Space of modular forms of level 8925, weight 2, and trivial character

• Label: 8925.2.a
• Level: $8925$
• Weight: $2$
• Character orbit: 8925.a
• Rep. character: $\chi_{8925}(1,\cdot)$
• Character field: $\Q$
• Dimension: $304$
• Newform subspaces: $76$
• Sturm bound: $2880$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 8925 = 3 \cdot 5^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8925.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 76 \)
Sturm bound:			\(2880\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(2\), \(11\), \(13\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8925))\).

	Total	New	Old
Modular forms	1464	304	1160
Cusp forms	1417	304	1113
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.

\(3\)	\(5\)	\(7\)	\(17\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(16\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(17\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(22\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(17\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(20\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(22\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(16\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(22\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(17\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(16\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(17\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(22\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(22\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(20\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(22\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(16\)
Plus space				\(+\)	\(142\)
Minus space				\(-\)	\(162\)

Trace form

\( 304 q + 4 q^{2} + 308 q^{4} + 4 q^{7} + 12 q^{8} + 304 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8925))\) 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	7	17
8925.2.a.a	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓				357.2.a.d	$1$	$1$	\(-2\)	\(-1\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+q^{7}+q^{9}+\cdots\)
8925.2.a.b	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓	✓			8925.2.a.b	$1$	$0$	\(-2\)	\(-1\)	\(0\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+q^{7}+q^{9}+\cdots\)
8925.2.a.c	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓	✓			8925.2.a.c	$1$	$1$	\(-2\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+2q^{4}-2q^{6}-q^{7}+q^{9}+\cdots\)
8925.2.a.d	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓				1785.2.g.a	$1$	$1$	\(-2\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+2q^{4}-2q^{6}+q^{7}+q^{9}+\cdots\)
8925.2.a.e	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓				1785.2.a.o	$1$	$0$	\(-1\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+q^{6}-q^{7}+3q^{8}+\cdots\)
8925.2.a.f	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓				1785.2.a.n	$1$	$0$	\(-1\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+q^{6}-q^{7}+3q^{8}+\cdots\)
8925.2.a.g	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓				1785.2.a.m	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+q^{6}+q^{7}+3q^{8}+\cdots\)
8925.2.a.h	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓				1785.2.a.j	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-q^{6}-q^{7}+3q^{8}+\cdots\)
8925.2.a.i	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓				1785.2.a.l	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-q^{6}-q^{7}+3q^{8}+\cdots\)
8925.2.a.j	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓				1785.2.a.i	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-q^{6}+q^{7}+3q^{8}+\cdots\)
8925.2.a.k	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓				1785.2.a.k	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-q^{6}+q^{7}+3q^{8}+\cdots\)
8925.2.a.l	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓				1785.2.a.h	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-q^{7}+q^{9}-6q^{11}+2q^{12}+\cdots\)
8925.2.a.m	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓	✓			8925.2.a.m	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-q^{7}+q^{9}-5q^{11}+2q^{12}+\cdots\)
8925.2.a.n	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓	✓			8925.2.a.n	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-q^{7}+q^{9}+3q^{11}+2q^{12}+\cdots\)
