Space of modular forms of level 13552, weight 2, and trivial character

• Label: 13552.2.a
• Level: $13552$
• Weight: $2$
• Character orbit: 13552.a
• Rep. character: $\chi_{13552}(1,\cdot)$
• Character field: $\Q$
• Dimension: $327$
• Newform subspaces: $106$
• Sturm bound: $4224$

Defining parameters

Level:	\( N \)	\(=\)	\( 13552 = 2^{4} \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	13552.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 106 \)
Sturm bound:			\(4224\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(13552))\).

	Total	New	Old
Modular forms	2184	327	1857
Cusp forms	2041	327	1714
Eisenstein series	143	0	143

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

\(2\)	\(7\)	\(11\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(264\)	\(42\)	\(222\)		\(247\)	\(42\)	\(205\)		\(17\)	\(0\)	\(17\)
\(+\)	\(+\)	\(-\)	\(-\)		\(279\)	\(40\)	\(239\)		\(261\)	\(40\)	\(221\)		\(18\)	\(0\)	\(18\)
\(+\)	\(-\)	\(+\)	\(-\)		\(282\)	\(42\)	\(240\)		\(264\)	\(42\)	\(222\)		\(18\)	\(0\)	\(18\)
\(+\)	\(-\)	\(-\)	\(+\)		\(267\)	\(40\)	\(227\)		\(249\)	\(40\)	\(209\)		\(18\)	\(0\)	\(18\)
\(-\)	\(+\)	\(+\)	\(-\)		\(270\)	\(41\)	\(229\)		\(252\)	\(41\)	\(211\)		\(18\)	\(0\)	\(18\)
\(-\)	\(+\)	\(-\)	\(+\)		\(275\)	\(40\)	\(235\)		\(257\)	\(40\)	\(217\)		\(18\)	\(0\)	\(18\)
\(-\)	\(-\)	\(+\)	\(+\)		\(276\)	\(37\)	\(239\)		\(258\)	\(37\)	\(221\)		\(18\)	\(0\)	\(18\)
\(-\)	\(-\)	\(-\)	\(-\)		\(271\)	\(45\)	\(226\)		\(253\)	\(45\)	\(208\)		\(18\)	\(0\)	\(18\)
Plus space			\(+\)		\(1082\)	\(159\)	\(923\)		\(1011\)	\(159\)	\(852\)		\(71\)	\(0\)	\(71\)
Minus space			\(-\)		\(1102\)	\(168\)	\(934\)		\(1030\)	\(168\)	\(862\)		\(72\)	\(0\)	\(72\)

