LMFDB - Space of modular forms of level 5082, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 5082 = 2 \cdot 3 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5082.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 59 $
Sturm bound:			$2112$
Trace bound:			$13$
Distinguishing $T_p$:			$5$, $13$, $17$, $19$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(5082))$.

	Total	New	Old
Modular forms	1104	110	994
Cusp forms	1009	110	899
Eisenstein series	95	0	95

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

$2$	$3$	$7$	$11$	Fricke	Total			Cusp			Eisenstein
$2$	$3$	$7$	$11$	Fricke	All	New	Old	All	New	Old	All	New	Old
$+$	$+$	$+$	$+$	$+$	$60$	$7$	$53$	$55$	$7$	$48$	$5$	$0$	$5$
$+$	$+$	$+$	$-$	$-$	$77$	$6$	$71$	$71$	$6$	$65$	$6$	$0$	$6$
$+$	$+$	$-$	$+$	$-$	$72$	$8$	$64$	$66$	$8$	$58$	$6$	$0$	$6$
$+$	$+$	$-$	$-$	$+$	$66$	$6$	$60$	$60$	$6$	$54$	$6$	$0$	$6$
$+$	$-$	$+$	$+$	$-$	$72$	$8$	$64$	$66$	$8$	$58$	$6$	$0$	$6$
$+$	$-$	$+$	$-$	$+$	$67$	$6$	$61$	$61$	$6$	$55$	$6$	$0$	$6$
$+$	$-$	$-$	$+$	$+$	$72$	$7$	$65$	$66$	$7$	$59$	$6$	$0$	$6$
$+$	$-$	$-$	$-$	$-$	$66$	$6$	$60$	$60$	$6$	$54$	$6$	$0$	$6$
$-$	$+$	$+$	$+$	$-$	$72$	$10$	$62$	$66$	$10$	$56$	$6$	$0$	$6$
$-$	$+$	$+$	$-$	$+$	$66$	$4$	$62$	$60$	$4$	$56$	$6$	$0$	$6$
$-$	$+$	$-$	$+$	$+$	$66$	$5$	$61$	$60$	$5$	$55$	$6$	$0$	$6$
$-$	$+$	$-$	$-$	$-$	$73$	$9$	$64$	$67$	$9$	$58$	$6$	$0$	$6$
$-$	$-$	$+$	$+$	$+$	$72$	$5$	$67$	$66$	$5$	$61$	$6$	$0$	$6$
$-$	$-$	$+$	$-$	$-$	$66$	$9$	$57$	$60$	$9$	$51$	$6$	$0$	$6$
$-$	$-$	$-$	$+$	$-$	$66$	$10$	$56$	$60$	$10$	$50$	$6$	$0$	$6$
$-$	$-$	$-$	$-$	$+$	$71$	$4$	$67$	$65$	$4$	$61$	$6$	$0$	$6$
Plus space				$+$	$540$	$44$	$496$	$493$	$44$	$449$	$47$	$0$	$47$
Minus space				$-$	$564$	$66$	$498$	$516$	$66$	$450$	$48$	$0$	$48$

Trace form

$ 110 q + 2 q^{2} + 110 q^{4} + 4 q^{5} + 2 q^{8} + 110 q^{9} + 4 q^{10} - 12 q^{13} - 8 q^{15} + 110 q^{16} + 4 q^{17} + 2 q^{18} + 4 q^{20} - 2 q^{21} + 114 q^{25} + 4 q^{26} + 28 q^{29} - 8 q^{30} - 32 q^{31}+ \cdots + 2 q^{98}+O(q^{100}) $

110 * q + 2 * q^2 + 110 * q^4 + 4 * q^5 + 2 * q^8 + 110 * q^9 + 4 * q^10 - 12 * q^13 - 8 * q^15 + 110 * q^16 + 4 * q^17 + 2 * q^18 + 4 * q^20 - 2 * q^21 + 114 * q^25 + 4 * q^26 + 28 * q^29 - 8 * q^30 - 32 * q^31 + 2 * q^32 + 4 * q^34 + 8 * q^35 + 110 * q^36 + 4 * q^37 - 8 * q^39 + 4 * q^40 + 20 * q^41 + 2 * q^42 + 4 * q^45 - 8 * q^46 - 16 * q^47 + 110 * q^49 - 2 * q^50 - 8 * q^51 - 12 * q^52 - 4 * q^53 - 24 * q^57 - 4 * q^58 - 8 * q^60 + 4 * q^61 + 110 * q^64 - 8 * q^65 - 24 * q^67 + 4 * q^68 + 2 * q^72 + 4 * q^73 + 28 * q^74 + 8 * q^78 + 48 * q^79 + 4 * q^80 + 110 * q^81 - 12 * q^82 + 16 * q^83 - 2 * q^84 - 8 * q^85 - 8 * q^86 + 36 * q^89 + 4 * q^90 + 8 * q^91 + 8 * q^93 + 16 * q^95 + 20 * q^97 + 2 * q^98

