LMFDB - Space of modular forms of level 16830, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 16830 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	16830.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 137 $
Sturm bound:			$7776$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(16830))$.

	Total	New	Old
Modular forms	3920	272	3648
Cusp forms	3857	272	3585
Eisenstein series	63	0	63

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

$2$	$3$	$5$	$11$	$17$	Fricke	Total			Cusp			Eisenstein
$2$	$3$	$5$	$11$	$17$	Fricke	All	New	Old	All	New	Old	All	New	Old
$+$	$+$	$+$	$+$	$+$	$+$	$107$	$5$	$102$	$106$	$5$	$101$	$1$	$0$	$1$
$+$	$+$	$+$	$+$	$-$	$-$	$131$	$8$	$123$	$129$	$8$	$121$	$2$	$0$	$2$
$+$	$+$	$+$	$-$	$+$	$-$	$137$	$9$	$128$	$135$	$9$	$126$	$2$	$0$	$2$
$+$	$+$	$+$	$-$	$-$	$+$	$115$	$6$	$109$	$113$	$6$	$107$	$2$	$0$	$2$
$+$	$+$	$-$	$+$	$+$	$-$	$131$	$7$	$124$	$129$	$7$	$122$	$2$	$0$	$2$
$+$	$+$	$-$	$+$	$-$	$+$	$121$	$6$	$115$	$119$	$6$	$113$	$2$	$0$	$2$
$+$	$+$	$-$	$-$	$+$	$+$	$115$	$7$	$108$	$113$	$7$	$106$	$2$	$0$	$2$
$+$	$+$	$-$	$-$	$-$	$-$	$123$	$8$	$115$	$121$	$8$	$113$	$2$	$0$	$2$
$+$	$-$	$+$	$+$	$+$	$-$	$126$	$10$	$116$	$124$	$10$	$114$	$2$	$0$	$2$
$+$	$-$	$+$	$+$	$-$	$+$	$123$	$10$	$113$	$121$	$10$	$111$	$2$	$0$	$2$
$+$	$-$	$+$	$-$	$+$	$+$	$120$	$8$	$112$	$118$	$8$	$110$	$2$	$0$	$2$
$+$	$-$	$+$	$-$	$-$	$-$	$121$	$11$	$110$	$119$	$11$	$108$	$2$	$0$	$2$
$+$	$-$	$-$	$+$	$+$	$+$	$119$	$11$	$108$	$117$	$11$	$106$	$2$	$0$	$2$
$+$	$-$	$-$	$+$	$-$	$-$	$122$	$10$	$112$	$120$	$10$	$110$	$2$	$0$	$2$
$+$	$-$	$-$	$-$	$+$	$-$	$125$	$11$	$114$	$123$	$11$	$112$	$2$	$0$	$2$
$+$	$-$	$-$	$-$	$-$	$+$	$124$	$9$	$115$	$122$	$9$	$113$	$2$	$0$	$2$
$-$	$+$	$+$	$+$	$+$	$-$	$119$	$8$	$111$	$117$	$8$	$109$	$2$	$0$	$2$
$-$	$+$	$+$	$+$	$-$	$+$	$125$	$7$	$118$	$123$	$7$	$116$	$2$	$0$	$2$
$-$	$+$	$+$	$-$	$+$	$+$	$125$	$6$	$119$	$123$	$6$	$117$	$2$	$0$	$2$
$-$	$+$	$+$	$-$	$-$	$-$	$121$	$7$	$114$	$119$	$7$	$112$	$2$	$0$	$2$
$-$	$+$	$-$	$+$	$+$	$+$	$133$	$6$	$127$	$131$	$6$	$125$	$2$	$0$	$2$
$-$	$+$	$-$	$+$	$-$	$-$	$113$	$9$	$104$	$111$	$9$	$102$	$2$	$0$	$2$
$-$	$+$	$-$	$-$	$+$	$-$	$113$	$8$	$105$	$111$	$8$	$103$	$2$	$0$	$2$
$-$	$+$	$-$	$-$	$-$	$+$	$131$	$5$	$126$	$129$	$5$	$124$	$2$	$0$	$2$
$-$	$-$	$+$	$+$	$+$	$+$	$124$	$10$	$114$	$122$	$10$	$112$	$2$	$0$	$2$
$-$	$-$	$+$	$+$	$-$	$-$	$125$	$9$	$116$	$123$	$9$	$114$	$2$	$0$	$2$
$-$	$-$	$+$	$-$	$+$	$-$	$122$	$11$	$111$	$120$	$11$	$109$	$2$	$0$	$2$
$-$	$-$	$+$	$-$	$-$	$+$	$119$	$9$	$110$	$117$	$9$	$108$	$2$	$0$	$2$
$-$	$-$	$-$	$+$	$+$	$-$	$121$	$10$	$111$	$119$	$10$	$109$	$2$	$0$	$2$
$-$	$-$	$-$	$+$	$-$	$+$	$120$	$10$	$110$	$118$	$10$	$108$	$2$	$0$	$2$
$-$	$-$	$-$	$-$	$+$	$+$	$123$	$9$	$114$	$121$	$9$	$112$	$2$	$0$	$2$
$-$	$-$	$-$	$-$	$-$	$-$	$126$	$12$	$114$	$124$	$12$	$112$	$2$	$0$	$2$
Plus space					$+$	$1944$	$124$	$1820$	$1913$	$124$	$1789$	$31$	$0$	$31$
Minus space					$-$	$1976$	$148$	$1828$	$1944$	$148$	$1796$	$32$	$0$	$32$

Trace form

$ 272 q + 272 q^{4} + 4 q^{5} + 8 q^{14} + 272 q^{16} + 4 q^{20} - 4 q^{22} - 8 q^{23} + 272 q^{25} - 8 q^{26} + 8 q^{29} - 8 q^{31} + 24 q^{37} - 24 q^{38} - 24 q^{41} + 16 q^{43} - 40 q^{46} - 32 q^{47}+ \cdots - 64 q^{98}+O(q^{100}) $

272 * q + 272 * q^4 + 4 * q^5 + 8 * q^14 + 272 * q^16 + 4 * q^20 - 4 * q^22 - 8 * q^23 + 272 * q^25 - 8 * q^26 + 8 * q^29 - 8 * q^31 + 24 * q^37 - 24 * q^38 - 24 * q^41 + 16 * q^43 - 40 * q^46 - 32 * q^47 + 272 * q^49 - 40 * q^53 + 8 * q^56 - 16 * q^58 - 40 * q^59 - 104 * q^61 - 32 * q^62 + 272 * q^64 - 16 * q^65 - 8 * q^67 - 24 * q^70 - 40 * q^71 - 32 * q^73 - 16 * q^74 - 8 * q^77 + 80 * q^79 + 4 * q^80 + 16 * q^82 - 32 * q^83 - 48 * q^86 - 4 * q^88 - 24 * q^89 - 80 * q^91 - 8 * q^92 - 8 * q^94 - 8 * q^97 - 64 * q^98