8925.2.a.o	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓				357.2.a.c	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}-q^{7}+q^{9}-5q^{11}-2q^{12}+\cdots\)
8925.2.a.p	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓				1785.2.a.f	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}-q^{7}+q^{9}+2q^{11}-2q^{12}+\cdots\)
8925.2.a.q	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓	✓			8925.2.a.m	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+q^{7}+q^{9}-5q^{11}-2q^{12}+\cdots\)
8925.2.a.r	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓				1785.2.a.g	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+q^{7}+q^{9}-2q^{11}-2q^{12}+\cdots\)
8925.2.a.s	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓				357.2.a.b	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+q^{7}+q^{9}+3q^{11}-2q^{12}+\cdots\)
8925.2.a.t	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓	✓			8925.2.a.n	$1$	$0$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+q^{7}+q^{9}+3q^{11}-2q^{12}+\cdots\)
8925.2.a.u	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓				1785.2.a.e	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}-q^{6}-q^{7}-3q^{8}+\cdots\)
8925.2.a.v	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓				1785.2.a.c	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}-q^{6}-q^{7}-3q^{8}+\cdots\)
8925.2.a.w	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓				1785.2.a.d	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}-q^{6}+q^{7}-3q^{8}+\cdots\)
8925.2.a.x	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓				1785.2.a.a	$1$	$1$	\(1\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}+q^{6}-q^{7}-3q^{8}+\cdots\)
8925.2.a.y	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓				1785.2.a.b	$1$	$0$	\(1\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}+q^{6}-q^{7}-3q^{8}+\cdots\)
8925.2.a.z	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓				357.2.a.a	$1$	$0$	\(2\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}-2q^{6}-q^{7}+q^{9}+\cdots\)
8925.2.a.ba	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓				1785.2.g.a	$1$	$0$	\(2\)	\(-1\)	\(0\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}-2q^{6}-q^{7}+q^{9}+\cdots\)
8925.2.a.bb	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓	✓			8925.2.a.c	$1$	$1$	\(2\)	\(-1\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}-2q^{6}+q^{7}+q^{9}+\cdots\)
8925.2.a.bc	$8925$	$2$	8925.a	1.a	$1$	$1$	$1$	$71.266$	\(\Q\)	None	✓	✓			8925.2.a.b	$1$	$0$	\(2\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}+2q^{6}-q^{7}+q^{9}+\cdots\)
8925.2.a.bd	$8925$	$2$	8925.a	1.a	$1$	$2$	$2$	$71.266$	\(\Q(\sqrt{17}) \)	None	✓				1785.2.a.t	$1$	$0$	\(-1\)	\(-2\)	\(0\)	\(-2\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+\beta q^{6}-q^{7}+\cdots\)
8925.2.a.be	$8925$	$2$	8925.a	1.a	$1$	$2$	$2$	$71.266$	\(\Q(\sqrt{17}) \)	None	✓				1785.2.a.s	$1$	$1$	\(-1\)	\(-2\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+\beta q^{6}+q^{7}+\cdots\)
8925.2.a.bf	$8925$	$2$	8925.a	1.a	$1$	$2$	$2$	$71.266$	\(\Q(\sqrt{3}) \)	None	✓				1785.2.g.b	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+q^{4}-\beta q^{6}-q^{7}-\beta q^{8}+\cdots\)
8925.2.a.bg	$8925$	$2$	8925.a	1.a	$1$	$2$	$2$	$71.266$	\(\Q(\sqrt{2}) \)	None	✓				357.2.a.f	$1$	$0$	\(0\)	\(2\)	\(0\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+\beta q^{6}+q^{7}-2\beta q^{8}+\cdots\)
8925.2.a.bh	$8925$	$2$	8925.a	1.a	$1$	$2$	$2$	$71.266$	\(\Q(\sqrt{3}) \)	None	✓				1785.2.a.q	$1$	$1$	\(0\)	\(2\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+q^{4}+\beta q^{6}+q^{7}-\beta q^{8}+\cdots\)
8925.2.a.bi	$8925$	$2$	8925.a	1.a	$1$	$2$	$2$	$71.266$	\(\Q(\sqrt{3}) \)	None	✓				1785.2.g.b	$1$	$1$	\(0\)	\(2\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+q^{4}+\beta q^{6}+q^{7}-\beta q^{8}+\cdots\)
8925.2.a.bj	$8925$	$2$	8925.a	1.a	$1$	$2$	$2$	$71.266$	\(\Q(\sqrt{5}) \)	None	✓				1785.2.a.r	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+3q^{4}-\beta q^{6}-q^{7}-\beta q^{8}+\cdots\)
8925.2.a.bk	$8925$	$2$	8925.a	1.a	$1$	$2$	$2$	$71.266$	\(\Q(\sqrt{2}) \)	None	✓				1785.2.a.p	$1$	$1$	\(2\)	\(-2\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
