Space of modular forms of level 20070, weight 2, and trivial character

• Label: 20070.2.a
• Level: $20070$
• Weight: $2$
• Character orbit: 20070.a
• Rep. character: $\chi_{20070}(1,\cdot)$
• Character field: $\Q$
• Dimension: $370$
• Newform subspaces: $83$
• Sturm bound: $8064$

Defining parameters

Level:	\( N \)	\(=\)	\( 20070 = 2 \cdot 3^{2} \cdot 5 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	20070.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 83 \)
Sturm bound:			\(8064\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(20070))\).

	Total	New	Old
Modular forms	4048	370	3678
Cusp forms	4017	370	3647
Eisenstein series	31	0	31

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

\(2\)	\(3\)	\(5\)	\(223\)	Fricke		Total				Cusp				Eisenstein
						All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)		\(234\)	\(16\)	\(218\)		\(233\)	\(16\)	\(217\)		\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)		\(270\)	\(21\)	\(249\)		\(268\)	\(21\)	\(247\)		\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)		\(256\)	\(21\)	\(235\)		\(254\)	\(21\)	\(233\)		\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)		\(252\)	\(16\)	\(236\)		\(250\)	\(16\)	\(234\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)		\(256\)	\(28\)	\(228\)		\(254\)	\(28\)	\(226\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)		\(251\)	\(28\)	\(223\)		\(249\)	\(28\)	\(221\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)		\(250\)	\(28\)	\(222\)		\(248\)	\(28\)	\(220\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)		\(255\)	\(28\)	\(227\)		\(253\)	\(28\)	\(225\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)		\(256\)	\(21\)	\(235\)		\(254\)	\(21\)	\(233\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)		\(250\)	\(16\)	\(234\)		\(248\)	\(16\)	\(232\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)		\(266\)	\(16\)	\(250\)		\(264\)	\(16\)	\(248\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)		\(240\)	\(21\)	\(219\)		\(238\)	\(21\)	\(217\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)		\(250\)	\(25\)	\(225\)		\(248\)	\(25\)	\(223\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)		\(255\)	\(30\)	\(225\)		\(253\)	\(30\)	\(223\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)		\(256\)	\(30\)	\(226\)		\(254\)	\(30\)	\(224\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)		\(251\)	\(25\)	\(226\)		\(249\)	\(25\)	\(224\)		\(2\)	\(0\)	\(2\)
Plus space				\(+\)		\(2004\)	\(170\)	\(1834\)		\(1989\)	\(170\)	\(1819\)		\(15\)	\(0\)	\(15\)
Minus space				\(-\)		\(2044\)	\(200\)	\(1844\)		\(2028\)	\(200\)	\(1828\)		\(16\)	\(0\)	\(16\)