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(16830))$ 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	11	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
16830.2.a.a	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$-4$	$+$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots$
16830.2.a.b	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$-4$	$+$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots$
16830.2.a.c	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$-4$	$+$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots$
16830.2.a.d	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$-4$	$+$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots$
16830.2.a.e	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$-2$	$+$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots$
16830.2.a.f	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$-2$	$+$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots$
16830.2.a.g	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$-2$	$+$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots$
16830.2.a.h	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$-1$	$+$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots$
16830.2.a.i	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$0$	$+$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-q^{11}+\cdots$
16830.2.a.j	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$0$	$+$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-q^{11}+\cdots$
16830.2.a.k	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$0$	$+$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+q^{11}+\cdots$
16830.2.a.l	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$0$	$+$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+q^{11}+\cdots$
16830.2.a.m	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$1$	$+$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots$
16830.2.a.n	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$1$	$+$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots$
16830.2.a.o	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$1$	$+$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots$
16830.2.a.p	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$2$	$+$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\cdots$
16830.2.a.q	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$3$	$+$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+3q^{7}-q^{8}+q^{10}+\cdots$
16830.2.a.r	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$3$	$+$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+3q^{7}-q^{8}+q^{10}+\cdots$
16830.2.a.s	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$-1$	$4$	$+$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+4q^{7}-q^{8}+q^{10}+\cdots$
16830.2.a.t	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$-4$	$+$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots$
16830.2.a.u	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$-4$	$+$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots$
16830.2.a.v	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$-4$	$+$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots$
16830.2.a.w	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$-4$	$+$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots$
16830.2.a.x	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$-4$	$+$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots$
16830.2.a.y	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$-2$	$+$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots$
