Space of modular forms of level 48552, weight 2, and trivial character

• Label: 48552.2.a
• Level: $48552$
• Weight: $2$
• Character orbit: 48552.a
• Rep. character: $\chi_{48552}(1,\cdot)$
• Character field: $\Q$
• Dimension: $814$
• Newform subspaces: $103$
• Sturm bound: $19584$

Defining parameters

Level:	\( N \)	\(=\)	\( 48552 = 2^{3} \cdot 3 \cdot 7 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	48552.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 103 \)
Sturm bound:			\(19584\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(48552))\).

	Total	New	Old
Modular forms	9936	814	9122
Cusp forms	9649	814	8835
Eisenstein series	287	0	287

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

\(2\)	\(3\)	\(7\)	\(17\)	Fricke		Total				Cusp				Eisenstein
						All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)		\(603\)	\(46\)	\(557\)		\(586\)	\(46\)	\(540\)		\(17\)	\(0\)	\(17\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)		\(638\)	\(56\)	\(582\)		\(620\)	\(56\)	\(564\)		\(18\)	\(0\)	\(18\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)		\(630\)	\(53\)	\(577\)		\(612\)	\(53\)	\(559\)		\(18\)	\(0\)	\(18\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)		\(613\)	\(48\)	\(565\)		\(595\)	\(48\)	\(547\)		\(18\)	\(0\)	\(18\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)		\(621\)	\(53\)	\(568\)		\(603\)	\(53\)	\(550\)		\(18\)	\(0\)	\(18\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)		\(622\)	\(48\)	\(574\)		\(604\)	\(48\)	\(556\)		\(18\)	\(0\)	\(18\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)		\(630\)	\(46\)	\(584\)		\(612\)	\(46\)	\(566\)		\(18\)	\(0\)	\(18\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)		\(611\)	\(56\)	\(555\)		\(593\)	\(56\)	\(537\)		\(18\)	\(0\)	\(18\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)		\(639\)	\(50\)	\(589\)		\(621\)	\(50\)	\(571\)		\(18\)	\(0\)	\(18\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)		\(604\)	\(52\)	\(552\)		\(586\)	\(52\)	\(534\)		\(18\)	\(0\)	\(18\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)		\(612\)	\(50\)	\(562\)		\(594\)	\(50\)	\(544\)		\(18\)	\(0\)	\(18\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)		\(629\)	\(52\)	\(577\)		\(611\)	\(52\)	\(559\)		\(18\)	\(0\)	\(18\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)		\(621\)	\(50\)	\(571\)		\(603\)	\(50\)	\(553\)		\(18\)	\(0\)	\(18\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)		\(620\)	\(52\)	\(568\)		\(602\)	\(52\)	\(550\)		\(18\)	\(0\)	\(18\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)		\(612\)	\(50\)	\(562\)		\(594\)	\(50\)	\(544\)		\(18\)	\(0\)	\(18\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)		\(631\)	\(52\)	\(579\)		\(613\)	\(52\)	\(561\)		\(18\)	\(0\)	\(18\)
Plus space				\(+\)		\(4936\)	\(392\)	\(4544\)		\(4793\)	\(392\)	\(4401\)		\(143\)	\(0\)	\(143\)
Minus space				\(-\)		\(5000\)	\(422\)	\(4578\)		\(4856\)	\(422\)	\(4434\)		\(144\)	\(0\)	\(144\)

Trace form

814 * q - 4 * q^5 + 814 * q^9 - 4 * q^13 + 2 * q^21 - 8 * q^23 + 818 * q^25 + 4 * q^29 - 4 * q^37 + 8 * q^39 - 4 * q^41 - 8 * q^43 - 4 * q^45 - 48 * q^47 + 814 * q^49 - 12 * q^53 - 32 * q^55 - 32 * q^59 - 4 * q^61 - 8 * q^65 - 40 * q^67 - 40 * q^71 - 20 * q^73 - 16 * q^79 + 814 * q^81 - 32 * q^83 - 32 * q^87 + 44 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 + 28 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(48552))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	7	17
48552.2.a.a	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(-4\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
48552.2.a.b	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-q^{7}+q^{9}+3q^{11}+2q^{13}+\cdots\)
48552.2.a.c	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(-3\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+q^{7}+q^{9}-5q^{11}-3q^{13}+\cdots\)
48552.2.a.d	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(-3\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+q^{7}+q^{9}+5q^{11}-4q^{13}+\cdots\)
48552.2.a.e	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(-2\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots\)
