Space of modular forms of level 4851, weight 2, and trivial character

• Label: 4851.2.a
• Level: $4851$
• Weight: $2$
• Character orbit: 4851.a
• Rep. character: $\chi_{4851}(1,\cdot)$
• Character field: $\Q$
• Dimension: $172$
• Newform subspaces: $60$
• Sturm bound: $1344$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 4851 = 3^{2} \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4851.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 60 \)
Sturm bound:			\(1344\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(2\), \(5\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4851))\).

	Total	New	Old
Modular forms	704	172	532
Cusp forms	641	172	469
Eisenstein series	63	0	63

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

\(3\)	\(7\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(19\)
\(+\)	\(+\)	\(-\)	\(-\)	\(19\)
\(+\)	\(-\)	\(+\)	\(-\)	\(16\)
\(+\)	\(-\)	\(-\)	\(+\)	\(16\)
\(-\)	\(+\)	\(+\)	\(-\)	\(28\)
\(-\)	\(+\)	\(-\)	\(+\)	\(20\)
\(-\)	\(-\)	\(+\)	\(+\)	\(24\)
\(-\)	\(-\)	\(-\)	\(-\)	\(30\)
Plus space			\(+\)	\(79\)
Minus space			\(-\)	\(93\)

Trace form

172 * q + q^2 + 171 * q^4 + 5 * q^5 - 9 * q^8 - 8 * q^10 - 2 * q^11 + 10 * q^13 + 165 * q^16 + 16 * q^17 - 12 * q^20 + q^22 + q^23 + 185 * q^25 - 6 * q^26 + 14 * q^29 - 13 * q^31 + 3 * q^32 + 22 * q^34 - 3 * q^37 - 16 * q^38 + 30 * q^40 + 10 * q^41 - 30 * q^43 - 9 * q^44 + 14 * q^46 + 9 * q^50 + 42 * q^52 + 28 * q^53 - q^55 + 82 * q^58 - 21 * q^59 - 10 * q^61 - 18 * q^62 + 205 * q^64 + 84 * q^65 - 19 * q^67 + 22 * q^68 - 9 * q^71 + 34 * q^73 + 88 * q^74 + 12 * q^76 - 42 * q^79 + 18 * q^80 + 58 * q^82 + 30 * q^83 + 58 * q^85 + 56 * q^86 + 15 * q^88 + 51 * q^89 + 30 * q^92 - 20 * q^94 - 32 * q^95 + 51 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4851))\) 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	7	11
4851.2.a.a	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	\(\Q\)	None	✓				77.2.a.c	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{5}+3q^{8}+2q^{10}+\cdots\)
4851.2.a.b	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	\(\Q\)	None	✓				33.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{5}+3q^{8}+2q^{10}+\cdots\)
4851.2.a.c	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	\(\Q\)	None	✓				1617.2.a.f	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+3q^{8}+q^{11}-4q^{13}+\cdots\)
4851.2.a.d	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	\(\Q\)	None	✓				231.2.i.a	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+3q^{8}+q^{11}-4q^{13}+\cdots\)
4851.2.a.e	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	\(\Q\)	None	✓				231.2.i.a	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+3q^{8}+q^{11}+4q^{13}+\cdots\)
4851.2.a.f	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	\(\Q\)	None	✓				1617.2.a.f	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+3q^{8}+q^{11}+4q^{13}+\cdots\)
4851.2.a.g	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	\(\Q\)	None	✓				99.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+4q^{5}+3q^{8}-4q^{10}+\cdots\)
4851.2.a.h	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	\(\Q\)	None	✓				693.2.i.c	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-4q^{5}-q^{11}+5q^{13}+4q^{16}+\cdots\)
4851.2.a.i	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	\(\Q\)	None	✓				693.2.i.c	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-4q^{5}+q^{11}-5q^{13}+4q^{16}+\cdots\)
4851.2.a.j	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	\(\Q\)	None	✓				77.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-q^{5}+q^{11}+4q^{13}+4q^{16}+\cdots\)
4851.2.a.k	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	\(\Q\)	None	✓				77.2.a.b	$1$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+3q^{5}+q^{11}+4q^{13}+4q^{16}+\cdots\)
4851.2.a.l	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	\(\Q\)	None	✓				693.2.i.c	$1$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+4q^{5}-q^{11}-5q^{13}+4q^{16}+\cdots\)
4851.2.a.m	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	\(\Q\)	None	✓				693.2.i.c	$1$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+4q^{5}+q^{11}+5q^{13}+4q^{16}+\cdots\)
4851.2.a.n	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	\(\Q\)	None	✓				231.2.i.b	$1$	$1$	\(1\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-4q^{5}-3q^{8}-4q^{10}+\cdots\)
4851.2.a.o	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	\(\Q\)	None	✓				99.2.a.a	$1$	$1$	\(1\)	\(0\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-4q^{5}-3q^{8}-4q^{10}+\cdots\)