16830.2.a.z	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$-1$	$+$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
16830.2.a.ba	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$-1$	$+$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
16830.2.a.bb	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$-1$	$+$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
16830.2.a.bc	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$-1$	$+$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
16830.2.a.bd	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$0$	$+$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-q^{11}+\cdots$
16830.2.a.be	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$4$	$+$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+4q^{7}-q^{8}-q^{10}+\cdots$
16830.2.a.bf	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$4$	$+$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+4q^{7}-q^{8}-q^{10}+\cdots$
16830.2.a.bg	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$4$	$+$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+4q^{7}-q^{8}-q^{10}+\cdots$
16830.2.a.bh	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$1$	$5$	$+$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+5q^{7}-q^{8}-q^{10}+\cdots$
16830.2.a.bi	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$-4$	$-$	$+$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots$
16830.2.a.bj	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$-4$	$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots$
16830.2.a.bk	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$-4$	$-$	$-$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots$
16830.2.a.bl	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$-4$	$-$	$+$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots$
16830.2.a.bm	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$-3$	$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-3q^{7}+q^{8}-q^{10}+\cdots$
16830.2.a.bn	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$-1$	$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots$
16830.2.a.bo	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$-1$	$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots$
16830.2.a.bp	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$-1$	$-$	$+$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots$
16830.2.a.bq	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$0$	$-$	$-$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-q^{11}+\cdots$
16830.2.a.br	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$0$	$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{11}+\cdots$
16830.2.a.bs	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$2$	$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots$
16830.2.a.bt	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$2$	$-$	$-$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots$
16830.2.a.bu	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$2$	$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots$
16830.2.a.bv	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$3$	$-$	$-$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+3q^{7}+q^{8}-q^{10}+\cdots$
16830.2.a.bw	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$4$	$-$	$+$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+4q^{7}+q^{8}-q^{10}+\cdots$
16830.2.a.bx	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$-1$	$4$	$-$	$-$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+4q^{7}+q^{8}-q^{10}+\cdots$
16830.2.a.by	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$-4$	$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots$
