LMFDB - Space of modular forms of level 32490, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 32490 = 2 \cdot 3^{2} \cdot 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	32490.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 178 $
Sturm bound:			$13680$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(32490))$.

	Total	New	Old
Modular forms	7000	567	6433
Cusp forms	6681	567	6114
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.

$2$	$3$	$5$	$19$	Fricke	Total			Cusp			Eisenstein
$2$	$3$	$5$	$19$	Fricke	All	New	Old	All	New	Old	All	New	Old
$+$	$+$	$+$	$+$	$+$	$425$	$24$	$401$	$406$	$24$	$382$	$19$	$0$	$19$
$+$	$+$	$+$	$-$	$-$	$449$	$33$	$416$	$429$	$33$	$396$	$20$	$0$	$20$
$+$	$+$	$-$	$+$	$-$	$445$	$32$	$413$	$425$	$32$	$393$	$20$	$0$	$20$
$+$	$+$	$-$	$-$	$+$	$431$	$24$	$407$	$411$	$24$	$387$	$20$	$0$	$20$
$+$	$-$	$+$	$+$	$-$	$445$	$40$	$405$	$425$	$40$	$385$	$20$	$0$	$20$
$+$	$-$	$+$	$-$	$+$	$431$	$45$	$386$	$411$	$45$	$366$	$20$	$0$	$20$
$+$	$-$	$-$	$+$	$+$	$435$	$41$	$394$	$415$	$41$	$374$	$20$	$0$	$20$
$+$	$-$	$-$	$-$	$-$	$439$	$45$	$394$	$419$	$45$	$374$	$20$	$0$	$20$
$-$	$+$	$+$	$+$	$-$	$435$	$32$	$403$	$415$	$32$	$383$	$20$	$0$	$20$
$-$	$+$	$+$	$-$	$+$	$441$	$24$	$417$	$421$	$24$	$397$	$20$	$0$	$20$
$-$	$+$	$-$	$+$	$+$	$435$	$24$	$411$	$415$	$24$	$391$	$20$	$0$	$20$
$-$	$+$	$-$	$-$	$-$	$439$	$33$	$406$	$419$	$33$	$386$	$20$	$0$	$20$
$-$	$-$	$+$	$+$	$+$	$435$	$40$	$395$	$415$	$40$	$375$	$20$	$0$	$20$
$-$	$-$	$+$	$-$	$-$	$439$	$45$	$394$	$419$	$45$	$374$	$20$	$0$	$20$
$-$	$-$	$-$	$+$	$-$	$445$	$49$	$396$	$425$	$49$	$376$	$20$	$0$	$20$
$-$	$-$	$-$	$-$	$+$	$431$	$36$	$395$	$411$	$36$	$375$	$20$	$0$	$20$
Plus space				$+$	$3464$	$258$	$3206$	$3305$	$258$	$3047$	$159$	$0$	$159$
Minus space				$-$	$3536$	$309$	$3227$	$3376$	$309$	$3067$	$160$	$0$	$160$

Trace form

$ 567 q - q^{2} + 567 q^{4} + q^{5} - q^{8} + q^{10} - 2 q^{13} + 8 q^{14} + 567 q^{16} + 6 q^{17} + q^{20} + 12 q^{22} + 16 q^{23} + 567 q^{25} + 14 q^{26} - 2 q^{29} + 8 q^{31} - q^{32} + 2 q^{34}+ \cdots + 7 q^{98}+O(q^{100}) $

567 * q - q^2 + 567 * q^4 + q^5 - q^8 + q^10 - 2 * q^13 + 8 * q^14 + 567 * q^16 + 6 * q^17 + q^20 + 12 * q^22 + 16 * q^23 + 567 * q^25 + 14 * q^26 - 2 * q^29 + 8 * q^31 - q^32 + 2 * q^34 - 2 * q^37 + q^40 - 2 * q^41 + 8 * q^43 + 12 * q^46 - 32 * q^47 + 547 * q^49 - q^50 - 2 * q^52 - 22 * q^53 + 12 * q^55 + 8 * q^56 - 6 * q^58 - 48 * q^59 + 10 * q^61 + 567 * q^64 - 2 * q^65 + 12 * q^67 + 6 * q^68 - 4 * q^70 - 8 * q^71 + 18 * q^73 - 26 * q^74 + q^80 - 30 * q^82 - 40 * q^83 - 18 * q^85 + 16 * q^86 + 12 * q^88 + 14 * q^89 - 8 * q^91 + 16 * q^92 - 4 * q^94 + 10 * q^97 + 7 * q^98

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(32490))$ 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	5	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
32490.2.a.a	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$-5$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-5q^{7}-q^{8}+q^{10}+\cdots$
32490.2.a.b	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$-5$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-5q^{7}-q^{8}+q^{10}+\cdots$
32490.2.a.c	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$-4$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots$
32490.2.a.d	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$-3$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-3q^{7}-q^{8}+q^{10}+\cdots$
32490.2.a.e	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$-2$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots$
32490.2.a.f	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$-2$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots$
32490.2.a.g	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-2q^{11}+\cdots$
32490.2.a.h	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+4q^{11}+\cdots$
32490.2.a.i	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$2$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\cdots$
32490.2.a.j	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$2$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\cdots$
32490.2.a.k	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$-5$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-5q^{7}-q^{8}-q^{10}+\cdots$
32490.2.a.l	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$-4$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots$
32490.2.a.m	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$-4$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots$
