LMFDB - Space of modular forms of level 45486, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 45486 = 2 \cdot 3^{2} \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	45486.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 187 $
Sturm bound:			$18240$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(45486))$.

	Total	New	Old
Modular forms	9280	852	8428
Cusp forms	8961	852	8109
Eisenstein series	319	0	319

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

$2$	$3$	$7$	$19$	Fricke	Total			Cusp			Eisenstein
$2$	$3$	$7$	$19$	Fricke	All	New	Old	All	New	Old	All	New	Old
$+$	$+$	$+$	$+$	$+$	$560$	$40$	$520$	$541$	$40$	$501$	$19$	$0$	$19$
$+$	$+$	$+$	$-$	$-$	$598$	$45$	$553$	$578$	$45$	$533$	$20$	$0$	$20$
$+$	$+$	$-$	$+$	$-$	$600$	$40$	$560$	$580$	$40$	$540$	$20$	$0$	$20$
$+$	$+$	$-$	$-$	$+$	$562$	$45$	$517$	$542$	$45$	$497$	$20$	$0$	$20$
$+$	$-$	$+$	$+$	$-$	$590$	$67$	$523$	$570$	$67$	$503$	$20$	$0$	$20$
$+$	$-$	$+$	$-$	$+$	$570$	$61$	$509$	$550$	$61$	$489$	$20$	$0$	$20$
$+$	$-$	$-$	$+$	$+$	$570$	$59$	$511$	$550$	$59$	$491$	$20$	$0$	$20$
$+$	$-$	$-$	$-$	$-$	$590$	$70$	$520$	$570$	$70$	$500$	$20$	$0$	$20$
$-$	$+$	$+$	$+$	$-$	$580$	$40$	$540$	$560$	$40$	$520$	$20$	$0$	$20$
$-$	$+$	$+$	$-$	$+$	$582$	$45$	$537$	$562$	$45$	$517$	$20$	$0$	$20$
$-$	$+$	$-$	$+$	$+$	$580$	$40$	$540$	$560$	$40$	$520$	$20$	$0$	$20$
$-$	$+$	$-$	$-$	$-$	$578$	$45$	$533$	$558$	$45$	$513$	$20$	$0$	$20$
$-$	$-$	$+$	$+$	$+$	$590$	$63$	$527$	$570$	$63$	$507$	$20$	$0$	$20$
$-$	$-$	$+$	$-$	$-$	$570$	$65$	$505$	$550$	$65$	$485$	$20$	$0$	$20$
$-$	$-$	$-$	$+$	$-$	$570$	$71$	$499$	$550$	$71$	$479$	$20$	$0$	$20$
$-$	$-$	$-$	$-$	$+$	$590$	$56$	$534$	$570$	$56$	$514$	$20$	$0$	$20$
Plus space				$+$	$4604$	$409$	$4195$	$4445$	$409$	$4036$	$159$	$0$	$159$
Minus space				$-$	$4676$	$443$	$4233$	$4516$	$443$	$4073$	$160$	$0$	$160$

Trace form

$ 852 q - 2 q^{2} + 852 q^{4} + 2 q^{5} - 2 q^{8} - 2 q^{10} - 14 q^{13} - 2 q^{14} + 852 q^{16} - 4 q^{17} + 2 q^{20} + 4 q^{22} + 8 q^{23} + 828 q^{25} - 2 q^{26} - 12 q^{29} + 4 q^{31} - 2 q^{32} + 8 q^{34}+ \cdots - 2 q^{98}+O(q^{100}) $

852 * q - 2 * q^2 + 852 * q^4 + 2 * q^5 - 2 * q^8 - 2 * q^10 - 14 * q^13 - 2 * q^14 + 852 * q^16 - 4 * q^17 + 2 * q^20 + 4 * q^22 + 8 * q^23 + 828 * q^25 - 2 * q^26 - 12 * q^29 + 4 * q^31 - 2 * q^32 + 8 * q^34 + 6 * q^35 - 4 * q^37 - 2 * q^40 - 28 * q^41 + 8 * q^43 + 16 * q^46 - 20 * q^47 + 852 * q^49 - 10 * q^50 - 14 * q^52 - 16 * q^55 - 2 * q^56 - 4 * q^58 - 26 * q^59 - 34 * q^61 - 4 * q^62 + 852 * q^64 - 28 * q^65 - 16 * q^67 - 4 * q^68 - 2 * q^70 + 32 * q^71 + 48 * q^73 - 12 * q^74 + 12 * q^77 + 8 * q^79 + 2 * q^80 - 16 * q^82 + 6 * q^83 - 28 * q^85 - 12 * q^86 + 4 * q^88 + 24 * q^89 - 6 * q^91 + 8 * q^92 - 4 * q^94 - 12 * q^97 - 2 * q^98

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(45486))$ 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
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	7	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
45486.2.a.a	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-4$	$1$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{5}+q^{7}-q^{8}+4q^{10}+\cdots$
45486.2.a.b	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-3$	$1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{10}+\cdots$
45486.2.a.c	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-2$	$-1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots$
45486.2.a.d	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$-1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots$
45486.2.a.e	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$1$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots$
45486.2.a.f	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots$
45486.2.a.g	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$1$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots$
45486.2.a.h	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$0$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{7}-q^{8}-4q^{11}+2q^{13}+\cdots$
45486.2.a.i	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$0$	$-1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{7}-q^{8}-2q^{11}+4q^{13}+\cdots$