16830.2.a.bz	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$-4$	$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots$
16830.2.a.ca	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$-4$	$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots$
16830.2.a.cb	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$-3$	$-$	$-$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-3q^{7}+q^{8}+q^{10}+\cdots$
16830.2.a.cc	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$-3$	$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-3q^{7}+q^{8}+q^{10}+\cdots$
16830.2.a.cd	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$-2$	$-$	$-$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-2q^{7}+q^{8}+q^{10}+\cdots$
16830.2.a.ce	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$-2$	$-$	$-$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-2q^{7}+q^{8}+q^{10}+\cdots$
16830.2.a.cf	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$-2$	$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-2q^{7}+q^{8}+q^{10}+\cdots$
16830.2.a.cg	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$-1$	$-$	$+$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots$
16830.2.a.ch	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$0$	$-$	$-$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-q^{11}+\cdots$
16830.2.a.ci	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$0$	$-$	$-$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-q^{11}+\cdots$
16830.2.a.cj	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$0$	$-$	$+$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-q^{11}+\cdots$
16830.2.a.ck	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$0$	$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+q^{11}+\cdots$
16830.2.a.cl	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$0$	$-$	$-$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+q^{11}+\cdots$
16830.2.a.cm	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$0$	$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+q^{11}+\cdots$
16830.2.a.cn	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$0$	$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+q^{11}+\cdots$
16830.2.a.co	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$0$	$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+q^{11}+\cdots$
16830.2.a.cp	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$0$	$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+q^{11}+\cdots$
16830.2.a.cq	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$1$	$-$	$+$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots$
16830.2.a.cr	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$1$	$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots$
16830.2.a.cs	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$1$	$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots$
16830.2.a.ct	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$1$	$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots$
16830.2.a.cu	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$2$	$-$	$-$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots$
16830.2.a.cv	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$2$	$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots$
16830.2.a.cw	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$3$	$-$	$-$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+3q^{7}+q^{8}+q^{10}+\cdots$
16830.2.a.cx	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$3$	$-$	$+$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+3q^{7}+q^{8}+q^{10}+\cdots$
