Space of modular forms of level 4725, weight 2, and trivial character

• Label: 4725.2.a
• Level: $4725$
• Weight: $2$
• Character orbit: 4725.a
• Rep. character: $\chi_{4725}(1,\cdot)$
• Character field: $\Q$
• Dimension: $152$
• Newform subspaces: $58$
• Sturm bound: $1440$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 4725 = 3^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4725.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 58 \)
Sturm bound:			\(1440\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(2\), \(11\), \(13\), \(37\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4725))\).

	Total	New	Old
Modular forms	756	152	604
Cusp forms	685	152	533
Eisenstein series	71	0	71

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

\(3\)	\(5\)	\(7\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(17\)
\(+\)	\(+\)	\(-\)	$-$	\(19\)
\(+\)	\(-\)	\(+\)	$-$	\(22\)
\(+\)	\(-\)	\(-\)	$+$	\(18\)
\(-\)	\(+\)	\(+\)	$-$	\(19\)
\(-\)	\(+\)	\(-\)	$+$	\(17\)
\(-\)	\(-\)	\(+\)	$+$	\(18\)
\(-\)	\(-\)	\(-\)	$-$	\(22\)
Plus space			\(+\)	\(70\)
Minus space			\(-\)	\(82\)

Trace form

\( 152 q + 148 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4725))\) 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	7
4725.2.a.a	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-q^{7}-3q^{13}+2q^{14}+\cdots\)
4725.2.a.b	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+q^{7}+3q^{13}-2q^{14}+\cdots\)
4725.2.a.c	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+q^{7}+4q^{11}+2q^{13}+\cdots\)
4725.2.a.d	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{7}+3q^{8}+3q^{11}-3q^{13}+\cdots\)
4725.2.a.e	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{7}+3q^{8}+3q^{11}+7q^{13}+\cdots\)
4725.2.a.f	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{7}+3q^{8}-3q^{11}-7q^{13}+\cdots\)
4725.2.a.g	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{7}+3q^{8}-3q^{11}+3q^{13}+\cdots\)
4725.2.a.h	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-q^{7}-6q^{11}+q^{13}+4q^{16}+\cdots\)
4725.2.a.i	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-q^{7}-6q^{11}+4q^{13}+4q^{16}+\cdots\)
4725.2.a.j	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-q^{7}+6q^{11}+q^{13}+4q^{16}+\cdots\)
4725.2.a.k	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-q^{7}+6q^{11}+4q^{13}+4q^{16}+\cdots\)
4725.2.a.l	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{7}-6q^{11}-q^{13}+4q^{16}+\cdots\)
4725.2.a.m	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{7}+6q^{11}-q^{13}+4q^{16}+\cdots\)
4725.2.a.n	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{7}-3q^{8}-3q^{11}-3q^{13}+\cdots\)
4725.2.a.o	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{7}-3q^{8}-3q^{11}+7q^{13}+\cdots\)
4725.2.a.p	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{7}-3q^{8}+3q^{11}-7q^{13}+\cdots\)
4725.2.a.q	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{7}-3q^{8}+3q^{11}+3q^{13}+\cdots\)
4725.2.a.r	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{7}-3q^{13}-2q^{14}+\cdots\)
4725.2.a.s	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+q^{7}-4q^{11}+2q^{13}+\cdots\)
4725.2.a.t	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+q^{7}+3q^{13}+2q^{14}+\cdots\)
4725.2.a.u	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(-3\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+3\beta q^{4}-q^{7}+(-1+\cdots)q^{8}+\cdots\)
4725.2.a.v	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{7}+(-3+\cdots)q^{8}+\cdots\)
4725.2.a.w	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+q^{7}+(-1+2\beta )q^{8}+\cdots\)
4725.2.a.x	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+q^{7}+(-1+2\beta )q^{8}+\cdots\)
4725.2.a.y	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+q^{7}+(-1+2\beta )q^{8}+\cdots\)
4725.2.a.z	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1+\beta )q^{4}-q^{7}-3q^{8}+3q^{11}+\cdots\)
4725.2.a.ba	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}-q^{7}-\beta q^{8}+\beta q^{11}+\cdots\)
4725.2.a.bb	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	\(\Q(\sqrt{7}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+5q^{4}+q^{7}+3\beta q^{8}+\beta q^{11}+\cdots\)
4725.2.a.bc	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+q^{7}+(1-2\beta )q^{8}+\cdots\)
4725.2.a.bd	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+q^{7}+(1-2\beta )q^{8}+\cdots\)