Trace form

370 * q - 2 * q^2 + 370 * q^4 - 2 * q^8 + 4 * q^11 + 8 * q^13 + 370 * q^16 - 4 * q^17 + 12 * q^19 + 12 * q^22 - 16 * q^23 + 370 * q^25 - 16 * q^26 + 8 * q^29 + 8 * q^31 - 2 * q^32 - 12 * q^34 + 8 * q^35 - 12 * q^37 - 8 * q^38 - 4 * q^41 + 16 * q^43 + 4 * q^44 - 16 * q^47 + 362 * q^49 - 2 * q^50 + 8 * q^52 - 44 * q^53 - 8 * q^55 - 12 * q^58 - 20 * q^59 - 24 * q^62 + 370 * q^64 - 8 * q^65 + 28 * q^67 - 4 * q^68 - 32 * q^71 + 52 * q^73 - 16 * q^74 + 12 * q^76 - 40 * q^77 - 16 * q^79 + 4 * q^82 + 8 * q^83 + 8 * q^85 + 20 * q^86 + 12 * q^88 - 36 * q^89 + 56 * q^91 - 16 * q^92 - 16 * q^94 + 16 * q^95 + 4 * q^97 - 34 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(20070))\) 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	5	223
20070.2.a.a	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-1\)	\(-5\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-5q^{7}-q^{8}+q^{10}+\cdots\)
20070.2.a.b	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-1\)	\(-3\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-3q^{7}-q^{8}+q^{10}+\cdots\)
20070.2.a.c	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-1\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots\)
20070.2.a.d	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
20070.2.a.e	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-q^{11}+\cdots\)
20070.2.a.f	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+5q^{11}+\cdots\)
20070.2.a.g	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-1\)	\(1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
20070.2.a.h	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-1\)	\(1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
20070.2.a.i	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-1\)	\(1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
20070.2.a.j	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-1\)	\(4\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+4q^{7}-q^{8}+q^{10}+\cdots\)
20070.2.a.k	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(1\)	\(-4\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots\)
20070.2.a.l	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(1\)	\(-4\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots\)
20070.2.a.m	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(1\)	\(-3\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-3q^{7}-q^{8}-q^{10}+\cdots\)
20070.2.a.n	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
20070.2.a.o	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
20070.2.a.p	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(1\)	\(-1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
20070.2.a.q	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(1\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
20070.2.a.r	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(1\)	\(3\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+3q^{7}-q^{8}-q^{10}+\cdots\)
20070.2.a.s	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(1\)	\(4\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+4q^{7}-q^{8}-q^{10}+\cdots\)
20070.2.a.t	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(1\)	\(4\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+4q^{7}-q^{8}-q^{10}+\cdots\)
20070.2.a.u	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-1\)	\(-3\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-3q^{7}+q^{8}-q^{10}+\cdots\)
20070.2.a.v	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-1\)	\(-3\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-3q^{7}+q^{8}-q^{10}+\cdots\)
20070.2.a.w	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
20070.2.a.x	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
20070.2.a.y	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-1\)	\(3\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+3q^{7}+q^{8}-q^{10}+\cdots\)
20070.2.a.z	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-1\)	\(3\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+3q^{7}+q^{8}-q^{10}+\cdots\)
20070.2.a.ba	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-1\)	\(4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+4q^{7}+q^{8}-q^{10}+\cdots\)
20070.2.a.bb	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(1\)	\(-3\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}-3q^{7}+q^{8}+q^{10}+\cdots\)
20070.2.a.bc	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
20070.2.a.bd	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(1\)	\(-1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
20070.2.a.be	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-4q^{11}+\cdots\)
20070.2.a.bf	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+q^{11}+\cdots\)