16830.2.a.cy	$16830$	$2$	16830.a	1.a	$1$	$1$	$1$	$134.388$	$\Q$	None	✓	?				$-1$		$1$	$0$	$1$	$4$	$-$	$-$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+4q^{7}+q^{8}+q^{10}+\cdots$
16830.2.a.cz	$16830$	$2$	16830.a	1.a	$1$	$2$	$2$	$134.388$	$\Q(\sqrt{41}) $	None	✓	?				$-1$		$-2$	$0$	$-2$	$-3$	$+$	$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
16830.2.a.da	$16830$	$2$	16830.a	1.a	$1$	$2$	$2$	$134.388$	$\Q(\sqrt{17}) $	None	✓	?				$-1$		$-2$	$0$	$-2$	$0$	$+$	$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
16830.2.a.db	$16830$	$2$	16830.a	1.a	$1$	$2$	$2$	$134.388$	$\Q(\sqrt{33}) $	None	✓	?				$-1$		$-2$	$0$	$-2$	$1$	$+$	$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
16830.2.a.dc	$16830$	$2$	16830.a	1.a	$1$	$2$	$2$	$134.388$	$\Q(\sqrt{41}) $	None	✓	?				$-1$		$-2$	$0$	$2$	$-3$	$+$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
16830.2.a.dd	$16830$	$2$	16830.a	1.a	$1$	$2$	$2$	$134.388$	$\Q(\sqrt{33}) $	None	✓	?				$-1$		$-2$	$0$	$2$	$-1$	$+$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
16830.2.a.de	$16830$	$2$	16830.a	1.a	$1$	$2$	$2$	$134.388$	$\Q(\sqrt{2}) $	None	✓	?				$-1$		$-2$	$0$	$2$	$0$	$+$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
16830.2.a.df	$16830$	$2$	16830.a	1.a	$1$	$2$	$2$	$134.388$	$\Q(\sqrt{17}) $	None	✓	?				$-1$		$-2$	$0$	$2$	$0$	$+$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
16830.2.a.dg	$16830$	$2$	16830.a	1.a	$1$	$2$	$2$	$134.388$	$\Q(\sqrt{2}) $	None	✓	?				$-1$		$-2$	$0$	$2$	$0$	$+$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
16830.2.a.dh	$16830$	$2$	16830.a	1.a	$1$	$2$	$2$	$134.388$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-2$	$0$	$2$	$2$	$+$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
16830.2.a.di	$16830$	$2$	16830.a	1.a	$1$	$2$	$2$	$134.388$	$\Q(\sqrt{41}) $	None	✓	?				$-1$		$2$	$0$	$-2$	$-3$	$-$	$+$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
16830.2.a.dj	$16830$	$2$	16830.a	1.a	$1$	$2$	$2$	$134.388$	$\Q(\sqrt{33}) $	None	✓	?				$-1$		$2$	$0$	$-2$	$-1$	$-$	$-$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
16830.2.a.dk	$16830$	$2$	16830.a	1.a	$1$	$2$	$2$	$134.388$	$\Q(\sqrt{33}) $	None	✓	?				$-1$		$2$	$0$	$-2$	$-1$	$-$	$+$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
16830.2.a.dl	$16830$	$2$	16830.a	1.a	$1$	$2$	$2$	$134.388$	$\Q(\sqrt{2}) $	None	✓	?				$-1$		$2$	$0$	$-2$	$0$	$-$	$-$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
16830.2.a.dm	$16830$	$2$	16830.a	1.a	$1$	$2$	$2$	$134.388$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$2$	$0$	$-2$	$2$	$-$	$-$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
16830.2.a.dn	$16830$	$2$	16830.a	1.a	$1$	$2$	$2$	$134.388$	$\Q(\sqrt{3}) $	None	✓	?				$-1$		$2$	$0$	$-2$	$2$	$-$	$-$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
16830.2.a.do	$16830$	$2$	16830.a	1.a	$1$	$2$	$2$	$134.388$	$\Q(\sqrt{17}) $	None	✓	?				$-1$		$2$	$0$	$2$	$-2$	$-$	$-$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
16830.2.a.dp	$16830$	$2$	16830.a	1.a	$1$	$2$	$2$	$134.388$	$\Q(\sqrt{17}) $	None	✓	?				$-1$		$2$	$0$	$2$	$-1$	$-$	$-$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
16830.2.a.dq	$16830$	$2$	16830.a	1.a	$1$	$2$	$2$	$134.388$	$\Q(\sqrt{41}) $	None	✓	?				$-1$		$2$	$0$	$2$	$-1$	$-$	$-$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
16830.2.a.dr	$16830$	$2$	16830.a	1.a	$1$	$2$	$2$	$134.388$	$\Q(\sqrt{33}) $	None	✓	?				$-1$		$2$	$0$	$2$	$1$	$-$	$-$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
16830.2.a.ds	$16830$	$2$	16830.a	1.a	$1$	$2$	$2$	$134.388$	$\Q(\sqrt{13}) $	None	✓	?	✓			$-1$		$2$	$0$	$2$	$2$	$-$	$-$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