4851.2.a.p	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	\(\Q\)	None	✓				231.2.a.a	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-2q^{5}-3q^{8}-2q^{10}+\cdots\)
4851.2.a.q	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	\(\Q\)	None	✓				231.2.i.b	$1$	$0$	\(1\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+4q^{5}-3q^{8}+4q^{10}+\cdots\)
4851.2.a.r	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	\(\Q\)	None	✓				231.2.i.c	$1$	$1$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+q^{11}-5q^{13}-4q^{16}+\cdots\)
4851.2.a.s	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	\(\Q\)	None	✓				231.2.i.c	$1$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+q^{11}+5q^{13}-4q^{16}+\cdots\)
4851.2.a.t	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	\(\Q\)	None	✓				11.2.a.a	$1$	$1$	\(2\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+q^{5}+2q^{10}-q^{11}+\cdots\)
4851.2.a.u	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	\(\Q(\sqrt{5}) \)	None	✓				693.2.a.e	$1$	$1$	\(-3\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+3\beta q^{4}+q^{5}+(-1+\cdots)q^{8}+\cdots\)
4851.2.a.v	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	\(\Q(\sqrt{2}) \)	None	✓	✓			4851.2.a.v	$2$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+\beta q^{5}+3q^{8}-\beta q^{10}+\cdots\)
4851.2.a.w	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	\(\Q(\sqrt{5}) \)	None	✓				231.2.a.c	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-1+2\beta )q^{8}+\cdots\)
4851.2.a.x	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	\(\Q(\sqrt{13}) \)	None	✓				693.2.a.g	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1+\beta )q^{4}+q^{5}-3q^{8}-\beta q^{10}+\cdots\)
4851.2.a.y	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	\(\Q(\sqrt{5}) \)	None	✓				77.2.a.d	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+3q^{4}-2q^{5}-\beta q^{8}+2\beta q^{10}+\cdots\)
4851.2.a.z	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	\(\Q(\sqrt{13}) \)	None	✓				693.2.a.g	$1$	$1$	\(1\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1+\beta )q^{4}-q^{5}+3q^{8}-\beta q^{10}+\cdots\)
4851.2.a.ba	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	\(\Q(\sqrt{21}) \)	None	✓				231.2.a.b	$1$	$0$	\(1\)	\(0\)	\(6\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(3+\beta )q^{4}+3q^{5}+(5+2\beta )q^{8}+\cdots\)
4851.2.a.bb	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	\(\Q(\sqrt{2}) \)	None	✓	✓			4851.2.a.v	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-\beta q^{5}-3q^{8}-\beta q^{10}+\cdots\)
4851.2.a.bc	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	\(\Q(\sqrt{2}) \)	None	✓				539.2.a.e	$2$	$1$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-\beta q^{5}-3q^{8}-\beta q^{10}+\cdots\)
4851.2.a.bd	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	\(\Q(\sqrt{2}) \)	None	✓				231.2.i.d	$1$	$1$	\(2\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-2q^{5}+(3+\cdots)q^{8}+\cdots\)
4851.2.a.be	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	\(\Q(\sqrt{2}) \)	None	✓				231.2.i.d	$1$	$0$	\(2\)	\(0\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+2q^{5}+(3+\cdots)q^{8}+\cdots\)
4851.2.a.bf	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	\(\Q(\sqrt{5}) \)	None	✓				693.2.a.e	$1$	$0$	\(3\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+3\beta q^{4}-q^{5}+(1+4\beta )q^{8}+\cdots\)
4851.2.a.bg	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	\(\Q(\sqrt{5}) \)	None	✓				1617.2.a.k	$1$	$0$	\(3\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+3\beta q^{4}+(1-2\beta )q^{5}+(1+\cdots)q^{8}+\cdots\)
4851.2.a.bh	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	\(\Q(\sqrt{5}) \)	None	✓				1617.2.a.k	$1$	$0$	\(3\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+3\beta q^{4}+(-1+2\beta )q^{5}+\cdots\)
4851.2.a.bi	$4851$	$2$	4851.a	1.a	$1$	$3$	$3$	$38.735$	3.3.229.1	None	✓				231.2.a.e	$1$	$0$	\(-2\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(2+\beta _{1})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
4851.2.a.bj	$4851$	$2$	4851.a	1.a	$1$	$3$	$3$	$38.735$	\(\Q(\zeta_{18})^+\)	None	✓				77.2.e.a	$1$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(-2-\beta _{2})q^{5}+(-1+\cdots)q^{8}+\cdots\)
4851.2.a.bk	$4851$	$2$	4851.a	1.a	$1$	$3$	$3$	$38.735$	\(\Q(\zeta_{18})^+\)	None	✓				77.2.e.a	$1$	$1$	\(0\)	\(0\)	\(6\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(2+\beta _{2})q^{5}+(-1+\cdots)q^{8}+\cdots\)