8925.2.a.bl	$8925$	$2$	8925.a	1.a	$1$	$2$	$2$	$71.266$	\(\Q(\sqrt{3}) \)	None	✓				357.2.a.e	$1$	$0$	\(2\)	\(-2\)	\(0\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}-q^{3}+(2+2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
8925.2.a.bm	$8925$	$2$	8925.a	1.a	$1$	$3$	$3$	$71.266$	3.3.316.1	None	✓				357.2.a.g	$1$	$1$	\(-1\)	\(-3\)	\(0\)	\(-3\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
8925.2.a.bn	$8925$	$2$	8925.a	1.a	$1$	$3$	$3$	$71.266$	3.3.148.1	None	✓				1785.2.a.w	$1$	$1$	\(1\)	\(-3\)	\(0\)	\(3\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
8925.2.a.bo	$8925$	$2$	8925.a	1.a	$1$	$3$	$3$	$71.266$	3.3.148.1	None	✓				1785.2.a.v	$1$	$0$	\(1\)	\(-3\)	\(0\)	\(3\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
8925.2.a.bp	$8925$	$2$	8925.a	1.a	$1$	$3$	$3$	$71.266$	3.3.564.1	None	✓				1785.2.a.x	$1$	$0$	\(1\)	\(-3\)	\(0\)	\(-3\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
8925.2.a.bq	$8925$	$2$	8925.a	1.a	$1$	$3$	$3$	$71.266$	3.3.148.1	None	✓				1785.2.a.u	$1$	$0$	\(3\)	\(3\)	\(0\)	\(-3\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
8925.2.a.br	$8925$	$2$	8925.a	1.a	$1$	$4$	$4$	$71.266$	4.4.19664.1	None	✓				1785.2.g.c	$1$	$1$	\(-2\)	\(-4\)	\(0\)	\(4\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-q^{3}+(2+\beta _{2})q^{4}+\cdots\)
8925.2.a.bs	$8925$	$2$	8925.a	1.a	$1$	$4$	$4$	$71.266$	4.4.7232.1	None	✓				357.2.a.h	$1$	$1$	\(-2\)	\(4\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+q^{3}+(1-\beta _{2}-\beta _{3})q^{4}+\beta _{2}q^{6}+\cdots\)
8925.2.a.bt	$8925$	$2$	8925.a	1.a	$1$	$4$	$4$	$71.266$	4.4.11348.1	None	✓				1785.2.a.ba	$1$	$1$	\(-2\)	\(4\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+q^{3}+(2+\beta _{2}-\beta _{3})q^{4}+\cdots\)
8925.2.a.bu	$8925$	$2$	8925.a	1.a	$1$	$4$	$4$	$71.266$	4.4.8468.1	None	✓				1785.2.a.z	$1$	$1$	\(1\)	\(4\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
8925.2.a.bv	$8925$	$2$	8925.a	1.a	$1$	$4$	$4$	$71.266$	4.4.19664.1	None	✓				1785.2.g.c	$1$	$0$	\(2\)	\(4\)	\(0\)	\(-4\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
8925.2.a.bw	$8925$	$2$	8925.a	1.a	$1$	$4$	$4$	$71.266$	4.4.8468.1	None	✓				1785.2.a.y	$1$	$0$	\(2\)	\(4\)	\(0\)	\(4\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+q^{3}+(2-\beta _{1})q^{4}-\beta _{2}q^{6}+\cdots\)
8925.2.a.bx	$8925$	$2$	8925.a	1.a	$1$	$5$	$5$	$71.266$	5.5.36497.1	None	✓	✓			8925.2.a.bx	$1$	$1$	\(0\)	\(-5\)	\(0\)	\(5\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{3}+\beta _{4})q^{2}-q^{3}+(-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
8925.2.a.by	$8925$	$2$	8925.a	1.a	$1$	$5$	$5$	$71.266$	5.5.36497.1	None	✓	✓	✓		8925.2.a.bx	$1$	$1$	\(0\)	\(5\)	\(0\)	\(-5\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{3}-\beta _{4})q^{2}+q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots\)
8925.2.a.bz	$8925$	$2$	8925.a	1.a	$1$	$5$	$5$	$71.266$	5.5.674848.1	None	✓				1785.2.a.bc	$1$	$1$	\(1\)	\(-5\)	\(0\)	\(-5\)		$+$	$+$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
8925.2.a.ca	$8925$	$2$	8925.a	1.a	$1$	$5$	$5$	$71.266$	5.5.246832.1	None	✓				1785.2.a.bb	$1$	$0$	\(2\)	\(5\)	\(0\)	\(5\)		$-$	$+$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{4})q^{4}+\beta _{1}q^{6}+\cdots\)
8925.2.a.cb	$8925$	$2$	8925.a	1.a	$1$	$6$	$6$	$71.266$	6.6.17749184.1	None	✓				1785.2.a.bd	$1$	$0$	\(-3\)	\(-6\)	\(0\)	\(6\)		$+$	$+$	$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-q^{3}+(2+\beta _{4})q^{4}+\cdots\)
8925.2.a.cc	$8925$	$2$	8925.a	1.a	$1$	$6$	$6$	$71.266$	6.6.7836289.1	None	✓	✓			8925.2.a.cc	$1$	$1$	\(-2\)	\(6\)	\(0\)	\(6\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
8925.2.a.cd	$8925$	$2$	8925.a	1.a	$1$	$6$	$6$	$71.266$	6.6.5869904.1	None	✓		✓		1785.2.g.d	$1$	$1$	\(-1\)	\(-6\)	\(0\)	\(6\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+\beta _{1}q^{6}+q^{7}+\cdots\)
8925.2.a.ce	$8925$	$2$	8925.a	1.a	$1$	$6$	$6$	$71.266$	6.6.5869904.1	None	✓				1785.2.g.d	$1$	$0$	\(1\)	\(6\)	\(0\)	\(-6\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+\beta _{1}q^{6}-q^{7}+\cdots\)
8925.2.a.cf	$8925$	$2$	8925.a	1.a	$1$	$6$	$6$	$71.266$	6.6.7836289.1	None	✓	✓	✓		8925.2.a.cc	$1$	$1$	\(2\)	\(-6\)	\(0\)	\(-6\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
8925.2.a.cg	$8925$	$2$	8925.a	1.a	$1$	$7$	$7$	$71.266$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓		8925.2.a.cg	$1$	$0$	\(-4\)	\(-7\)	\(0\)	\(-7\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-q^{3}+(2+\beta _{2})q^{4}+\cdots\)