16830.2.a.dt	$16830$	$2$	16830.a	1.a	$1$	$3$	$3$	$134.388$	3.3.148.1	None	✓	?				$-1$		$-3$	$0$	$-3$	$-6$	$+$	$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
16830.2.a.du	$16830$	$2$	16830.a	1.a	$1$	$3$	$3$	$134.388$	3.3.2089.1	None	✓	?				$-1$		$-3$	$0$	$-3$	$-2$	$+$	$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
16830.2.a.dv	$16830$	$2$	16830.a	1.a	$1$	$3$	$3$	$134.388$	$\Q(\zeta_{14})^+$	None	✓	?				$-1$		$-3$	$0$	$-3$	$-2$	$+$	$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
16830.2.a.dw	$16830$	$2$	16830.a	1.a	$1$	$3$	$3$	$134.388$	3.3.1396.1	None	✓	?	✓			$-1$		$-3$	$0$	$-3$	$0$	$+$	$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
16830.2.a.dx	$16830$	$2$	16830.a	1.a	$1$	$3$	$3$	$134.388$	3.3.756.1	None	✓	?				$-1$		$-3$	$0$	$-3$	$6$	$+$	$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
16830.2.a.dy	$16830$	$2$	16830.a	1.a	$1$	$3$	$3$	$134.388$	3.3.940.1	None	✓	?	✓			$-1$		$-3$	$0$	$3$	$-2$	$+$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
16830.2.a.dz	$16830$	$2$	16830.a	1.a	$1$	$3$	$3$	$134.388$	3.3.2089.1	None	✓	?				$-1$		$-3$	$0$	$3$	$1$	$+$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
16830.2.a.ea	$16830$	$2$	16830.a	1.a	$1$	$3$	$3$	$134.388$	3.3.148.1	None	✓	?	✓			$-1$		$-3$	$0$	$3$	$2$	$+$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
16830.2.a.eb	$16830$	$2$	16830.a	1.a	$1$	$3$	$3$	$134.388$	3.3.1101.1	None	✓	?				$-1$		$-3$	$0$	$3$	$5$	$+$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
16830.2.a.ec	$16830$	$2$	16830.a	1.a	$1$	$3$	$3$	$134.388$	3.3.148.1	None	✓	?				$-1$		$3$	$0$	$-3$	$-4$	$-$	$-$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
16830.2.a.ed	$16830$	$2$	16830.a	1.a	$1$	$3$	$3$	$134.388$	3.3.148.1	None	✓	?	✓			$-1$		$3$	$0$	$-3$	$-4$	$-$	$-$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
16830.2.a.ee	$16830$	$2$	16830.a	1.a	$1$	$3$	$3$	$134.388$	3.3.961.1	None	✓	?	✓			$-1$		$3$	$0$	$-3$	$1$	$-$	$-$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
16830.2.a.ef	$16830$	$2$	16830.a	1.a	$1$	$3$	$3$	$134.388$	3.3.148.1	None	✓	?	✓			$-1$		$3$	$0$	$-3$	$2$	$-$	$+$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
16830.2.a.eg	$16830$	$2$	16830.a	1.a	$1$	$3$	$3$	$134.388$	3.3.2089.1	None	✓	?				$-1$		$3$	$0$	$-3$	$3$	$-$	$-$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
16830.2.a.eh	$16830$	$2$	16830.a	1.a	$1$	$3$	$3$	$134.388$	3.3.1101.1	None	✓	?				$-1$		$3$	$0$	$-3$	$5$	$-$	$+$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
16830.2.a.ei	$16830$	$2$	16830.a	1.a	$1$	$3$	$3$	$134.388$	3.3.756.1	None	✓	?	✓			$-1$		$3$	$0$	$-3$	$6$	$-$	$-$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
16830.2.a.ej	$16830$	$2$	16830.a	1.a	$1$	$3$	$3$	$134.388$	3.3.2089.1	None	✓	?				$-1$		$3$	$0$	$3$	$-2$	$-$	$+$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
16830.2.a.ek	$16830$	$2$	16830.a	1.a	$1$	$3$	$3$	$134.388$	3.3.1396.1	None	✓	?	✓			$-1$		$3$	$0$	$3$	$0$	$-$	$+$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
16830.2.a.el	$16830$	$2$	16830.a	1.a	$1$	$3$	$3$	$134.388$	$\Q(\zeta_{18})^+$	None	✓	?	✓			$-1$		$3$	$0$	$3$	$0$	$-$	$-$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
16830.2.a.em	$16830$	$2$	16830.a	1.a	$1$	$3$	$3$	$134.388$	3.3.564.1	None	✓	?				$-1$		$3$	$0$	$3$	$2$	$-$	$-$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
16830.2.a.en	$16830$	$2$	16830.a	1.a	$1$	$3$	$3$	$134.388$	3.3.756.1	None	✓	?				$-1$		$3$	$0$	$3$	$6$	$-$	$+$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
16830.2.a.eo	$16830$	$2$	16830.a	1.a	$1$	$4$	$4$	$134.388$	4.4.25492.1	None	✓	?				$-1$		$-4$	$0$	$-4$	$0$	$+$	$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