45486.2.a.j	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$0$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{7}-q^{8}+6q^{11}+2q^{13}+\cdots$
45486.2.a.k	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$0$	$1$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{7}-q^{8}-6q^{11}+4q^{13}+\cdots$
45486.2.a.l	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{13}-q^{14}+\cdots$
45486.2.a.m	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$0$	$1$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{7}-q^{8}+4q^{13}-q^{14}+\cdots$
45486.2.a.n	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{7}-q^{8}+6q^{11}-2q^{13}+\cdots$
45486.2.a.o	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$-1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
45486.2.a.p	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
45486.2.a.q	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
45486.2.a.r	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$2$	$-1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots$
45486.2.a.s	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$2$	$1$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots$
45486.2.a.t	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$3$	$-1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}-q^{7}-q^{8}-3q^{10}+\cdots$
45486.2.a.u	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$3$	$1$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{10}+\cdots$
45486.2.a.v	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$4$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{5}+q^{7}-q^{8}-4q^{10}+\cdots$
45486.2.a.w	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-4$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{5}+q^{7}+q^{8}-4q^{10}+\cdots$
45486.2.a.x	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-3$	$1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{10}+\cdots$
45486.2.a.y	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-2$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}-2q^{10}+\cdots$
45486.2.a.z	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$-1$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots$
45486.2.a.ba	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots$
45486.2.a.bb	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots$
45486.2.a.bc	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots$
45486.2.a.bd	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$1$	$0$	$0$	$-1$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{7}+q^{8}-4q^{11}-2q^{13}+\cdots$
45486.2.a.be	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$1$	$0$	$0$	$-1$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{7}+q^{8}+6q^{11}-2q^{13}+\cdots$
45486.2.a.bf	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$1$	$0$	$0$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{7}+q^{8}-6q^{11}-2q^{13}+\cdots$
45486.2.a.bg	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$1$	$0$	$0$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{7}+q^{8}-2q^{13}+q^{14}+\cdots$
45486.2.a.bh	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots$
45486.2.a.bi	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots$
45486.2.a.bj	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$-1$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots$
45486.2.a.bk	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$1$	$0$	$2$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots$
45486.2.a.bl	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$1$	$0$	$2$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots$
45486.2.a.bm	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$1$	$0$	$3$	$-1$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}-q^{7}+q^{8}+3q^{10}+\cdots$
45486.2.a.bn	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$1$	$0$	$3$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots$
45486.2.a.bo	$45486$	$2$	45486.a	1.a	$1$	$1$	$1$	$363.208$	$\Q$	None	✓	?				$-1$		$1$	$0$	$4$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{5}-q^{7}+q^{8}+4q^{10}+\cdots$