32490.2.a.n	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$-4$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots$
32490.2.a.o	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$-2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots$
32490.2.a.p	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$-2$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots$
32490.2.a.q	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$-1$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
32490.2.a.r	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$-1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
32490.2.a.s	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$-1$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
32490.2.a.t	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$-1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
32490.2.a.u	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-4q^{11}+\cdots$
32490.2.a.v	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots$
32490.2.a.w	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$2$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots$
32490.2.a.x	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots$
32490.2.a.y	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots$
32490.2.a.z	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$3$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+3q^{7}-q^{8}-q^{10}+\cdots$
32490.2.a.ba	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$4$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+4q^{7}-q^{8}-q^{10}+\cdots$
32490.2.a.bb	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$-5$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-5q^{7}+q^{8}-q^{10}+\cdots$
32490.2.a.bc	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$-5$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-5q^{7}+q^{8}-q^{10}+\cdots$
32490.2.a.bd	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$-4$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots$
32490.2.a.be	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$-3$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-3q^{7}+q^{8}-q^{10}+\cdots$
32490.2.a.bf	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$-2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots$
32490.2.a.bg	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$-2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots$
32490.2.a.bh	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots$
32490.2.a.bi	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-2q^{11}+\cdots$
32490.2.a.bj	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+4q^{11}+\cdots$
32490.2.a.bk	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$4$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+4q^{7}+q^{8}-q^{10}+\cdots$
32490.2.a.bl	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$4$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+4q^{7}+q^{8}-q^{10}+\cdots$
32490.2.a.bm	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$-5$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-5q^{7}+q^{8}+q^{10}+\cdots$
32490.2.a.bn	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$-5$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-5q^{7}+q^{8}+q^{10}+\cdots$
32490.2.a.bo	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$-4$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots$
32490.2.a.bp	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$-2$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-2q^{7}+q^{8}+q^{10}+\cdots$
32490.2.a.bq	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$-2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-2q^{7}+q^{8}+q^{10}+\cdots$
32490.2.a.br	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$-1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots$
32490.2.a.bs	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$-1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots$
32490.2.a.bt	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$-1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots$
32490.2.a.bu	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-4q^{11}+\cdots$
32490.2.a.bv	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-4q^{11}+\cdots$
32490.2.a.bw	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots$
32490.2.a.bx	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$2$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots$