48552.2.a.f	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(-2\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{7}+q^{9}-2q^{13}+2q^{15}+\cdots\)
48552.2.a.g	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(-2\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
48552.2.a.h	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}+q^{11}+q^{15}+\cdots\)
48552.2.a.i	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(-1\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}+3q^{11}-q^{13}+\cdots\)
48552.2.a.j	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots\)
48552.2.a.k	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
48552.2.a.l	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
48552.2.a.m	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}-q^{11}-3q^{13}+\cdots\)
48552.2.a.n	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(1\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
48552.2.a.o	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(1\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+3q^{11}+q^{13}+\cdots\)
48552.2.a.p	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(2\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots\)
48552.2.a.q	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(2\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
48552.2.a.r	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(2\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{7}+q^{9}+2q^{13}-2q^{15}+\cdots\)
48552.2.a.s	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(-2\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-q^{7}+q^{9}+6q^{13}-2q^{15}+\cdots\)
48552.2.a.t	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
48552.2.a.u	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
48552.2.a.v	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
48552.2.a.w	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
48552.2.a.x	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots\)
48552.2.a.y	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
48552.2.a.z	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(1\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}-q^{11}+q^{15}+\cdots\)
48552.2.a.ba	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(2\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
48552.2.a.bb	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(3\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}-q^{7}+q^{9}-5q^{11}-4q^{13}+\cdots\)
48552.2.a.bc	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(3\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+q^{7}+q^{9}-3q^{11}+2q^{13}+\cdots\)
48552.2.a.bd	$48552$	$2$	48552.a	1.a	$1$	$1$	$1$	$387.690$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(4\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
48552.2.a.be	$48552$	$2$	48552.a	1.a	$1$	$2$	$2$	$387.690$	\(\Q(\sqrt{201}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(-6\)	\(-2\)		$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
48552.2.a.bf	$48552$	$2$	48552.a	1.a	$1$	$2$	$2$	$387.690$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(-2\)		$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.bg	$48552$	$2$	48552.a	1.a	$1$	$2$	$2$	$387.690$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
48552.2.a.bh	$48552$	$2$	48552.a	1.a	$1$	$2$	$2$	$387.690$	\(\Q(\sqrt{15}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(2\)		$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.bi	$48552$	$2$	48552.a	1.a	$1$	$2$	$2$	$387.690$	\(\Q(\sqrt{33}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(1\)	\(2\)		$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
48552.2.a.bj	$48552$	$2$	48552.a	1.a	$1$	$2$	$2$	$387.690$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(3\)	\(2\)		$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.bk	$48552$	$2$	48552.a	1.a	$1$	$2$	$2$	$387.690$	\(\Q(\sqrt{33}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
48552.2.a.bl	$48552$	$2$	48552.a	1.a	$1$	$2$	$2$	$387.690$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(2\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.bm	$48552$	$2$	48552.a	1.a	$1$	$2$	$2$	$387.690$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(2\)	\(2\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.bn	$48552$	$2$	48552.a	1.a	$1$	$2$	$2$	$387.690$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(3\)	\(2\)		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