Trace form

327 * q - 2 * q^5 + q^7 + 331 * q^9 - 2 * q^13 - 16 * q^15 + 6 * q^17 - 8 * q^19 - 4 * q^23 + 329 * q^25 - 24 * q^27 - 6 * q^29 - 8 * q^31 - 6 * q^35 - 14 * q^37 - 16 * q^39 - 2 * q^41 + 12 * q^43 - 10 * q^45 - 24 * q^47 + 327 * q^49 - 32 * q^51 - 6 * q^53 - 8 * q^57 - 24 * q^59 + 6 * q^61 + 5 * q^63 + 4 * q^65 - 8 * q^67 + 16 * q^69 - 12 * q^71 + 22 * q^73 - 24 * q^75 + 327 * q^81 + 32 * q^83 + 12 * q^85 - 64 * q^87 + 22 * q^89 + 6 * q^91 + 32 * q^93 + 48 * q^95 + 22 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(13552))\) 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	7	11
13552.2.a.a	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-3\)	\(2\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+2q^{5}-q^{7}+6q^{9}-5q^{13}+\cdots\)
13552.2.a.b	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-3\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+2q^{5}+q^{7}+6q^{9}+5q^{13}+\cdots\)
13552.2.a.c	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(-4\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-4q^{5}+q^{7}+q^{9}+8q^{15}+\cdots\)
13552.2.a.d	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(-2\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{5}-q^{7}+q^{9}-4q^{13}+\cdots\)
13552.2.a.e	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(2\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+2q^{5}-q^{7}+q^{9}+4q^{13}+\cdots\)
13552.2.a.f	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(2\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+2q^{5}+q^{7}+q^{9}-4q^{15}+\cdots\)
13552.2.a.g	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(1\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}-2q^{9}-q^{15}+8q^{19}+\cdots\)
13552.2.a.h	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}-2q^{9}-q^{15}-8q^{19}+\cdots\)
13552.2.a.i	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+q^{7}-2q^{9}+4q^{13}+\cdots\)
13552.2.a.j	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-q^{7}-3q^{9}-2q^{13}+4q^{17}+\cdots\)
13552.2.a.k	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}-3q^{9}-2q^{13}+2q^{17}+\cdots\)
13552.2.a.l	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-3q^{9}+q^{13}+q^{17}-4q^{23}+\cdots\)
13552.2.a.m	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-3q^{9}-q^{13}-q^{17}-4q^{23}+\cdots\)
13552.2.a.n	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-3q^{9}+6q^{13}-2q^{19}-4q^{23}+\cdots\)
13552.2.a.o	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{7}-3q^{9}-2q^{13}-2q^{17}+\cdots\)
13552.2.a.p	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{7}-3q^{9}-2q^{13}+6q^{17}+\cdots\)
13552.2.a.q	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(-1\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}-2q^{9}+4q^{13}-q^{15}+\cdots\)
13552.2.a.r	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(-1\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}-2q^{9}-q^{15}+2q^{17}+\cdots\)
13552.2.a.s	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(2\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-q^{7}-2q^{9}+7q^{13}+\cdots\)
13552.2.a.t	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{7}-2q^{9}-7q^{13}+\cdots\)
13552.2.a.u	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(-2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{5}-q^{7}+q^{9}-6q^{13}+\cdots\)
13552.2.a.v	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(-2\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{5}+q^{7}+q^{9}+6q^{13}+\cdots\)
13552.2.a.w	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{7}+q^{9}+4q^{13}-6q^{17}+\cdots\)
13552.2.a.x	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(2\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+2q^{5}+q^{7}+q^{9}-4q^{13}+\cdots\)
13552.2.a.y	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(3\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+3q^{5}-q^{7}+q^{9}-q^{13}+6q^{15}+\cdots\)
13552.2.a.z	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+3q^{5}+q^{7}+q^{9}+q^{13}+6q^{15}+\cdots\)
13552.2.a.ba	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(3\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-3q^{5}-q^{7}+6q^{9}-4q^{13}+\cdots\)
13552.2.a.bb	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(3\)	\(-3\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-3q^{5}+q^{7}+6q^{9}+4q^{13}+\cdots\)
13552.2.a.bc	$13552$	$2$	13552.a	1.a	$1$	$1$	$1$	$108.213$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(3\)	\(-1\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{5}-q^{7}+6q^{9}+4q^{13}+\cdots\)
13552.2.a.bd	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(-6\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
13552.2.a.be	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(-6\)	\(-1\)	\(2\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
13552.2.a.bf	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(-4\)	\(2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
13552.2.a.bg	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
13552.2.a.bh	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
13552.2.a.bi	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(2\)	\(-2\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
13552.2.a.bj	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(2\)	\(-2\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
13552.2.a.bk	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(2\)	\(2\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
13552.2.a.bl	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(2\)	\(2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