16830.2.a.ep	$16830$	$2$	16830.a	1.a	$1$	$4$	$4$	$134.388$	4.4.23252.1	None	✓	?	✓			$-1$		$-4$	$0$	$4$	$-4$	$+$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
16830.2.a.eq	$16830$	$2$	16830.a	1.a	$1$	$4$	$4$	$134.388$	4.4.25492.1	None	✓	?	✓			$-1$		$-4$	$0$	$4$	$1$	$+$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
16830.2.a.er	$16830$	$2$	16830.a	1.a	$1$	$4$	$4$	$134.388$	4.4.65905.1	None	✓	?	✓			$-1$		$-4$	$0$	$4$	$1$	$+$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
16830.2.a.es	$16830$	$2$	16830.a	1.a	$1$	$4$	$4$	$134.388$	4.4.17428.1	None	✓	?				$-1$		$-4$	$0$	$4$	$2$	$+$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
16830.2.a.et	$16830$	$2$	16830.a	1.a	$1$	$4$	$4$	$134.388$	4.4.145108.1	None	✓	?	✓			$-1$		$-4$	$0$	$4$	$3$	$+$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
16830.2.a.eu	$16830$	$2$	16830.a	1.a	$1$	$4$	$4$	$134.388$	4.4.54764.1	None	✓	?				$-1$		$-4$	$0$	$4$	$4$	$+$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
16830.2.a.ev	$16830$	$2$	16830.a	1.a	$1$	$4$	$4$	$134.388$	4.4.2777.1	None	✓	?	✓			$-1$		$4$	$0$	$-4$	$-1$	$-$	$-$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
16830.2.a.ew	$16830$	$2$	16830.a	1.a	$1$	$4$	$4$	$134.388$	4.4.25492.1	None	✓	?	✓			$-1$		$4$	$0$	$-4$	$1$	$-$	$+$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
16830.2.a.ex	$16830$	$2$	16830.a	1.a	$1$	$4$	$4$	$134.388$	4.4.145108.1	None	✓	?	✓			$-1$		$4$	$0$	$-4$	$3$	$-$	$+$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
16830.2.a.ey	$16830$	$2$	16830.a	1.a	$1$	$4$	$4$	$134.388$	4.4.17428.1	None	✓	?	✓			$-1$		$4$	$0$	$4$	$5$	$-$	$-$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
16830.2.a.ez	$16830$	$2$	16830.a	1.a	$1$	$5$	$5$	$134.388$	5.5.1284160.1	None	✓	?	✓			$-1$		$-5$	$0$	$-5$	$1$	$+$	$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
16830.2.a.fa	$16830$	$2$	16830.a	1.a	$1$	$5$	$5$	$134.388$	5.5.18569692.1	None	✓	?	✓			$-1$		$-5$	$0$	$-5$	$2$	$+$	$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
16830.2.a.fb	$16830$	$2$	16830.a	1.a	$1$	$5$	$5$	$134.388$	5.5.19985813.1	None	✓	?	✓			$-1$		$-5$	$0$	$-5$	$2$	$+$	$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
16830.2.a.fc	$16830$	$2$	16830.a	1.a	$1$	$5$	$5$	$134.388$	5.5.3102944.1	None	✓	?	✓			$-1$		$5$	$0$	$5$	$-8$	$-$	$-$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
16830.2.a.fd	$16830$	$2$	16830.a	1.a	$1$	$6$	$6$	$134.388$	6.6.133649728.1	None	✓	?	✓			$-1$		$-6$	$0$	$6$	$2$	$+$	$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
16830.2.a.fe	$16830$	$2$	16830.a	1.a	$1$	$6$	$6$	$134.388$	6.6.133649728.1	None	✓	?	✓			$-1$		$6$	$0$	$-6$	$2$	$-$	$+$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
16830.2.a.ff	$16830$	$2$	16830.a	1.a	$1$	$8$	$8$	$134.388$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	?	✓			$-1$		$-8$	$0$	$-8$	$1$	$+$	$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
16830.2.a.fg	$16830$	$2$	16830.a	1.a	$1$	$8$	$8$	$134.388$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	?	✓			$-1$		$8$	$0$	$8$	$1$	$-$	$+$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(16830))$ 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:	\( N \)	\(=\)	\( 16830 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	16830.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 137 \)
Sturm bound:			\(7776\)

\(2\)	\(3\)	\(5\)	\(11\)	\(17\)	Fricke	Total			Cusp			Eisenstein