20070.2.a.bg	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(1\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
20070.2.a.bh	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(1\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
20070.2.a.bi	$20070$	$2$	20070.a	1.a	$1$	$1$	$1$	$160.260$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
20070.2.a.bj	$20070$	$2$	20070.a	1.a	$1$	$2$	$2$	$160.260$	\(\Q(\sqrt{37}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(-2\)	\(-4\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
20070.2.a.bk	$20070$	$2$	20070.a	1.a	$1$	$2$	$2$	$160.260$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(-2\)	\(-2\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
20070.2.a.bl	$20070$	$2$	20070.a	1.a	$1$	$2$	$2$	$160.260$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
20070.2.a.bm	$20070$	$2$	20070.a	1.a	$1$	$2$	$2$	$160.260$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
20070.2.a.bn	$20070$	$2$	20070.a	1.a	$1$	$2$	$2$	$160.260$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
20070.2.a.bo	$20070$	$2$	20070.a	1.a	$1$	$2$	$2$	$160.260$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
20070.2.a.bp	$20070$	$2$	20070.a	1.a	$1$	$2$	$2$	$160.260$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
20070.2.a.bq	$20070$	$2$	20070.a	1.a	$1$	$2$	$2$	$160.260$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
20070.2.a.br	$20070$	$2$	20070.a	1.a	$1$	$2$	$2$	$160.260$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(2\)	\(-1\)		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
20070.2.a.bs	$20070$	$2$	20070.a	1.a	$1$	$2$	$2$	$160.260$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
20070.2.a.bt	$20070$	$2$	20070.a	1.a	$1$	$2$	$2$	$160.260$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
20070.2.a.bu	$20070$	$2$	20070.a	1.a	$1$	$3$	$3$	$160.260$	3.3.1509.1	None	✓	?				$-1$		\(-3\)	\(0\)	\(3\)	\(4\)		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
20070.2.a.bv	$20070$	$2$	20070.a	1.a	$1$	$3$	$3$	$160.260$	3.3.316.1	None	✓	?				$-1$		\(3\)	\(0\)	\(3\)	\(-1\)		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
20070.2.a.bw	$20070$	$2$	20070.a	1.a	$1$	$4$	$4$	$160.260$	4.4.84677.1	None	✓	?				$-1$		\(-4\)	\(0\)	\(-4\)	\(-6\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
20070.2.a.bx	$20070$	$2$	20070.a	1.a	$1$	$4$	$4$	$160.260$	4.4.725.1	None	✓	?				$-1$		\(-4\)	\(0\)	\(-4\)	\(-5\)		$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
20070.2.a.by	$20070$	$2$	20070.a	1.a	$1$	$4$	$4$	$160.260$	4.4.2225.1	None	✓	?				$-1$		\(-4\)	\(0\)	\(4\)	\(-4\)		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
20070.2.a.bz	$20070$	$2$	20070.a	1.a	$1$	$4$	$4$	$160.260$	\(\Q(\zeta_{20})^+\)	None	✓	?				$-1$		\(4\)	\(0\)	\(-4\)	\(-6\)		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
20070.2.a.ca	$20070$	$2$	20070.a	1.a	$1$	$4$	$4$	$160.260$	4.4.48389.1	None	✓	?				$-1$		\(4\)	\(0\)	\(4\)	\(5\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
20070.2.a.cb	$20070$	$2$	20070.a	1.a	$1$	$5$	$5$	$160.260$	5.5.2817605.1	None	✓	?				$-1$		\(-5\)	\(0\)	\(5\)	\(0\)		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
20070.2.a.cc	$20070$	$2$	20070.a	1.a	$1$	$5$	$5$	$160.260$	5.5.8693777.1	None	✓	?				$-1$		\(5\)	\(0\)	\(-5\)	\(3\)		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
20070.2.a.cd	$20070$	$2$	20070.a	1.a	$1$	$5$	$5$	$160.260$	5.5.504568.1	None	✓	?				$-1$		\(5\)	\(0\)	\(-5\)	\(5\)		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
20070.2.a.ce	$20070$	$2$	20070.a	1.a	$1$	$5$	$5$	$160.260$	5.5.81589.1	None	✓	?				$-1$		\(5\)	\(0\)	\(5\)	\(0\)		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
20070.2.a.cf	$20070$	$2$	20070.a	1.a	$1$	$5$	$5$	$160.260$	5.5.1052869.1	None	✓	?				$-1$		\(5\)	\(0\)	\(5\)	\(8\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
20070.2.a.cg	$20070$	$2$	20070.a	1.a	$1$	$6$	$6$	$160.260$	6.6.6848593.1	None	✓	?				$-1$		\(-6\)	\(0\)	\(-6\)	\(-1\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
20070.2.a.ch	$20070$	$2$	20070.a	1.a	$1$	$6$	$6$	$160.260$	6.6.5224841.1	None	✓	?				$-1$		\(-6\)	\(0\)	\(6\)	\(-5\)		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
20070.2.a.ci	$20070$	$2$	20070.a	1.a	$1$	$6$	$6$	$160.260$	6.6.5173625.1	None	✓	?				$-1$		\(-6\)	\(0\)	\(6\)	\(5\)		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
20070.2.a.cj	$20070$	$2$	20070.a	1.a	$1$	$6$	$6$	$160.260$	6.6.11623961.1	None	✓	?				$-1$		\(6\)	\(0\)	\(-6\)	\(-6\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
20070.2.a.ck	$20070$	$2$	20070.a	1.a	$1$	$6$	$6$	$160.260$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	?				$-1$		\(6\)	\(0\)	\(-6\)	\(3\)		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