32490.2.a.by	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots$
32490.2.a.bz	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots$
32490.2.a.ca	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$2$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots$
32490.2.a.cb	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$2$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots$
32490.2.a.cc	$32490$	$2$	32490.a	1.a	$1$	$1$	$1$	$259.434$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$3$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+3q^{7}+q^{8}+q^{10}+\cdots$
32490.2.a.cd	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$-2$	$-4$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.ce	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$-2$	$-2$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.cf	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{73}) $	None	✓	?				$-1$		$-2$	$0$	$-2$	$-2$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.cg	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$-2$	$-2$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.ch	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{17}) $	None	✓	?				$-1$		$-2$	$0$	$-2$	$-1$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.ci	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$-2$	$0$	$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.cj	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$-2$	$1$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.ck	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{17}) $	None	✓	?				$-1$		$-2$	$0$	$-2$	$2$	$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.cl	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{6}) $	None	✓	?				$-1$		$-2$	$0$	$-2$	$2$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.cm	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{6}) $	None	✓	?				$-1$		$-2$	$0$	$-2$	$4$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.cn	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{17}) $	None	✓	?				$-1$		$-2$	$0$	$-2$	$5$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.co	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$2$	$-2$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.cp	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$2$	$-2$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.cq	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$2$	$0$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.cr	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$2$	$0$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.cs	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{7}) $	None	✓	?				$-1$		$-2$	$0$	$2$	$0$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.ct	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$2$	$0$	$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.cu	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{19}) $	None	✓	?				$-1$		$-2$	$0$	$2$	$0$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.cv	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{17}) $	None	✓	?				$-1$		$-2$	$0$	$2$	$3$	$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.cw	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{3}) $	None	✓	?				$-1$		$-2$	$0$	$2$	$4$	$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.cx	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$-2$	$-4$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.cy	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$-2$	$-2$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.cz	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{73}) $	None	✓	?				$-1$		$2$	$0$	$-2$	$-2$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.da	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$-2$	$-2$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.db	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$-2$	$0$	$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.dc	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$-2$	$1$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.dd	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{6}) $	None	✓	?				$-1$		$2$	$0$	$-2$	$2$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.de	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{3}) $	None	✓	?				$-1$		$2$	$0$	$-2$	$4$	$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.df	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{6}) $	None	✓	?				