\(2\)	\(3\)	\(5\)	\(11\)	\(17\)	Fricke	All	New	Old	All	New	Old	All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(107\)	\(5\)	\(102\)	\(106\)	\(5\)	\(101\)	\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(131\)	\(8\)	\(123\)	\(129\)	\(8\)	\(121\)	\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(137\)	\(9\)	\(128\)	\(135\)	\(9\)	\(126\)	\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(115\)	\(6\)	\(109\)	\(113\)	\(6\)	\(107\)	\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(131\)	\(7\)	\(124\)	\(129\)	\(7\)	\(122\)	\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(121\)	\(6\)	\(115\)	\(119\)	\(6\)	\(113\)	\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(115\)	\(7\)	\(108\)	\(113\)	\(7\)	\(106\)	\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(123\)	\(8\)	\(115\)	\(121\)	\(8\)	\(113\)	\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(126\)	\(10\)	\(116\)	\(124\)	\(10\)	\(114\)	\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(123\)	\(10\)	\(113\)	\(121\)	\(10\)	\(111\)	\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(120\)	\(8\)	\(112\)	\(118\)	\(8\)	\(110\)	\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(121\)	\(11\)	\(110\)	\(119\)	\(11\)	\(108\)	\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(119\)	\(11\)	\(108\)	\(117\)	\(11\)	\(106\)	\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(122\)	\(10\)	\(112\)	\(120\)	\(10\)	\(110\)	\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(125\)	\(11\)	\(114\)	\(123\)	\(11\)	\(112\)	\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(124\)	\(9\)	\(115\)	\(122\)	\(9\)	\(113\)	\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(+\)	\(+\)	\(-\)	\(119\)	\(8\)	\(111\)	\(117\)	\(8\)	\(109\)	\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(+\)	\(125\)	\(7\)	\(118\)	\(123\)	\(7\)	\(116\)	\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(+\)	\(125\)	\(6\)	\(119\)	\(123\)	\(6\)	\(117\)	\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	\(-\)	\(-\)	\(121\)	\(7\)	\(114\)	\(119\)	\(7\)	\(112\)	\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(+\)	\(133\)	\(6\)	\(127\)	\(131\)	\(6\)	\(125\)	\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)	\(-\)	\(-\)	\(113\)	\(9\)	\(104\)	\(111\)	\(9\)	\(102\)	\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(-\)	\(+\)	\(-\)	\(113\)	\(8\)	\(105\)	\(111\)	\(8\)	\(103\)	\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(+\)	\(131\)	\(5\)	\(126\)	\(129\)	\(5\)	\(124\)	\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(+\)	\(124\)	\(10\)	\(114\)	\(122\)	\(10\)	\(112\)	\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	\(-\)	\(-\)	\(125\)	\(9\)	\(116\)	\(123\)	\(9\)	\(114\)	\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(-\)	\(+\)	\(-\)	\(122\)	\(11\)	\(111\)	\(120\)	\(11\)	\(109\)	\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(+\)	\(119\)	\(9\)	\(110\)	\(117\)	\(9\)	\(108\)	\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(+\)	\(+\)	\(-\)	\(121\)	\(10\)	\(111\)	\(119\)	\(10\)	\(109\)	\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(+\)	\(120\)	\(10\)	\(110\)	\(118\)	\(10\)	\(108\)	\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(+\)	\(123\)	\(9\)	\(114\)	\(121\)	\(9\)	\(112\)	\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)	\(-\)	\(-\)	\(126\)	\(12\)	\(114\)	\(124\)	\(12\)	\(112\)	\(2\)	\(0\)	\(2\)
Plus space					\(+\)	\(1944\)	\(124\)	\(1820\)	\(1913\)	\(124\)	\(1789\)	\(31\)	\(0\)	\(31\)
Minus space					\(-\)	\(1976\)	\(148\)	\(1828\)	\(1944\)	\(148\)	\(1796\)	\(32\)	\(0\)	\(32\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(16830))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(16830))\) 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	16830.2.a
Level	$16830$
Weight	$2$
Character orbit	16830.a
Rep. character	$\chi_{16830}(1,\cdot)$
Character field	$\Q$
Dimension	$272$
Newform subspaces	$137$
Sturm bound	$7776$