8925.2.a.ch	$8925$	$2$	8925.a	1.a	$1$	$7$	$7$	$71.266$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓		8925.2.a.ch	$1$	$1$	\(-3\)	\(7\)	\(0\)	\(7\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
8925.2.a.ci	$8925$	$2$	8925.a	1.a	$1$	$7$	$7$	$71.266$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓		8925.2.a.ci	$1$	$0$	\(-2\)	\(7\)	\(0\)	\(-7\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
8925.2.a.cj	$8925$	$2$	8925.a	1.a	$1$	$7$	$7$	$71.266$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓		✓		1785.2.g.e	$1$	$1$	\(-1\)	\(7\)	\(0\)	\(7\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(-\beta _{3}+\beta _{4}+\beta _{6})q^{4}+\cdots\)
8925.2.a.ck	$8925$	$2$	8925.a	1.a	$1$	$7$	$7$	$71.266$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				1785.2.g.e	$1$	$0$	\(1\)	\(-7\)	\(0\)	\(-7\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(-\beta _{3}+\beta _{4}+\beta _{6})q^{4}+\cdots\)
8925.2.a.cl	$8925$	$2$	8925.a	1.a	$1$	$7$	$7$	$71.266$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			8925.2.a.ci	$1$	$0$	\(2\)	\(-7\)	\(0\)	\(7\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
8925.2.a.cm	$8925$	$2$	8925.a	1.a	$1$	$7$	$7$	$71.266$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			8925.2.a.ch	$1$	$1$	\(3\)	\(-7\)	\(0\)	\(-7\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
8925.2.a.cn	$8925$	$2$	8925.a	1.a	$1$	$7$	$7$	$71.266$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			8925.2.a.cg	$1$	$0$	\(4\)	\(7\)	\(0\)	\(7\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
8925.2.a.co	$8925$	$2$	8925.a	1.a	$1$	$8$	$8$	$71.266$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓			8925.2.a.co	$1$	$1$	\(-1\)	\(8\)	\(0\)	\(-8\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
8925.2.a.cp	$8925$	$2$	8925.a	1.a	$1$	$8$	$8$	$71.266$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓	✓		8925.2.a.co	$1$	$1$	\(1\)	\(-8\)	\(0\)	\(8\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
8925.2.a.cq	$8925$	$2$	8925.a	1.a	$1$	$10$	$10$	$71.266$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓	✓		8925.2.a.cq	$1$	$0$	\(-3\)	\(-10\)	\(0\)	\(-10\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
8925.2.a.cr	$8925$	$2$	8925.a	1.a	$1$	$10$	$10$	$71.266$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓	✓		8925.2.a.cr	$1$	$0$	\(-1\)	\(-10\)	\(0\)	\(10\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
8925.2.a.cs	$8925$	$2$	8925.a	1.a	$1$	$10$	$10$	$71.266$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓	✓		8925.2.a.cr	$1$	$0$	\(1\)	\(10\)	\(0\)	\(-10\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
8925.2.a.ct	$8925$	$2$	8925.a	1.a	$1$	$10$	$10$	$71.266$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓	✓		8925.2.a.cq	$1$	$0$	\(3\)	\(10\)	\(0\)	\(10\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
8925.2.a.cu	$8925$	$2$	8925.a	1.a	$1$	$14$	$14$	$71.266$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓		✓		1785.2.g.g	$1$	$1$	\(-3\)	\(-14\)	\(0\)	\(-14\)		$+$	$-$	$+$	$-$	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
8925.2.a.cv	$8925$	$2$	8925.a	1.a	$1$	$14$	$14$	$71.266$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓		✓		1785.2.g.f	$1$	$1$	\(-3\)	\(14\)	\(0\)	\(-14\)		$-$	$-$	$+$	$+$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
8925.2.a.cw	$8925$	$2$	8925.a	1.a	$1$	$14$	$14$	$71.266$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓		✓		1785.2.g.f	$1$	$0$	\(3\)	\(-14\)	\(0\)	\(14\)		$+$	$-$	$-$	$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
8925.2.a.cx	$8925$	$2$	8925.a	1.a	$1$	$14$	$14$	$71.266$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓		✓		1785.2.g.g	$1$	$0$	\(3\)	\(14\)	\(0\)	\(14\)		$-$	$-$	$-$	$+$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8925))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8925)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(255))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(357))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(425))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(525))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(595))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1275))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1785))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2975))\)\(^{\oplus 2}\)