$-1$		$2$	$0$	$-2$	$4$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.dg	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{17}) $	None	✓	?				$-1$		$2$	$0$	$-2$	$5$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.dh	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$2$	$-2$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.di	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$2$	$-2$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.dj	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$2$	$0$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.dk	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$2$	$0$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.dl	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$2$	$0$	$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.dm	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{7}) $	None	✓	?				$-1$		$2$	$0$	$2$	$0$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.dn	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{19}) $	None	✓	?				$-1$		$2$	$0$	$2$	$0$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.do	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{17}) $	None	✓	?				$-1$		$2$	$0$	$2$	$2$	$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.dp	$32490$	$2$	32490.a	1.a	$1$	$2$	$2$	$259.434$	$\Q(\sqrt{17}) $	None	✓	?				$-1$		$2$	$0$	$2$	$3$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.dq	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	3.3.3144.1	None	✓	?				$-1$		$-3$	$0$	$-3$	$-3$	$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.dr	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	$\Q(\zeta_{18})^+$	None	✓	?				$-1$		$-3$	$0$	$-3$	$-3$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.ds	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	$\Q(\zeta_{18})^+$	None	✓	?				$-1$		$-3$	$0$	$-3$	$0$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.dt	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	3.3.3144.1	None	✓	?				$-1$		$-3$	$0$	$-3$	$1$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.du	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	$\Q(\zeta_{18})^+$	None	✓	?				$-1$		$-3$	$0$	$-3$	$3$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.dv	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	$\Q(\zeta_{18})^+$	None	✓	?				$-1$		$-3$	$0$	$3$	$-9$	$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.dw	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	$\Q(\zeta_{18})^+$	None	✓	?				$-1$		$-3$	$0$	$3$	$-3$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.dx	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	3.3.3144.1	None	✓	?				$-1$		$-3$	$0$	$3$	$-3$	$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.dy	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	$\Q(\zeta_{18})^+$	None	✓	?				$-1$		$-3$	$0$	$3$	$-3$	$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.dz	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	$\Q(\zeta_{18})^+$	None	✓	?				$-1$		$-3$	$0$	$3$	$3$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.ea	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	$\Q(\zeta_{18})^+$	None	✓	?				$-1$		$-3$	$0$	$3$	$6$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.eb	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	$\Q(\zeta_{18})^+$	None	✓	?				$-1$		$-3$	$0$	$3$	$6$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.ec	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	3.3.3144.1	None	✓	?				$-1$		$3$	$0$	$-3$	$-3$	$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.ed	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	$\Q(\zeta_{18})^+$	None	✓	?				$-1$		$3$	$0$	$-3$	$-3$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.ee	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	$\Q(\zeta_{18})^+$	None	✓	?				$-1$		$3$	$0$	$-3$	$0$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.ef	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	3.3.3144.1	None	✓	?				$-1$		$3$	$0$	$-3$	$1$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.eg	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	$\Q(\zeta_{18})^+$	None	✓	?				$-1$		$3$	$0$	$-3$	$3$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.eh	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	$\Q(\zeta_{18})^+$	None	✓	?				$-1$		$3$	$0$	$3$	$-9$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.ei	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	$\Q(\zeta_{18})^+$	None	✓	?				$-1$		$3$	$0$	$3$	$-3$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.ej	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	3.3.3144.1	None	✓	?				