48552.2.a.bo	$48552$	$2$	48552.a	1.a	$1$	$3$	$3$	$387.690$	3.3.1129.1	None	✓	?				$-1$		\(0\)	\(-3\)	\(2\)	\(-3\)		$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
48552.2.a.bp	$48552$	$2$	48552.a	1.a	$1$	$3$	$3$	$387.690$	3.3.316.1	None	✓	?				$-1$		\(0\)	\(-3\)	\(2\)	\(3\)		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
48552.2.a.bq	$48552$	$2$	48552.a	1.a	$1$	$3$	$3$	$387.690$	3.3.961.1	None	✓	?				$-1$		\(0\)	\(3\)	\(-2\)	\(-3\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.br	$48552$	$2$	48552.a	1.a	$1$	$3$	$3$	$387.690$	3.3.1129.1	None	✓	?				$-1$		\(0\)	\(3\)	\(-2\)	\(3\)		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
48552.2.a.bs	$48552$	$2$	48552.a	1.a	$1$	$3$	$3$	$387.690$	3.3.568.1	None	✓	?				$-1$		\(0\)	\(3\)	\(4\)	\(-3\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.bt	$48552$	$2$	48552.a	1.a	$1$	$4$	$4$	$387.690$	4.4.10889.1	None	✓	?				$-1$		\(0\)	\(-4\)	\(-1\)	\(4\)		$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
48552.2.a.bu	$48552$	$2$	48552.a	1.a	$1$	$4$	$4$	$387.690$	4.4.51153.1	None	✓	?				$-1$		\(0\)	\(-4\)	\(5\)	\(4\)		$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.bv	$48552$	$2$	48552.a	1.a	$1$	$4$	$4$	$387.690$	4.4.51153.1	None	✓	?				$-1$		\(0\)	\(4\)	\(-5\)	\(-4\)		$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
48552.2.a.bw	$48552$	$2$	48552.a	1.a	$1$	$4$	$4$	$387.690$	4.4.183064.1	None	✓	?				$-1$		\(0\)	\(4\)	\(-5\)	\(4\)		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
48552.2.a.bx	$48552$	$2$	48552.a	1.a	$1$	$4$	$4$	$387.690$	4.4.7232.1	None	✓	?				$-1$		\(0\)	\(4\)	\(-2\)	\(4\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.by	$48552$	$2$	48552.a	1.a	$1$	$4$	$4$	$387.690$	4.4.81416.1	None	✓	?				$-1$		\(0\)	\(4\)	\(1\)	\(-4\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
48552.2.a.bz	$48552$	$2$	48552.a	1.a	$1$	$4$	$4$	$387.690$	4.4.10889.1	None	✓	?				$-1$		\(0\)	\(4\)	\(1\)	\(-4\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
48552.2.a.ca	$48552$	$2$	48552.a	1.a	$1$	$5$	$5$	$387.690$	5.5.14050576.1	None	✓	?				$-1$		\(0\)	\(-5\)	\(-1\)	\(-5\)		$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.cb	$48552$	$2$	48552.a	1.a	$1$	$5$	$5$	$387.690$	5.5.32195949.1	None	✓	?				$-1$		\(0\)	\(-5\)	\(0\)	\(5\)		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
48552.2.a.cc	$48552$	$2$	48552.a	1.a	$1$	$5$	$5$	$387.690$	5.5.934448.1	None	✓	?				$-1$		\(0\)	\(-5\)	\(5\)	\(5\)		$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.cd	$48552$	$2$	48552.a	1.a	$1$	$5$	$5$	$387.690$	5.5.934448.1	None	✓	?				$-1$		\(0\)	\(5\)	\(-5\)	\(-5\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.ce	$48552$	$2$	48552.a	1.a	$1$	$5$	$5$	$387.690$	5.5.32195949.1	None	✓	?				$-1$		\(0\)	\(5\)	\(0\)	\(-5\)		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
48552.2.a.cf	$48552$	$2$	48552.a	1.a	$1$	$6$	$6$	$387.690$	6.6.274063172.1	None	✓	?				$-1$		\(0\)	\(-6\)	\(-4\)	\(-6\)		$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.cg	$48552$	$2$	48552.a	1.a	$1$	$6$	$6$	$387.690$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-6\)	\(-2\)	\(6\)		$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
48552.2.a.ch	$48552$	$2$	48552.a	1.a	$1$	$6$	$6$	$387.690$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-6\)	\(0\)	\(-6\)		$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
48552.2.a.ci	$48552$	$2$	48552.a	1.a	$1$	$6$	$6$	$387.690$	6.6.734916349.1	None	✓	?				$-1$		\(0\)	\(-6\)	\(0\)	\(-6\)		$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.cj	$48552$	$2$	48552.a	1.a	$1$	$6$	$6$	$387.690$	6.6.382404292.1	None	✓	?				$-1$		\(0\)	\(-6\)	\(0\)	\(6\)		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
48552.2.a.ck	$48552$	$2$	48552.a	1.a	$1$	$6$	$6$	$387.690$	6.6.346669661.1	None	✓	?				$-1$		\(0\)	\(-6\)	\(2\)	\(-6\)		$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
48552.2.a.cl	$48552$	$2$	48552.a	1.a	$1$	$6$	$6$	$387.690$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-6\)	\(4\)	\(-6\)		$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