13552.2.a.bm	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(4\)	\(-2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
13552.2.a.bn	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(4\)	\(2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
13552.2.a.bo	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(-1\)	\(-4\)	\(-2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
13552.2.a.bp	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(-1\)	\(-4\)	\(2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
13552.2.a.bq	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-3\)	\(-2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
13552.2.a.br	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-3\)	\(2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
13552.2.a.bs	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
13552.2.a.bt	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
13552.2.a.bu	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{6}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(-2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
13552.2.a.bv	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(0\)	\(1\)	\(-3\)	\(-2\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
13552.2.a.bw	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
13552.2.a.bx	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
13552.2.a.by	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
13552.2.a.bz	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
13552.2.a.ca	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(1\)	\(2\)	\(-2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
13552.2.a.cb	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(1\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
13552.2.a.cc	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(1\)	\(4\)	\(-2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
13552.2.a.cd	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(1\)	\(4\)	\(2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
13552.2.a.ce	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(-3\)	\(-2\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
13552.2.a.cf	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(-3\)	\(2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
13552.2.a.cg	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
13552.2.a.ch	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(-2\)	\(2\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
13552.2.a.ci	$13552$	$2$	13552.a	1.a	$1$	$2$	$2$	$108.213$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
13552.2.a.cj	$13552$	$2$	13552.a	1.a	$1$	$3$	$3$	$108.213$	3.3.2024.1	None	✓	?				$-1$		\(0\)	\(-2\)	\(-1\)	\(-3\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
13552.2.a.ck	$13552$	$2$	13552.a	1.a	$1$	$3$	$3$	$108.213$	3.3.2024.1	None	✓	?				$-1$		\(0\)	\(-2\)	\(-1\)	\(3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
13552.2.a.cl	$13552$	$2$	13552.a	1.a	$1$	$3$	$3$	$108.213$	3.3.229.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(1\)	\(3\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
13552.2.a.cm	$13552$	$2$	13552.a	1.a	$1$	$3$	$3$	$108.213$	3.3.316.1	None	✓	?				$-1$		\(0\)	\(1\)	\(-3\)	\(-3\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
13552.2.a.cn	$13552$	$2$	13552.a	1.a	$1$	$3$	$3$	$108.213$	3.3.1509.1	None	✓	?				$-1$		\(0\)	\(1\)	\(-3\)	\(-3\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
13552.2.a.co	$13552$	$2$	13552.a	1.a	$1$	$3$	$3$	$108.213$	3.3.3021.1	None	✓	?				$-1$		\(0\)	\(1\)	\(-3\)	\(-3\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
13552.2.a.cp	$13552$	$2$	13552.a	1.a	$1$	$3$	$3$	$108.213$	3.3.316.1	None	✓	?				$-1$		\(0\)	\(1\)	\(-3\)	\(3\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
13552.2.a.cq	$13552$	$2$	13552.a	1.a	$1$	$3$	$3$	$108.213$	3.3.1509.1	None	✓	?				$-1$		\(0\)	\(1\)	\(-3\)	\(3\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
13552.2.a.cr	$13552$	$2$	13552.a	1.a	$1$	$3$	$3$	$108.213$	3.3.3021.1	None	✓	?				$-1$		\(0\)	\(1\)	\(-3\)	\(3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
13552.2.a.cs	$13552$	$2$	13552.a	1.a	$1$	$3$	$3$	$108.213$	3.3.1016.1	None	✓	?				$-1$		\(0\)	\(1\)	\(-1\)	\(3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
13552.2.a.ct	$13552$	$2$	13552.a	1.a	$1$	$3$	$3$	$108.213$	3.3.568.1	None	✓	?				$-1$		\(0\)	\(1\)	\(1\)	\(-3\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
13552.2.a.cu	$13552$	$2$	13552.a	1.a	$1$	$3$	$3$	$108.213$	3.3.568.1	None	✓	?				$-1$		\(0\)	\(1\)	\(1\)	\(3\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
13552.2.a.cv	$13552$	$2$	13552.a	1.a	$1$	$4$	$4$	$108.213$	4.4.37525.1	None	✓	?				$-1$		\(0\)	\(-6\)	\(2\)	\(-4\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
13552.2.a.cw	$13552$	$2$	13552.a	1.a	$1$	$4$	$4$	$108.213$	4.4.37525.1	None	✓	?				$-1$		\(0\)	\(-6\)	\(2\)	\(4\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
13552.2.a.cx	$13552$	$2$	13552.a	1.a	$1$	$4$	$4$	$108.213$	4.4.13824.1	None	✓	?				$-1$		\(0\)	\(-4\)	\(4\)	\(-4\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
13552.2.a.cy	$13552$	$2$	13552.a	1.a	$1$	$4$	$4$	$108.213$	4.4.13824.1	None	✓	?				$-1$		\(0\)	\(-4\)	\(4\)	\(4\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
13552.2.a.cz	$13552$	$2$	13552.a	1.a	$1$	$4$	$4$	$108.213$	4.4.31288.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(2\)	\(-4\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