$-1$		$3$	$0$	$3$	$-3$	$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.ek	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	$\Q(\zeta_{18})^+$	None	✓	?				$-1$		$3$	$0$	$3$	$-3$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.el	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	$\Q(\zeta_{18})^+$	None	✓	?				$-1$		$3$	$0$	$3$	$3$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.em	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	$\Q(\zeta_{18})^+$	None	✓	?				$-1$		$3$	$0$	$3$	$6$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.en	$32490$	$2$	32490.a	1.a	$1$	$3$	$3$	$259.434$	$\Q(\zeta_{18})^+$	None	✓	?				$-1$		$3$	$0$	$3$	$6$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.eo	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	$\Q(\zeta_{20})^+$	None	✓	?				$-1$		$-4$	$0$	$-4$	$-10$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.ep	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	$\Q(\zeta_{20})^+$	None	✓	?				$-1$		$-4$	$0$	$-4$	$-2$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.eq	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	$\Q(\zeta_{20})^+$	None	✓	?				$-1$		$-4$	$0$	$-4$	$-2$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.er	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	4.4.5225.1	None	✓	?				$-1$		$-4$	$0$	$-4$	$3$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.es	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	4.4.76400.1	None	✓	?				$-1$		$-4$	$0$	$-4$	$4$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.et	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	4.4.12400.1	None	✓	?				$-1$		$-4$	$0$	$-4$	$6$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.eu	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	4.4.7600.1	None	✓	?				$-1$		$-4$	$0$	$-4$	$6$	$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.ev	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	$\Q(\zeta_{20})^+$	None	✓	?				$-1$		$-4$	$0$	$-4$	$8$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.ew	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	$\Q(\zeta_{20})^+$	None	✓	?				$-1$		$-4$	$0$	$4$	$-2$	$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.ex	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	$\Q(\zeta_{20})^+$	None	✓	?				$-1$		$-4$	$0$	$4$	$-2$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.ey	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	$\Q(\sqrt{5}, \sqrt{6})$	None	✓	?				$-1$		$-4$	$0$	$4$	$0$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.ez	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	$\Q(\zeta_{20})^+$	None	✓	?				$-1$		$-4$	$0$	$4$	$2$	$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.fa	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	$\Q(\zeta_{20})^+$	None	✓	?				$-1$		$-4$	$0$	$4$	$4$	$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.fb	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	4.4.7600.1	None	✓	?				$-1$		$-4$	$0$	$4$	$6$	$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.fc	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	$\Q(\zeta_{20})^+$	None	✓	?				$-1$		$4$	$0$	$-4$	$-10$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.fd	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	$\Q(\zeta_{20})^+$	None	✓	?				$-1$		$4$	$0$	$-4$	$-2$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.fe	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	$\Q(\zeta_{20})^+$	None	✓	?				$-1$		$4$	$0$	$-4$	$-2$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.ff	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	4.4.5225.1	None	✓	?				$-1$		$4$	$0$	$-4$	$3$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.fg	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	4.4.76400.1	None	✓	?				$-1$		$4$	$0$	$-4$	$4$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.fh	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	4.4.7600.1	None	✓	?				$-1$		$4$	$0$	$-4$	$6$	$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.fi	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	4.4.12400.1	None	✓	?				$-1$		$4$	$0$	$-4$	$6$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.fj	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	$\Q(\zeta_{20})^+$	None	✓	?				$-1$		$4$	$0$	$-4$	$8$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.fk	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	$\Q(\zeta_{20})^+$	None	✓	?				