$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(\beta _{2}-\beta _{6})q^{7}+\cdots\)
9225.2.a.cu	$9225$	$2$	9225.a	1.a	$1$	$9$	$9$	$73.662$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{8}q^{7}+(-1+\cdots)q^{8}+\cdots\)
9225.2.a.cv	$9225$	$2$	9225.a	1.a	$1$	$9$	$9$	$73.662$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{8}q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots\)
9225.2.a.cw	$9225$	$2$	9225.a	1.a	$1$	$9$	$9$	$73.662$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{8}q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots\)
9225.2.a.cx	$9225$	$2$	9225.a	1.a	$1$	$9$	$9$	$73.662$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{8}q^{7}+(1+\beta _{1}+\cdots)q^{8}+\cdots\)
9225.2.a.cy	$9225$	$2$	9225.a	1.a	$1$	$10$	$10$	$73.662$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{5}q^{7}+(-1+\cdots)q^{8}+\cdots\)
9225.2.a.cz	$9225$	$2$	9225.a	1.a	$1$	$10$	$10$	$73.662$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(-3\)	\(0\)	\(0\)	\(8\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots\)
9225.2.a.da	$9225$	$2$	9225.a	1.a	$1$	$10$	$10$	$73.662$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(0\)	\(0\)	\(-8\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots\)
9225.2.a.db	$9225$	$2$	9225.a	1.a	$1$	$10$	$10$	$73.662$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(3\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{5}q^{7}+(1+\beta _{1}+\cdots)q^{8}+\cdots\)
9225.2.a.dc	$9225$	$2$	9225.a	1.a	$1$	$14$	$14$	$73.662$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{13}q^{7}+(2\beta _{1}+\cdots)q^{8}+\cdots\)
9225.2.a.dd	$9225$	$2$	9225.a	1.a	$1$	$16$	$16$	$73.662$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{8}q^{7}+(\beta _{4}+\cdots)q^{8}+\cdots\)
9225.2.a.de	$9225$	$2$	9225.a	1.a	$1$	$16$	$16$	$73.662$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{8}q^{7}+(\beta _{4}+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9225))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9225)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(123))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(205))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(369))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(615))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1025))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1845))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3075))\)\(^{\oplus 2}\)