13552.2.a.da	$13552$	$2$	13552.a	1.a	$1$	$4$	$4$	$108.213$	4.4.31288.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(2\)	\(4\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
13552.2.a.db	$13552$	$2$	13552.a	1.a	$1$	$4$	$4$	$108.213$	4.4.11348.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(5\)	\(-4\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
13552.2.a.dc	$13552$	$2$	13552.a	1.a	$1$	$4$	$4$	$108.213$	4.4.2525.1	None	✓	?				$-1$		\(0\)	\(2\)	\(-6\)	\(-4\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
13552.2.a.dd	$13552$	$2$	13552.a	1.a	$1$	$4$	$4$	$108.213$	4.4.2525.1	None	✓	?				$-1$		\(0\)	\(2\)	\(-6\)	\(4\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
13552.2.a.de	$13552$	$2$	13552.a	1.a	$1$	$4$	$4$	$108.213$	4.4.4752.1	None	✓	?				$-1$		\(0\)	\(2\)	\(-2\)	\(-4\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
13552.2.a.df	$13552$	$2$	13552.a	1.a	$1$	$4$	$4$	$108.213$	4.4.4752.1	None	✓	?				$-1$		\(0\)	\(2\)	\(-2\)	\(4\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
13552.2.a.dg	$13552$	$2$	13552.a	1.a	$1$	$4$	$4$	$108.213$	4.4.7625.1	None	✓	?				$-1$		\(0\)	\(3\)	\(-5\)	\(-4\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
13552.2.a.dh	$13552$	$2$	13552.a	1.a	$1$	$4$	$4$	$108.213$	4.4.7625.1	None	✓	?				$-1$		\(0\)	\(3\)	\(-5\)	\(4\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
13552.2.a.di	$13552$	$2$	13552.a	1.a	$1$	$5$	$5$	$108.213$	5.5.3769928.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(-1\)	\(-5\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
13552.2.a.dj	$13552$	$2$	13552.a	1.a	$1$	$5$	$5$	$108.213$	5.5.3769928.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(-1\)	\(5\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
13552.2.a.dk	$13552$	$2$	13552.a	1.a	$1$	$6$	$6$	$108.213$	6.6.7674048.1	None	✓	?				$-1$		\(0\)	\(2\)	\(-4\)	\(-6\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
13552.2.a.dl	$13552$	$2$	13552.a	1.a	$1$	$6$	$6$	$108.213$	6.6.7674048.1	None	✓	?	✓			$-1$		\(0\)	\(2\)	\(-4\)	\(6\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
13552.2.a.dm	$13552$	$2$	13552.a	1.a	$1$	$6$	$6$	$108.213$	6.6.3162625.1	None	✓	?				$-1$		\(0\)	\(2\)	\(-2\)	\(-6\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
13552.2.a.dn	$13552$	$2$	13552.a	1.a	$1$	$6$	$6$	$108.213$	6.6.3162625.1	None	✓	?				$-1$		\(0\)	\(2\)	\(-2\)	\(6\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
13552.2.a.do	$13552$	$2$	13552.a	1.a	$1$	$6$	$6$	$108.213$	6.6.51592896.1	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(-6\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
13552.2.a.dp	$13552$	$2$	13552.a	1.a	$1$	$6$	$6$	$108.213$	6.6.51592896.1	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(6\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
13552.2.a.dq	$13552$	$2$	13552.a	1.a	$1$	$6$	$6$	$108.213$	6.6.988075625.1	None	✓	?				$-1$		\(0\)	\(3\)	\(-2\)	\(-6\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
13552.2.a.dr	$13552$	$2$	13552.a	1.a	$1$	$6$	$6$	$108.213$	6.6.988075625.1	None	✓	?				$-1$		\(0\)	\(3\)	\(-2\)	\(6\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
13552.2.a.ds	$13552$	$2$	13552.a	1.a	$1$	$8$	$8$	$108.213$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(-4\)	\(10\)	\(-8\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
13552.2.a.dt	$13552$	$2$	13552.a	1.a	$1$	$8$	$8$	$108.213$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(-4\)	\(10\)	\(8\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
13552.2.a.du	$13552$	$2$	13552.a	1.a	$1$	$8$	$8$	$108.213$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(-7\)	\(-8\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
13552.2.a.dv	$13552$	$2$	13552.a	1.a	$1$	$8$	$8$	$108.213$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(-2\)	\(-7\)	\(8\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
13552.2.a.dw	$13552$	$2$	13552.a	1.a	$1$	$8$	$8$	$108.213$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(2\)	\(7\)	\(-8\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
13552.2.a.dx	$13552$	$2$	13552.a	1.a	$1$	$8$	$8$	$108.213$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(2\)	\(7\)	\(8\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
13552.2.a.dy	$13552$	$2$	13552.a	1.a	$1$	$10$	$10$	$108.213$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(-2\)	\(4\)	\(-10\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
13552.2.a.dz	$13552$	$2$	13552.a	1.a	$1$	$10$	$10$	$108.213$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(4\)	\(10\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
13552.2.a.ea	$13552$	$2$	13552.a	1.a	$1$	$10$	$10$	$108.213$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(3\)	\(5\)	\(-10\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
13552.2.a.eb	$13552$	$2$	13552.a	1.a	$1$	$10$	$10$	$108.213$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(3\)	\(5\)	\(10\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(13552))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(13552)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(308))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(484))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(616))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(847))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(968))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1232))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1694))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1936))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3388))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(6776))\)\(^{\oplus 2}\)