48552.2.a.cm	$48552$	$2$	48552.a	1.a	$1$	$6$	$6$	$387.690$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(6\)	\(-4\)	\(6\)		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
48552.2.a.cn	$48552$	$2$	48552.a	1.a	$1$	$6$	$6$	$387.690$	6.6.346669661.1	None	✓	?				$-1$		\(0\)	\(6\)	\(-2\)	\(6\)		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
48552.2.a.co	$48552$	$2$	48552.a	1.a	$1$	$6$	$6$	$387.690$	6.6.382404292.1	None	✓	?				$-1$		\(0\)	\(6\)	\(0\)	\(-6\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
48552.2.a.cp	$48552$	$2$	48552.a	1.a	$1$	$6$	$6$	$387.690$	6.6.734916349.1	None	✓	?				$-1$		\(0\)	\(6\)	\(0\)	\(6\)		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
48552.2.a.cq	$48552$	$2$	48552.a	1.a	$1$	$6$	$6$	$387.690$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(6\)	\(0\)	\(6\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.cr	$48552$	$2$	48552.a	1.a	$1$	$6$	$6$	$387.690$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(6\)	\(2\)	\(-6\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.cs	$48552$	$2$	48552.a	1.a	$1$	$6$	$6$	$387.690$	6.6.274063172.1	None	✓	?				$-1$		\(0\)	\(6\)	\(4\)	\(6\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.ct	$48552$	$2$	48552.a	1.a	$1$	$10$	$10$	$387.690$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-10\)	\(4\)	\(-10\)		$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
48552.2.a.cu	$48552$	$2$	48552.a	1.a	$1$	$10$	$10$	$387.690$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(10\)	\(-4\)	\(10\)		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
48552.2.a.cv	$48552$	$2$	48552.a	1.a	$1$	$12$	$12$	$387.690$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-12\)	\(-4\)	\(-12\)		$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.cw	$48552$	$2$	48552.a	1.a	$1$	$12$	$12$	$387.690$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(12\)	\(4\)	\(12\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.cx	$48552$	$2$	48552.a	1.a	$1$	$14$	$14$	$387.690$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-14\)	\(0\)	\(14\)		$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.cy	$48552$	$2$	48552.a	1.a	$1$	$14$	$14$	$387.690$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-14\)	\(0\)	\(14\)		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
48552.2.a.cz	$48552$	$2$	48552.a	1.a	$1$	$14$	$14$	$387.690$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(14\)	\(0\)	\(-14\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
48552.2.a.da	$48552$	$2$	48552.a	1.a	$1$	$14$	$14$	$387.690$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(14\)	\(0\)	\(-14\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.db	$48552$	$2$	48552.a	1.a	$1$	$18$	$18$	$387.690$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(-18\)	\(-6\)	\(-18\)		$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
48552.2.a.dc	$48552$	$2$	48552.a	1.a	$1$	$18$	$18$	$387.690$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-18\)	\(-6\)	\(18\)		$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
48552.2.a.dd	$48552$	$2$	48552.a	1.a	$1$	$18$	$18$	$387.690$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-18\)	\(0\)	\(-18\)		$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
48552.2.a.de	$48552$	$2$	48552.a	1.a	$1$	$18$	$18$	$387.690$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(-18\)	\(0\)	\(-18\)		$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.df	$48552$	$2$	48552.a	1.a	$1$	$18$	$18$	$387.690$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-18\)	\(0\)	\(18\)		$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
48552.2.a.dg	$48552$	$2$	48552.a	1.a	$1$	$18$	$18$	$387.690$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(-18\)	\(0\)	\(18\)		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
48552.2.a.dh	$48552$	$2$	48552.a	1.a	$1$	$18$	$18$	$387.690$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-18\)	\(6\)	\(-18\)		$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