4851.2.a.bl	$4851$	$2$	4851.a	1.a	$1$	$3$	$3$	$38.735$	3.3.229.1	None	✓				1617.2.a.q	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
4851.2.a.bm	$4851$	$2$	4851.a	1.a	$1$	$3$	$3$	$38.735$	3.3.229.1	None	✓				1617.2.a.q	$1$	$1$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
4851.2.a.bn	$4851$	$2$	4851.a	1.a	$1$	$3$	$3$	$38.735$	3.3.257.1	None	✓				77.2.e.b	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
4851.2.a.bo	$4851$	$2$	4851.a	1.a	$1$	$3$	$3$	$38.735$	3.3.257.1	None	✓				77.2.e.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
4851.2.a.bp	$4851$	$2$	4851.a	1.a	$1$	$3$	$3$	$38.735$	3.3.837.1	None	✓				231.2.a.d	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
4851.2.a.bq	$4851$	$2$	4851.a	1.a	$1$	$4$	$4$	$38.735$	4.4.725.1	None	✓	✓			4851.2.a.bq	$2$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1-\beta _{1})q^{4}+\beta _{2}q^{5}+(-1+\cdots)q^{8}+\cdots\)
4851.2.a.br	$4851$	$2$	4851.a	1.a	$1$	$4$	$4$	$38.735$	4.4.2624.1	None	✓				1617.2.a.w	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{4}+(1-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
4851.2.a.bs	$4851$	$2$	4851.a	1.a	$1$	$4$	$4$	$38.735$	4.4.2624.1	None	✓				1617.2.a.w	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
4851.2.a.bt	$4851$	$2$	4851.a	1.a	$1$	$4$	$4$	$38.735$	4.4.11344.1	None	✓				231.2.i.e	$1$	$1$	\(-2\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
4851.2.a.bu	$4851$	$2$	4851.a	1.a	$1$	$4$	$4$	$38.735$	4.4.11344.1	None	✓				231.2.i.e	$1$	$0$	\(-2\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
4851.2.a.bv	$4851$	$2$	4851.a	1.a	$1$	$4$	$4$	$38.735$	4.4.9248.1	None	✓				539.2.a.k	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+(2-\beta _{3})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
4851.2.a.bw	$4851$	$2$	4851.a	1.a	$1$	$4$	$4$	$38.735$	4.4.725.1	None	✓	✓			4851.2.a.bq	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1-\beta _{1})q^{4}-\beta _{2}q^{5}+(1+\cdots)q^{8}+\cdots\)
4851.2.a.bx	$4851$	$2$	4851.a	1.a	$1$	$4$	$4$	$38.735$	4.4.2624.1	None	✓				1617.2.a.u	$1$	$0$	\(2\)	\(0\)	\(-8\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+\beta _{2}q^{4}+(-1-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
4851.2.a.by	$4851$	$2$	4851.a	1.a	$1$	$4$	$4$	$38.735$	4.4.2624.1	None	✓				1617.2.a.u	$1$	$0$	\(2\)	\(0\)	\(8\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+\beta _{2}q^{4}+(1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
4851.2.a.bz	$4851$	$2$	4851.a	1.a	$1$	$5$	$5$	$38.735$	5.5.3676752.1	None	✓		✓		231.2.i.f	$1$	$1$	\(-2\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1+\beta _{4})q^{5}+\cdots\)
4851.2.a.ca	$4851$	$2$	4851.a	1.a	$1$	$5$	$5$	$38.735$	5.5.3676752.1	None	✓				231.2.i.f	$1$	$0$	\(-2\)	\(0\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1-\beta _{4})q^{5}+\cdots\)
4851.2.a.cb	$4851$	$2$	4851.a	1.a	$1$	$6$	$6$	$38.735$	6.6.672323328.1	None	✓		✓		693.2.i.k	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
4851.2.a.cc	$4851$	$2$	4851.a	1.a	$1$	$6$	$6$	$38.735$	6.6.672323328.1	None	✓				693.2.i.k	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
4851.2.a.cd	$4851$	$2$	4851.a	1.a	$1$	$6$	$6$	$38.735$	6.6.672323328.1	None	✓				693.2.i.k	$1$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
4851.2.a.ce	$4851$	$2$	4851.a	1.a	$1$	$6$	$6$	$38.735$	6.6.672323328.1	None	✓		✓		693.2.i.k	$1$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
4851.2.a.cf	$4851$	$2$	4851.a	1.a	$1$	$10$	$10$	$38.735$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓	✓		4851.2.a.cf	$2$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(2+\beta _{2}+\beta _{8})q^{4}-\beta _{7}q^{5}+\cdots\)
4851.2.a.cg	$4851$	$2$	4851.a	1.a	$1$	$10$	$10$	$38.735$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		539.2.a.l	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{2}+(2+\beta _{9})q^{4}+\beta _{7}q^{5}+(1+\beta _{2}+\cdots)q^{8}+\cdots\)
4851.2.a.ch	$4851$	$2$	4851.a	1.a	$1$	$10$	$10$	$38.735$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓	✓		4851.2.a.cf	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(2+\beta _{2}+\beta _{8})q^{4}-\beta _{7}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4851))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4851)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(539))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(693))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1617))\)\(^{\oplus 2}\)