45486.2.a.bp	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{73}) $	None	✓	?				$-1$		$-2$	$0$	$-6$	$-2$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.bq	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{6}) $	None	✓	?				$-1$		$-2$	$0$	$-6$	$2$	$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.br	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{17}) $	None	✓	?				$-1$		$-2$	$0$	$-4$	$-2$	$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.bs	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$-4$	$-2$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.bt	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{2}) $	None	✓	?				$-1$		$-2$	$0$	$-4$	$2$	$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.bu	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$-2$	$-2$	$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.bv	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$-2$	$-2$	$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.bw	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$-2$	$-2$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.bx	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$-1$	$-2$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.by	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$-1$	$2$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.bz	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{3}) $	None	✓	?				$-1$		$-2$	$0$	$0$	$-2$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.ca	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$0$	$2$	$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.cb	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{29}) $	None	✓	?				$-1$		$-2$	$0$	$1$	$-2$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.cc	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$1$	$-2$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.cd	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{17}) $	None	✓	?				$-1$		$-2$	$0$	$1$	$-2$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.ce	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$2$	$-2$	$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.cf	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$2$	$2$	$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.cg	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$2$	$2$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.ch	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{2}) $	None	✓	?				$-1$		$-2$	$0$	$2$	$2$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.ci	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$3$	$-2$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.cj	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$3$	$2$	$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.ck	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$3$	$2$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.cl	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$4$	$-2$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.cm	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{17}) $	None	✓	?				$-1$		$-2$	$0$	$4$	$-2$	$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.cn	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$4$	$2$	$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.co	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{6}) $	None	✓	?				$-1$		$-2$	$0$	$6$	$2$	$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.cp	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{73}) $	None	✓	?				$-1$		$2$	$0$	$-6$	$-2$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.cq	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{6}) $	None	✓	?				$-1$		$2$	$0$	$-6$	$2$	$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.cr	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{17}) $	None	✓	?				$-1$		$2$	$0$	$-4$	$-2$	$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.cs	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$-4$	$-2$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.ct	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$-2$	$-2$	$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.cu	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$-2$	$-2$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.cv	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$-2$	$2$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.cw	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$-1$	$-2$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.cx	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{13}) $	None	✓	?				