$-1$		$4$	$0$	$4$	$-2$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.fl	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	$\Q(\zeta_{20})^+$	None	✓	?				$-1$		$4$	$0$	$4$	$-2$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.fm	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	$\Q(\sqrt{5}, \sqrt{6})$	None	✓	?				$-1$		$4$	$0$	$4$	$0$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.fn	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	$\Q(\zeta_{20})^+$	None	✓	?				$-1$		$4$	$0$	$4$	$2$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.fo	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	$\Q(\zeta_{20})^+$	None	✓	?				$-1$		$4$	$0$	$4$	$4$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.fp	$32490$	$2$	32490.a	1.a	$1$	$4$	$4$	$259.434$	4.4.7600.1	None	✓	?				$-1$		$4$	$0$	$4$	$6$	$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.fq	$32490$	$2$	32490.a	1.a	$1$	$6$	$6$	$259.434$	6.6.7978176.1	None	✓	?				$-1$		$-6$	$0$	$-6$	$-6$	$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.fr	$32490$	$2$	32490.a	1.a	$1$	$6$	$6$	$259.434$	6.6.6357609.1	None	✓	?				$-1$		$-6$	$0$	$-6$	$-3$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.fs	$32490$	$2$	32490.a	1.a	$1$	$6$	$6$	$259.434$	6.6.59778000.1	None	✓	?				$-1$		$-6$	$0$	$-6$	$0$	$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.ft	$32490$	$2$	32490.a	1.a	$1$	$6$	$6$	$259.434$	6.6.364498000.1	None	✓	?				$-1$		$-6$	$0$	$-6$	$0$	$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.fu	$32490$	$2$	32490.a	1.a	$1$	$6$	$6$	$259.434$	6.6.42889257.1	None	✓	?				$-1$		$-6$	$0$	$-6$	$3$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.fv	$32490$	$2$	32490.a	1.a	$1$	$6$	$6$	$259.434$	6.6.7978176.1	None	✓	?				$-1$		$-6$	$0$	$6$	$-6$	$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.fw	$32490$	$2$	32490.a	1.a	$1$	$6$	$6$	$259.434$	6.6.15536448.1	None	✓	?	✓			$-1$		$-6$	$0$	$6$	$-6$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.fx	$32490$	$2$	32490.a	1.a	$1$	$6$	$6$	$259.434$	6.6.364498000.1	None	✓	?				$-1$		$-6$	$0$	$6$	$0$	$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.fy	$32490$	$2$	32490.a	1.a	$1$	$6$	$6$	$259.434$	6.6.59778000.1	None	✓	?				$-1$		$-6$	$0$	$6$	$0$	$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.fz	$32490$	$2$	32490.a	1.a	$1$	$6$	$6$	$259.434$	6.6.23153769.1	None	✓	?				$-1$		$-6$	$0$	$6$	$6$	$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.ga	$32490$	$2$	32490.a	1.a	$1$	$6$	$6$	$259.434$	6.6.7978176.1	None	✓	?				$-1$		$6$	$0$	$-6$	$-6$	$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.gb	$32490$	$2$	32490.a	1.a	$1$	$6$	$6$	$259.434$	6.6.6357609.1	None	✓	?				$-1$		$6$	$0$	$-6$	$-3$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.gc	$32490$	$2$	32490.a	1.a	$1$	$6$	$6$	$259.434$	6.6.364498000.1	None	✓	?				$-1$		$6$	$0$	$-6$	$0$	$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.gd	$32490$	$2$	32490.a	1.a	$1$	$6$	$6$	$259.434$	6.6.59778000.1	None	✓	?				$-1$		$6$	$0$	$-6$	$0$	$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.ge	$32490$	$2$	32490.a	1.a	$1$	$6$	$6$	$259.434$	6.6.42889257.1	None	✓	?				$-1$		$6$	$0$	$-6$	$3$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.gf	$32490$	$2$	32490.a	1.a	$1$	$6$	$6$	$259.434$	6.6.7978176.1	None	✓	?				$-1$		$6$	$0$	$6$	$-6$	$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.gg	$32490$	$2$	32490.a	1.a	$1$	$6$	$6$	$259.434$	6.6.15536448.1	None	✓	?				$-1$		$6$	$0$	$6$	$-6$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.gh	$32490$	$2$	32490.a	1.a	$1$	$6$	$6$	$259.434$	6.6.59778000.1	None	✓	?				$-1$		$6$	$0$	$6$	$0$	$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.gi	$32490$	$2$	32490.a	1.a	$1$	$6$	$6$	$259.434$	6.6.364498000.1	None	✓	?				$-1$		$6$	$0$	$6$	$0$	$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.gj	$32490$	$2$	32490.a	1.a	$1$	$6$	$6$	$259.434$	6.6.23153769.1	None	✓	?	✓			$-1$		$6$	$0$	$6$	$6$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.gk	$32490$	$2$	32490.a	1.a	$1$	$8$	$8$	$259.434$	8.8.$\cdots$.1	None	✓	?	✓			$-1$		$-8$	$0$	$8$	$2$	$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.gl	$32490$	$2$	32490.a	1.a	$1$	$8$	$8$	$259.434$	8.8.$\cdots$.1	None	✓	?	✓			$-1$		$8$	$0$	$8$	$2$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.gm	$32490$	$2$	32490.a	1.a	$1$	$9$	$9$	$259.434$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	?	✓			$-1$		$-9$	$0$	$-9$	$0$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