4725.2.a.be	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+q^{7}+(1-2\beta )q^{8}+\cdots\)
4725.2.a.bf	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1+\beta )q^{4}-q^{7}+3q^{8}-3q^{11}+\cdots\)
4725.2.a.bg	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{7}+(3+\beta )q^{8}+\cdots\)
4725.2.a.bh	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(3\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+3\beta q^{4}-q^{7}+(1+4\beta )q^{8}+\cdots\)
4725.2.a.bi	$4725$	$2$	4725.a	1.a	$1$	$3$	$3$	$37.729$	3.3.257.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}-q^{7}+(-3+\cdots)q^{8}+\cdots\)
4725.2.a.bj	$4725$	$2$	4725.a	1.a	$1$	$3$	$3$	$37.729$	3.3.257.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}-q^{7}+(3+\cdots)q^{8}+\cdots\)
4725.2.a.bk	$4725$	$2$	4725.a	1.a	$1$	$3$	$3$	$37.729$	3.3.257.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+q^{7}+(-3+\cdots)q^{8}+\cdots\)
4725.2.a.bl	$4725$	$2$	4725.a	1.a	$1$	$3$	$3$	$37.729$	3.3.257.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+q^{7}+(3+\cdots)q^{8}+\cdots\)
4725.2.a.bm	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	4.4.15529.1	None	✓	$1$	$1$	\(-3\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots\)
4725.2.a.bn	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	4.4.15529.1	None	✓	$1$	$1$	\(-3\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots\)
4725.2.a.bo	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	4.4.144344.1	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{7}+(-1-2\beta _{1}+\cdots)q^{8}+\cdots\)
4725.2.a.bp	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	\(\Q(\sqrt{2}, \sqrt{29})\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{7}-2\beta _{1}q^{8}-\beta _{2}q^{11}+\cdots\)
4725.2.a.bq	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	\(\Q(\sqrt{2}, \sqrt{29})\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{7}-2\beta _{1}q^{8}+\beta _{2}q^{11}+\cdots\)
4725.2.a.br	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}-\beta _{2}q^{4}-q^{7}+(\beta _{1}+\beta _{3})q^{8}+\cdots\)
4725.2.a.bs	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}-\beta _{2}q^{4}+q^{7}+(\beta _{1}+\beta _{3})q^{8}+\cdots\)
4725.2.a.bt	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}-q^{7}+2\beta _{2}q^{8}+\cdots\)
4725.2.a.bu	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}-q^{7}+2\beta _{2}q^{8}+\cdots\)
4725.2.a.bv	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+q^{7}+2\beta _{2}q^{8}+\cdots\)
4725.2.a.bw	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+q^{7}+2\beta _{2}q^{8}+\cdots\)
4725.2.a.bx	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	4.4.144344.1	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{7}+(1+2\beta _{1}+\cdots)q^{8}+\cdots\)
4725.2.a.by	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	4.4.15529.1	None	✓	$1$	$0$	\(3\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots\)
4725.2.a.bz	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	4.4.15529.1	None	✓	$1$	$0$	\(3\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots\)
4725.2.a.ca	$4725$	$2$	4725.a	1.a	$1$	$5$	$5$	$37.729$	5.5.2161212.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{7}+(-1-\beta _{1}+\cdots)q^{8}+\cdots\)
4725.2.a.cb	$4725$	$2$	4725.a	1.a	$1$	$5$	$5$	$37.729$	5.5.2161212.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{7}+(1+\beta _{1}+\cdots)q^{8}+\cdots\)
4725.2.a.cc	$4725$	$2$	4725.a	1.a	$1$	$5$	$5$	$37.729$	5.5.2161212.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(5\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{7}+(-1-\beta _{1}+\cdots)q^{8}+\cdots\)
4725.2.a.cd	$4725$	$2$	4725.a	1.a	$1$	$5$	$5$	$37.729$	5.5.2161212.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{7}+(1+\beta _{1}+\cdots)q^{8}+\cdots\)
4725.2.a.ce	$4725$	$2$	4725.a	1.a	$1$	$8$	$8$	$37.729$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{3})q^{4}-q^{7}+(2\beta _{1}+\beta _{4}+\cdots)q^{8}+\cdots\)
4725.2.a.cf	$4725$	$2$	4725.a	1.a	$1$	$8$	$8$	$37.729$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{3})q^{4}+q^{7}+(2\beta _{1}+\beta _{4}+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4725))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4725)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(525))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(675))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(945))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1575))\)\(^{\oplus 2}\)