$-1$		$2$	$0$	$-1$	$2$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.cy	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{2}) $	None	✓	?				$-1$		$2$	$0$	$0$	$2$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.cz	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$0$	$2$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.da	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$1$	$-2$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.db	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{17}) $	None	✓	?				$-1$		$2$	$0$	$1$	$-2$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.dc	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$2$	$-2$	$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.dd	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$2$	$-2$	$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.de	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$2$	$2$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.df	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{2}) $	None	✓	?				$-1$		$2$	$0$	$2$	$2$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.dg	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$3$	$-2$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.dh	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$3$	$2$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.di	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$3$	$2$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.dj	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$4$	$-2$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.dk	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{17}) $	None	✓	?				$-1$		$2$	$0$	$4$	$-2$	$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.dl	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$4$	$2$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.dm	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{2}) $	None	✓	?				$-1$		$2$	$0$	$4$	$2$	$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.dn	$45486$	$2$	45486.a	1.a	$1$	$2$	$2$	$363.208$	$\Q(\sqrt{6}) $	None	✓	?				$-1$		$2$	$0$	$6$	$2$	$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.do	$45486$	$2$	45486.a	1.a	$1$	$3$	$3$	$363.208$	3.3.4860.1	None	✓	?				$-1$		$-3$	$0$	$-3$	$-3$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.dp	$45486$	$2$	45486.a	1.a	$1$	$3$	$3$	$363.208$	3.3.1304.1	None	✓	?				$-1$		$-3$	$0$	$-3$	$3$	$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.dq	$45486$	$2$	45486.a	1.a	$1$	$3$	$3$	$363.208$	3.3.148.1	None	✓	?				$-1$		$-3$	$0$	$-2$	$3$	$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.dr	$45486$	$2$	45486.a	1.a	$1$	$3$	$3$	$363.208$	$\Q(\zeta_{18})^+$	None	✓	?				$-1$		$-3$	$0$	$0$	$-3$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.ds	$45486$	$2$	45486.a	1.a	$1$	$3$	$3$	$363.208$	3.3.148.1	None	✓	?				$-1$		$-3$	$0$	$1$	$-3$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.dt	$45486$	$2$	45486.a	1.a	$1$	$3$	$3$	$363.208$	3.3.148.1	None	✓	?				$-1$		$-3$	$0$	$2$	$-3$	$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.du	$45486$	$2$	45486.a	1.a	$1$	$3$	$3$	$363.208$	3.3.1304.1	None	✓	?				$-1$		$-3$	$0$	$3$	$3$	$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.dv	$45486$	$2$	45486.a	1.a	$1$	$3$	$3$	$363.208$	$\Q(\zeta_{18})^+$	None	✓	?				$-1$		$-3$	$0$	$3$	$3$	$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.dw	$45486$	$2$	45486.a	1.a	$1$	$3$	$3$	$363.208$	3.3.469.1	None	✓	?				$-1$		$3$	$0$	$-5$	$-3$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.dx	$45486$	$2$	45486.a	1.a	$1$	$3$	$3$	$363.208$	3.3.4860.1	None	✓	?				$-1$		$3$	$0$	$-3$	$-3$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.dy	$45486$	$2$	45486.a	1.a	$1$	$3$	$3$	$363.208$	3.3.1304.1	None	✓	?				$-1$		$3$	$0$	$-3$	$3$	$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.dz	$45486$	$2$	45486.a	1.a	$1$	$3$	$3$	$363.208$	3.3.148.1	None	✓	?				