48552.2.a.di	$48552$	$2$	48552.a	1.a	$1$	$18$	$18$	$387.690$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(-18\)	\(6\)	\(18\)		$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.dj	$48552$	$2$	48552.a	1.a	$1$	$18$	$18$	$387.690$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(18\)	\(-6\)	\(-18\)		$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
48552.2.a.dk	$48552$	$2$	48552.a	1.a	$1$	$18$	$18$	$387.690$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(18\)	\(-6\)	\(18\)		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
48552.2.a.dl	$48552$	$2$	48552.a	1.a	$1$	$18$	$18$	$387.690$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(18\)	\(0\)	\(-18\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
48552.2.a.dm	$48552$	$2$	48552.a	1.a	$1$	$18$	$18$	$387.690$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(18\)	\(0\)	\(-18\)		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
48552.2.a.dn	$48552$	$2$	48552.a	1.a	$1$	$18$	$18$	$387.690$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(18\)	\(0\)	\(18\)		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
48552.2.a.do	$48552$	$2$	48552.a	1.a	$1$	$18$	$18$	$387.690$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(18\)	\(0\)	\(18\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.dp	$48552$	$2$	48552.a	1.a	$1$	$18$	$18$	$387.690$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(18\)	\(6\)	\(-18\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
48552.2.a.dq	$48552$	$2$	48552.a	1.a	$1$	$18$	$18$	$387.690$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(18\)	\(6\)	\(18\)		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
48552.2.a.dr	$48552$	$2$	48552.a	1.a	$1$	$24$	$24$	$387.690$		None	✓	?	✓			$-1$		\(0\)	\(-24\)	\(0\)	\(24\)		$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
48552.2.a.ds	$48552$	$2$	48552.a	1.a	$1$	$24$	$24$	$387.690$		None	✓	?	✓			$-1$		\(0\)	\(24\)	\(0\)	\(-24\)		$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
48552.2.a.dt	$48552$	$2$	48552.a	1.a	$1$	$28$	$28$	$387.690$		None	✓	?	✓			$-1$		\(0\)	\(-28\)	\(0\)	\(28\)		$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
48552.2.a.du	$48552$	$2$	48552.a	1.a	$1$	$28$	$28$	$387.690$		None	✓	?	✓			$-1$		\(0\)	\(-28\)	\(8\)	\(-28\)		$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
48552.2.a.dv	$48552$	$2$	48552.a	1.a	$1$	$28$	$28$	$387.690$		None	✓	?	✓			$-1$		\(0\)	\(28\)	\(-8\)	\(28\)		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
48552.2.a.dw	$48552$	$2$	48552.a	1.a	$1$	$28$	$28$	$387.690$		None	✓	?	✓			$-1$		\(0\)	\(28\)	\(0\)	\(-28\)		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
48552.2.a.dx	$48552$	$2$	48552.a	1.a	$1$	$32$	$32$	$387.690$		None	✓	?	✓			$-1$		\(0\)	\(-32\)	\(-8\)	\(-32\)		$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
48552.2.a.dy	$48552$	$2$	48552.a	1.a	$1$	$32$	$32$	$387.690$		None	✓	?	✓			$-1$		\(0\)	\(32\)	\(8\)	\(32\)		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(48552))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(48552)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(204))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(357))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(408))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(476))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(578))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(714))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(867))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(952))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1156))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1428))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1734))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2023))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2856))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3468))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4046))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(6069))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(6936))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(8092))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(12138))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(16184))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24276))\)\(^{\oplus 2}\)