32490.2.a.gn	$32490$	$2$	32490.a	1.a	$1$	$9$	$9$	$259.434$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	?	✓			$-1$		$9$	$0$	$-9$	$0$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.go	$32490$	$2$	32490.a	1.a	$1$	$12$	$12$	$259.434$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	?	✓			$-1$		$-12$	$0$	$-12$	$0$	$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.gp	$32490$	$2$	32490.a	1.a	$1$	$12$	$12$	$259.434$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	?	✓			$-1$		$-12$	$0$	$-12$	$6$	$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
32490.2.a.gq	$32490$	$2$	32490.a	1.a	$1$	$12$	$12$	$259.434$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	?				$-1$		$-12$	$0$	$12$	$0$	$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.gr	$32490$	$2$	32490.a	1.a	$1$	$12$	$12$	$259.434$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	?				$-1$		$-12$	$0$	$12$	$6$	$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.gs	$32490$	$2$	32490.a	1.a	$1$	$12$	$12$	$259.434$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	?				$-1$		$12$	$0$	$-12$	$0$	$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.gt	$32490$	$2$	32490.a	1.a	$1$	$12$	$12$	$259.434$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	?				$-1$		$12$	$0$	$-12$	$6$	$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
32490.2.a.gu	$32490$	$2$	32490.a	1.a	$1$	$12$	$12$	$259.434$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	?	✓			$-1$		$12$	$0$	$12$	$0$	$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
32490.2.a.gv	$32490$	$2$	32490.a	1.a	$1$	$12$	$12$	$259.434$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	?	✓			$-1$		$12$	$0$	$12$	$6$	$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(32490))$ 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:	\( N \)	\(=\)	\( 32490 = 2 \cdot 3^{2} \cdot 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	32490.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 178 \)
Sturm bound:			\(13680\)

\(2\)	\(3\)	\(5\)	\(19\)	Fricke	Total			Cusp			Eisenstein
\(2\)	\(3\)	\(5\)	\(19\)	Fricke	All	New	Old	All	New	Old	All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(425\)	\(24\)	\(401\)	\(406\)	\(24\)	\(382\)	\(19\)	\(0\)	\(19\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(449\)	\(33\)	\(416\)	\(429\)	\(33\)	\(396\)	\(20\)	\(0\)	\(20\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(445\)	\(32\)	\(413\)	\(425\)	\(32\)	\(393\)	\(20\)	\(0\)	\(20\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(431\)	\(24\)	\(407\)	\(411\)	\(24\)	\(387\)	\(20\)	\(0\)	\(20\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(445\)	\(40\)	\(405\)	\(425\)	\(40\)	\(385\)	\(20\)	\(0\)	\(20\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(431\)	\(45\)	\(386\)	\(411\)	\(45\)	\(366\)	\(20\)	\(0\)	\(20\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(435\)	\(41\)	\(394\)	\(415\)	\(41\)	\(374\)	\(20\)	\(0\)	\(20\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(439\)	\(45\)	\(394\)	\(419\)	\(45\)	\(374\)	\(20\)	\(0\)	\(20\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(435\)	\(32\)	\(403\)	\(415\)	\(32\)	\(383\)	\(20\)	\(0\)	\(20\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(441\)	\(24\)	\(417\)	\(421\)	\(24\)	\(397\)	\(20\)	\(0\)	\(20\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(435\)	\(24\)	\(411\)	\(415\)	\(24\)	\(391\)	\(20\)	\(0\)	\(20\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(439\)	\(33\)	\(406\)	\(419\)	\(33\)	\(386\)	\(20\)	\(0\)	\(20\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(435\)	\(40\)	\(395\)	\(415\)	\(40\)	\(375\)	\(20\)	\(0\)	\(20\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(439\)	\(45\)	\(394\)	\(419\)	\(45\)	\(374\)	\(20\)	\(0\)	\(20\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(445\)	\(49\)	\(396\)	\(425\)	\(49\)	\(376\)	\(20\)	\(0\)	\(20\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(431\)	\(36\)	\(395\)	\(411\)	\(36\)	\(375\)	\(20\)	\(0\)	\(20\)
Plus space				\(+\)	\(3464\)	\(258\)	\(3206\)	\(3305\)	\(258\)	\(3047\)	\(159\)	\(0\)	\(159\)
Minus space				\(-\)	\(3536\)	\(309\)	\(3227\)	\(3376\)	\(309\)	\(3067\)	\(160\)	\(0\)	\(160\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(32490))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(32490))\) 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	32490.2.a
Level	$32490$
Weight	$2$
Character orbit	32490.a
Rep. character	$\chi_{32490}(1,\cdot)$
Character field	$\Q$
Dimension	$567$
Newform subspaces	$178$
Sturm bound	$13680$