$-1$		$3$	$0$	$-2$	$-3$	$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.ea	$45486$	$2$	45486.a	1.a	$1$	$3$	$3$	$363.208$	3.3.148.1	None	✓	?				$-1$		$3$	$0$	$-2$	$3$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.eb	$45486$	$2$	45486.a	1.a	$1$	$3$	$3$	$363.208$	$\Q(\zeta_{18})^+$	None	✓	?				$-1$		$3$	$0$	$0$	$-3$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.ec	$45486$	$2$	45486.a	1.a	$1$	$3$	$3$	$363.208$	3.3.148.1	None	✓	?				$-1$		$3$	$0$	$1$	$-3$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.ed	$45486$	$2$	45486.a	1.a	$1$	$3$	$3$	$363.208$	3.3.1304.1	None	✓	?				$-1$		$3$	$0$	$3$	$3$	$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.ee	$45486$	$2$	45486.a	1.a	$1$	$3$	$3$	$363.208$	$\Q(\zeta_{18})^+$	None	✓	?				$-1$		$3$	$0$	$3$	$3$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.ef	$45486$	$2$	45486.a	1.a	$1$	$4$	$4$	$363.208$	4.4.9225.1	None	✓	?				$-1$		$-4$	$0$	$-5$	$4$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.eg	$45486$	$2$	45486.a	1.a	$1$	$4$	$4$	$363.208$	$\Q(\zeta_{20})^+$	None	✓	?				$-1$		$-4$	$0$	$-2$	$4$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.eh	$45486$	$2$	45486.a	1.a	$1$	$4$	$4$	$363.208$	4.4.151572.1	None	✓	?				$-1$		$-4$	$0$	$-1$	$4$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.ei	$45486$	$2$	45486.a	1.a	$1$	$4$	$4$	$363.208$	4.4.12400.1	None	✓	?				$-1$		$-4$	$0$	$0$	$-4$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.ej	$45486$	$2$	45486.a	1.a	$1$	$4$	$4$	$363.208$	$\Q(\zeta_{24})^+$	None	✓	?				$-1$		$-4$	$0$	$0$	$4$	$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.ek	$45486$	$2$	45486.a	1.a	$1$	$4$	$4$	$363.208$	$\Q(\zeta_{20})^+$	None	✓	?				$-1$		$-4$	$0$	$4$	$4$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.el	$45486$	$2$	45486.a	1.a	$1$	$4$	$4$	$363.208$	4.4.9225.1	None	✓	?				$-1$		$4$	$0$	$-5$	$4$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.em	$45486$	$2$	45486.a	1.a	$1$	$4$	$4$	$363.208$	$\Q(\zeta_{20})^+$	None	✓	?				$-1$		$4$	$0$	$-2$	$4$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.en	$45486$	$2$	45486.a	1.a	$1$	$4$	$4$	$363.208$	4.4.151572.1	None	✓	?				$-1$		$4$	$0$	$-1$	$4$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.eo	$45486$	$2$	45486.a	1.a	$1$	$4$	$4$	$363.208$	4.4.12400.1	None	✓	?				$-1$		$4$	$0$	$0$	$-4$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.ep	$45486$	$2$	45486.a	1.a	$1$	$4$	$4$	$363.208$	$\Q(\zeta_{24})^+$	None	✓	?				$-1$		$4$	$0$	$0$	$4$	$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.eq	$45486$	$2$	45486.a	1.a	$1$	$4$	$4$	$363.208$	$\Q(\zeta_{20})^+$	None	✓	?				$-1$		$4$	$0$	$4$	$4$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.er	$45486$	$2$	45486.a	1.a	$1$	$5$	$5$	$363.208$	5.5.1903616.1	None	✓	?				$-1$		$-5$	$0$	$-3$	$-5$	$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.es	$45486$	$2$	45486.a	1.a	$1$	$5$	$5$	$363.208$	5.5.1903616.1	None	✓	?				$-1$		$-5$	$0$	$3$	$-5$	$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.et	$45486$	$2$	45486.a	1.a	$1$	$5$	$5$	$363.208$	5.5.1903616.1	None	✓	?				$-1$		$5$	$0$	$-3$	$-5$	$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.eu	$45486$	$2$	45486.a	1.a	$1$	$5$	$5$	$363.208$	5.5.1903616.1	None	✓	?				$-1$		$5$	$0$	$3$	$-5$	$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.ev	$45486$	$2$	45486.a	1.a	$1$	$6$	$6$	$363.208$	6.6.583942000.1	None	✓	?				$-1$		$-6$	$0$	$-4$	$6$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.ew	$45486$	$2$	45486.a	1.a	$1$	$6$	$6$	$363.208$	6.6.309418000.1	None	✓	?				$-1$		$-6$	$0$	$0$	$-6$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.ex	$45486$	$2$	45486.a	1.a	$1$	$6$	$6$	$363.208$	6.6.17721261.1	None	✓	?				$-1$		$-6$	$0$	$0$	$-6$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.ey	$45486$	$2$	45486.a	1.a	$1$	$6$	$6$	$363.208$	6.6.1292517.1	None	✓	?				$-1$		$-6$	$0$	$0$	$6$	$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.ez	$45486$	$2$	45486.a	1.a	$1$	$6$	$6$	$363.208$	6.6.36538000.1	None	✓	?				$-1$		$-6$	$0$	$1$	$6$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.fa	$45486$	$2$	45486.a	1.a	$1$	$6$	$6$	$363.208$	6.6.1528713.1	None	✓	?				$-1$		$-6$	$0$	$3$	$-6$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.fb	$45486$	$2$	45486.a	1.a	$1$	$6$	$6$	$363.208$	6.6.48952000.1	None	✓	?				