20070.2.a.cl	$20070$	$2$	20070.a	1.a	$1$	$6$	$6$	$160.260$	6.6.67955408.1	None	✓	?				$-1$		\(6\)	\(0\)	\(6\)	\(-6\)		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
20070.2.a.cm	$20070$	$2$	20070.a	1.a	$1$	$7$	$7$	$160.260$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?				$-1$		\(7\)	\(0\)	\(-7\)	\(3\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
20070.2.a.cn	$20070$	$2$	20070.a	1.a	$1$	$7$	$7$	$160.260$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?				$-1$		\(7\)	\(0\)	\(7\)	\(9\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
20070.2.a.co	$20070$	$2$	20070.a	1.a	$1$	$8$	$8$	$160.260$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?	✓			$-1$		\(-8\)	\(0\)	\(-8\)	\(-6\)		$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
20070.2.a.cp	$20070$	$2$	20070.a	1.a	$1$	$8$	$8$	$160.260$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?	✓			$-1$		\(8\)	\(0\)	\(-8\)	\(0\)		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
20070.2.a.cq	$20070$	$2$	20070.a	1.a	$1$	$8$	$8$	$160.260$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?	✓			$-1$		\(8\)	\(0\)	\(8\)	\(-8\)		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
20070.2.a.cr	$20070$	$2$	20070.a	1.a	$1$	$8$	$8$	$160.260$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?	✓			$-1$		\(8\)	\(0\)	\(8\)	\(-6\)		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
20070.2.a.cs	$20070$	$2$	20070.a	1.a	$1$	$9$	$9$	$160.260$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?	✓			$-1$		\(-9\)	\(0\)	\(-9\)	\(8\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
20070.2.a.ct	$20070$	$2$	20070.a	1.a	$1$	$9$	$9$	$160.260$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?	✓			$-1$		\(9\)	\(0\)	\(-9\)	\(-7\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
20070.2.a.cu	$20070$	$2$	20070.a	1.a	$1$	$10$	$10$	$160.260$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?	✓			$-1$		\(-10\)	\(0\)	\(10\)	\(-2\)		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
20070.2.a.cv	$20070$	$2$	20070.a	1.a	$1$	$10$	$10$	$160.260$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?	✓			$-1$		\(10\)	\(0\)	\(10\)	\(-2\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
20070.2.a.cw	$20070$	$2$	20070.a	1.a	$1$	$11$	$11$	$160.260$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	?				$-1$		\(-11\)	\(0\)	\(-11\)	\(7\)		$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
20070.2.a.cx	$20070$	$2$	20070.a	1.a	$1$	$12$	$12$	$160.260$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?	✓			$-1$		\(-12\)	\(0\)	\(12\)	\(11\)		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
20070.2.a.cy	$20070$	$2$	20070.a	1.a	$1$	$13$	$13$	$160.260$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	?	✓			$-1$		\(-13\)	\(0\)	\(-13\)	\(3\)		$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
20070.2.a.cz	$20070$	$2$	20070.a	1.a	$1$	$15$	$15$	$160.260$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	?	✓			$-1$		\(-15\)	\(0\)	\(15\)	\(-7\)		$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
20070.2.a.da	$20070$	$2$	20070.a	1.a	$1$	$15$	$15$	$160.260$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	?	✓			$-1$		\(15\)	\(0\)	\(-15\)	\(-7\)		$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
20070.2.a.db	$20070$	$2$	20070.a	1.a	$1$	$18$	$18$	$160.260$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?	✓			$-1$		\(-18\)	\(0\)	\(18\)	\(6\)		$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
20070.2.a.dc	$20070$	$2$	20070.a	1.a	$1$	$18$	$18$	$160.260$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?	✓			$-1$		\(18\)	\(0\)	\(-18\)	\(6\)		$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
20070.2.a.dd	$20070$	$2$	20070.a	1.a	$1$	$20$	$20$	$160.260$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	?	✓			$-1$		\(-20\)	\(0\)	\(-20\)	\(9\)		$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
20070.2.a.de	$20070$	$2$	20070.a	1.a	$1$	$20$	$20$	$160.260$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	?	✓			$-1$		\(20\)	\(0\)	\(20\)	\(9\)		$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(20070))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(20070)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(223))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(446))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(669))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1115))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2007))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2230))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3345))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4014))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(6690))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(10035))\)\(^{\oplus 2}\)