$-1$		$-6$	$0$	$5$	$-6$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.fc	$45486$	$2$	45486.a	1.a	$1$	$6$	$6$	$363.208$	6.6.3549501.1	None	✓	?				$-1$		$-6$	$0$	$6$	$-6$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.fd	$45486$	$2$	45486.a	1.a	$1$	$6$	$6$	$363.208$	6.6.4126869.1	None	✓	?				$-1$		$-6$	$0$	$6$	$6$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.fe	$45486$	$2$	45486.a	1.a	$1$	$6$	$6$	$363.208$	6.6.583942000.1	None	✓	?				$-1$		$6$	$0$	$-4$	$6$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.ff	$45486$	$2$	45486.a	1.a	$1$	$6$	$6$	$363.208$	6.6.309418000.1	None	✓	?				$-1$		$6$	$0$	$0$	$-6$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.fg	$45486$	$2$	45486.a	1.a	$1$	$6$	$6$	$363.208$	6.6.17721261.1	None	✓	?				$-1$		$6$	$0$	$0$	$-6$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.fh	$45486$	$2$	45486.a	1.a	$1$	$6$	$6$	$363.208$	6.6.1292517.1	None	✓	?				$-1$		$6$	$0$	$0$	$6$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.fi	$45486$	$2$	45486.a	1.a	$1$	$6$	$6$	$363.208$	6.6.36538000.1	None	✓	?				$-1$		$6$	$0$	$1$	$6$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.fj	$45486$	$2$	45486.a	1.a	$1$	$6$	$6$	$363.208$	6.6.1528713.1	None	✓	?				$-1$		$6$	$0$	$3$	$-6$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.fk	$45486$	$2$	45486.a	1.a	$1$	$6$	$6$	$363.208$	6.6.48952000.1	None	✓	?				$-1$		$6$	$0$	$5$	$-6$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.fl	$45486$	$2$	45486.a	1.a	$1$	$6$	$6$	$363.208$	6.6.3549501.1	None	✓	?				$-1$		$6$	$0$	$6$	$-6$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.fm	$45486$	$2$	45486.a	1.a	$1$	$6$	$6$	$363.208$	6.6.4126869.1	None	✓	?				$-1$		$6$	$0$	$6$	$6$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.fn	$45486$	$2$	45486.a	1.a	$1$	$8$	$8$	$363.208$	8.8.$\cdots$.1	None	✓	?				$-1$		$-8$	$0$	$-6$	$-8$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.fo	$45486$	$2$	45486.a	1.a	$1$	$8$	$8$	$363.208$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	?				$-1$		$-8$	$0$	$-2$	$-8$	$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.fp	$45486$	$2$	45486.a	1.a	$1$	$8$	$8$	$363.208$	8.8.5120000000.1	None	✓	?				$-1$		$-8$	$0$	$0$	$-8$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.fq	$45486$	$2$	45486.a	1.a	$1$	$8$	$8$	$363.208$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	?				$-1$		$-8$	$0$	$2$	$-8$	$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.fr	$45486$	$2$	45486.a	1.a	$1$	$8$	$8$	$363.208$	8.8.$\cdots$.1	None	✓	?				$-1$		$-8$	$0$	$2$	$8$	$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.fs	$45486$	$2$	45486.a	1.a	$1$	$8$	$8$	$363.208$	8.8.$\cdots$.1	None	✓	?				$-1$		$-8$	$0$	$8$	$8$	$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.ft	$45486$	$2$	45486.a	1.a	$1$	$8$	$8$	$363.208$	8.8.$\cdots$.1	None	✓	?				$-1$		$8$	$0$	$-6$	$-8$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.fu	$45486$	$2$	45486.a	1.a	$1$	$8$	$8$	$363.208$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	?				$-1$		$8$	$0$	$-2$	$-8$	$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.fv	$45486$	$2$	45486.a	1.a	$1$	$8$	$8$	$363.208$	8.8.5120000000.1	None	✓	?				$-1$		$8$	$0$	$0$	$-8$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.fw	$45486$	$2$	45486.a	1.a	$1$	$8$	$8$	$363.208$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	?				$-1$		$8$	$0$	$2$	$-8$	$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.fx	$45486$	$2$	45486.a	1.a	$1$	$8$	$8$	$363.208$	8.8.$\cdots$.1	None	✓	?				$-1$		$8$	$0$	$2$	$8$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.fy	$45486$	$2$	45486.a	1.a	$1$	$8$	$8$	$363.208$	8.8.$\cdots$.1	None	✓	?				$-1$		$8$	$0$	$8$	$8$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.fz	$45486$	$2$	45486.a	1.a	$1$	$9$	$9$	$363.208$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	?	✓			$-1$		$-9$	$0$	$-6$	$-9$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.ga	$45486$	$2$	45486.a	1.a	$1$	$9$	$9$	$363.208$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	?				$-1$		$-9$	$0$	$-6$	$9$	$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.gb	$45486$	$2$	45486.a	1.a	$1$	$9$	$9$	$363.208$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	?				$-1$		$-9$	$0$	$-3$	$-9$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.gc	$45486$	$2$	45486.a	1.a	$1$	$9$	$9$	$363.208$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	?				$-1$		$-9$	$0$	$0$	$-9$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.gd	$45486$	$2$	45486.a	1.a	$1$	$9$	$9$	$363.208$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	?				$-1$		$-9$	$0$	$0$	$9$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.ge	$45486$	$2$	45486.a	1.a	$1$	$9$	$9$	$363.208$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	?				$-1$		$9$	$0$	$-6$	$-9$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.gf	$45486$	$2$	45486.a	1.a	$1$	$9$	$9$	$363.208$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	?	✓			$-1$		$9$	$0$	$-6$	$9$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.gg	$45486$	$2$	45486.a	1.a	$1$	$9$	$9$	$363.208$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	?				$-1$		$9$	$0$	$-3$	$-9$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.gh	$45486$	$2$	45486.a	1.a	$1$	$9$	$9$	$363.208$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	?				$-1$		$9$	$0$	$0$	$-9$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.gi	$45486$	$2$	45486.a	1.a	$1$	$9$	$9$	$363.208$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	?				$-1$		$9$	$0$	$0$	$9$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.gj	$45486$	$2$	45486.a	1.a	$1$	$10$	$10$	$363.208$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	?				$-1$		$-10$	$0$	$0$	$10$	$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.gk	$45486$	$2$	45486.a	1.a	$1$	$10$	$10$	$363.208$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	?				$-1$		$-10$	$0$	$0$	$10$	$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.gl	$45486$	$2$	45486.a	1.a	$1$	$10$	$10$	$363.208$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	?				$-1$		$10$	$0$	$0$	$10$	$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.gm	$45486$	$2$	45486.a	1.a	$1$	$10$	$10$	$363.208$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	?				$-1$		$10$	$0$	$0$	$10$	$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.gn	$45486$	$2$	45486.a	1.a	$1$	$12$	$12$	$363.208$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	?	✓			$-1$		$-12$	$0$	$-8$	$12$	$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.go	$45486$	$2$	45486.a	1.a	$1$	$12$	$12$	$363.208$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	?	✓			$-1$		$-12$	$0$	$-3$	$12$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.gp	$45486$	$2$	45486.a	1.a	$1$	$12$	$12$	$363.208$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	?	✓			$-1$		$-12$	$0$	$0$	$-12$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.gq	$45486$	$2$	45486.a	1.a	$1$	$12$	$12$	$363.208$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	?				$-1$		$12$	$0$	$-8$	$12$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.gr	$45486$	$2$	45486.a	1.a	$1$	$12$	$12$	$363.208$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	?				$-1$		$12$	$0$	$-3$	$12$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.gs	$45486$	$2$	45486.a	1.a	$1$	$12$	$12$	$363.208$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	?	✓			$-1$		$12$	$0$	$0$	$-12$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.gt	$45486$	$2$	45486.a	1.a	$1$	$15$	$15$	$363.208$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	?				$-1$		$-15$	$0$	$-6$	$-15$	$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.gu	$45486$	$2$	45486.a	1.a	$1$	$15$	$15$	$363.208$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	?	✓			$-1$		$-15$	$0$	$-6$	$15$	$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.gv	$45486$	$2$	45486.a	1.a	$1$	$15$	$15$	$363.208$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	?	✓			$-1$		$-15$	$0$	$6$	$-15$	$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.gw	$45486$	$2$	45486.a	1.a	$1$	$15$	$15$	$363.208$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	?				$-1$		$-15$	$0$	$6$	$15$	$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.gx	$45486$	$2$	45486.a	1.a	$1$	$15$	$15$	$363.208$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	?	✓			$-1$		$15$	$0$	$-6$	$-15$	$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
45486.2.a.gy	$45486$	$2$	45486.a	1.a	$1$	$15$	$15$	$363.208$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	?				$-1$		$15$	$0$	$-6$	$15$	$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.gz	$45486$	$2$	45486.a	1.a	$1$	$15$	$15$	$363.208$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	?				$-1$		$15$	$0$	$6$	$-15$	$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.ha	$45486$	$2$	45486.a	1.a	$1$	$15$	$15$	$363.208$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	?	✓			$-1$		$15$	$0$	$6$	$15$	$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
45486.2.a.hb	$45486$	$2$	45486.a	1.a	$1$	$16$	$16$	$363.208$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	?	✓			$-1$		$-16$	$0$	$0$	$-16$	$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
45486.2.a.hc	$45486$	$2$	45486.a	1.a	$1$	$16$	$16$	$363.208$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	?	✓			$-1$		$-16$	$0$	$0$	$16$	$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.hd	$45486$	$2$	45486.a	1.a	$1$	$16$	$16$	$363.208$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	?	✓			$-1$		$16$	$0$	$0$	$-16$	$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
45486.2.a.he	$45486$	$2$	45486.a	1.a	$1$	$16$	$16$	$363.208$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	?	✓			$-1$		$16$	$0$	$0$	$16$	$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(45486))$ into lower level spaces

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 45486 = 2 \cdot 3^{2} \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	45486.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 187 \)
Sturm bound:			\(18240\)

\(2\)	\(3\)	\(7\)	\(19\)	Fricke	Total			Cusp			Eisenstein
\(2\)	\(3\)	\(7\)	\(19\)	Fricke	All	New	Old	All	New	Old	All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(560\)	\(40\)	\(520\)	\(541\)	\(40\)	\(501\)	\(19\)	\(0\)	\(19\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(598\)	\(45\)	\(553\)	\(578\)	\(45\)	\(533\)	\(20\)	\(0\)	\(20\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(600\)	\(40\)	\(560\)	\(580\)	\(40\)	\(540\)	\(20\)	\(0\)	\(20\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(562\)	\(45\)	\(517\)	\(542\)	\(45\)	\(497\)	\(20\)	\(0\)	\(20\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(590\)	\(67\)	\(523\)	\(570\)	\(67\)	\(503\)	\(20\)	\(0\)	\(20\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(570\)	\(61\)	\(509\)	\(550\)	\(61\)	\(489\)	\(20\)	\(0\)	\(20\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(570\)	\(59\)	\(511\)	\(550\)	\(59\)	\(491\)	\(20\)	\(0\)	\(20\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(590\)	\(70\)	\(520\)	\(570\)	\(70\)	\(500\)	\(20\)	\(0\)	\(20\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(580\)	\(40\)	\(540\)	\(560\)	\(40\)	\(520\)	\(20\)	\(0\)	\(20\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(582\)	\(45\)	\(537\)	\(562\)	\(45\)	\(517\)	\(20\)	\(0\)	\(20\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(580\)	\(40\)	\(540\)	\(560\)	\(40\)	\(520\)	\(20\)	\(0\)	\(20\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(578\)	\(45\)	\(533\)	\(558\)	\(45\)	\(513\)	\(20\)	\(0\)	\(20\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(590\)	\(63\)	\(527\)	\(570\)	\(63\)	\(507\)	\(20\)	\(0\)	\(20\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(570\)	\(65\)	\(505\)	\(550\)	\(65\)	\(485\)	\(20\)	\(0\)	\(20\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(570\)	\(71\)	\(499\)	\(550\)	\(71\)	\(479\)	\(20\)	\(0\)	\(20\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(590\)	\(56\)	\(534\)	\(570\)	\(56\)	\(514\)	\(20\)	\(0\)	\(20\)
Plus space				\(+\)	\(4604\)	\(409\)	\(4195\)	\(4445\)	\(409\)	\(4036\)	\(159\)	\(0\)	\(159\)
Minus space				\(-\)	\(4676\)	\(443\)	\(4233\)	\(4516\)	\(443\)	\(4073\)	\(160\)	\(0\)	\(160\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(45486))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(45486))\) into lower level spaces

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	45486.2.a
Level	$45486$
Weight	$2$
Character orbit	45486.a
Rep. character	$\chi_{45486}(1,\cdot)$
Character field	$\Q$
Dimension	$852$
Newform subspaces	$187$
Sturm bound	$18240$