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(5082))$ 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	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5082.2.a.a	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓				462.2.a.e	$1$	$0$	$-1$	$-1$	$-4$	$-1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-q^{7}+\cdots$
5082.2.a.b	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	✓			5082.2.a.b	$1$	$0$	$-1$	$-1$	$-4$	$1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}+q^{7}+\cdots$
5082.2.a.c	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	✓			5082.2.a.c	$1$	$2$	$-1$	$-1$	$-3$	$-1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots$
5082.2.a.d	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓				42.2.a.a	$1$	$1$	$-1$	$-1$	$-2$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots$
5082.2.a.e	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	✓			5082.2.a.e	$1$	$1$	$-1$	$-1$	$0$	$-1$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots$
5082.2.a.f	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	✓			5082.2.a.f	$1$	$1$	$-1$	$-1$	$1$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
5082.2.a.g	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	✓			5082.2.a.g	$1$	$0$	$-1$	$-1$	$2$	$-1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots$
5082.2.a.h	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	✓			5082.2.a.h	$1$	$0$	$-1$	$-1$	$2$	$-1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots$
5082.2.a.i	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	✓			5082.2.a.i	$1$	$0$	$-1$	$-1$	$4$	$1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+4q^{5}+q^{6}+q^{7}+\cdots$
5082.2.a.j	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	✓			5082.2.a.j	$1$	$1$	$-1$	$1$	$-3$	$-1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots$
5082.2.a.k	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	✓			5082.2.a.k	$1$	$1$	$-1$	$1$	$-2$	$1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots$
5082.2.a.l	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓				462.2.a.f	$1$	$1$	$-1$	$1$	$0$	$-1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
5082.2.a.m	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	✓			5082.2.a.m	$1$	$0$	$-1$	$1$	$2$	$1$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots$
5082.2.a.n	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓				462.2.a.g	$1$	$0$	$-1$	$1$	$2$	$1$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots$
5082.2.a.o	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	✓			5082.2.a.b	$1$	$0$	$1$	$-1$	$-4$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-q^{7}+\cdots$
5082.2.a.p	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	✓			5082.2.a.c	$1$	$0$	$1$	$-1$	$-3$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{7}+\cdots$
5082.2.a.q	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓				462.2.a.a	$1$	$1$	$1$	$-1$	$-2$	$-1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots$
5082.2.a.r	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	✓			5082.2.a.e	$1$	$1$	$1$	$-1$	$0$	$1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
5082.2.a.s	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓				462.2.a.b	$1$	$0$	$1$	$-1$	$0$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
5082.2.a.t	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	✓			5082.2.a.f	$1$	$1$	$1$	$-1$	$1$	$-1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
5082.2.a.u	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	✓			5082.2.a.h	$1$	$0$	$1$	$-1$	$2$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots$
5082.2.a.v	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓				462.2.a.c	$1$	$0$	$1$	$-1$	$2$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots$
5082.2.a.w	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	✓			5082.2.a.g	$1$	$0$	$1$	$-1$	$2$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots$
5082.2.a.x	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	✓			5082.2.a.i	$1$	$0$	$1$	$-1$	$4$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}-q^{7}+\cdots$
5082.2.a.y	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	✓			5082.2.a.j	$1$	$1$	$1$	$1$	$-3$	$1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{7}+\cdots$
5082.2.a.z	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	✓			5082.2.a.k	$1$	$1$	$1$	$1$	$-2$	$-1$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-q^{7}+\cdots$
5082.2.a.ba	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓				462.2.a.d	$1$	$1$	$1$	$1$	$0$	$1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots$
5082.2.a.bb	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	✓			5082.2.a.m	$1$	$0$	$1$	$1$	$2$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots$
5082.2.a.bc	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{3}) $	None	✓	✓			5082.2.a.bc	$1$	$0$	$-2$	$-2$	$-4$	$2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots$
5082.2.a.bd	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{5}) $	None	✓		✓		462.2.j.b	$1$	$0$	$-2$	$-2$	$-3$	$-2$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots$
5082.2.a.be	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{3}) $	None	✓	✓			5082.2.a.be	$1$	$1$	$-2$	$-2$	$0$	$-2$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{7}+\cdots$
5082.2.a.bf	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{5}) $	None	✓				462.2.j.d	$1$	$0$	$-2$	$-2$	$1$	$2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}+q^{7}+\cdots$
5082.2.a.bg	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{3}) $	None	✓	✓			5082.2.a.bg	$1$	$0$	$-2$	$-2$	$4$	$2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(2+\beta )q^{5}+q^{6}+\cdots$
5082.2.a.bh	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{5}) $	None	✓				462.2.j.c	$1$	$0$	$-2$	$2$	$-5$	$-2$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(-2-\beta )q^{5}-q^{6}+\cdots$
5082.2.a.bi	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{3}) $	None	✓	✓			5082.2.a.bi	$1$	$1$	$-2$	$2$	$-4$	$2$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(-2+\beta )q^{5}-q^{6}+\cdots$
5082.2.a.bj	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{5}) $	None	✓				462.2.j.a	$1$	$0$	$-2$	$2$	$-1$	$2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}+q^{7}+\cdots$
5082.2.a.bk	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{5}) $	None	✓	✓			5082.2.a.bk	$1$	$0$	$-2$	$2$	$2$	$-2$	$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots$
5082.2.a.bl	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{33}) $	None	✓	✓			5082.2.a.bl	$1$	$0$	$-2$	$2$	$3$	$2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots$
5082.2.a.bm	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{3}) $	None	✓	✓			5082.2.a.bc	$1$	$0$	$2$	$-2$	$-4$	$-2$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots$
5082.2.a.bn	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{5}) $	None	✓				462.2.j.b	$1$	$1$	$2$	$-2$	$-3$	$2$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots$
5082.2.a.bo	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{3}) $	None	✓	✓			5082.2.a.be	$1$	$1$	$2$	$-2$	$0$	$2$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}+q^{7}+\cdots$
5082.2.a.bp	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{5}) $	None	✓		✓		462.2.j.d	$1$	$1$	$2$	$-2$	$1$	$-2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{7}+\cdots$
5082.2.a.bq	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{3}) $	None	✓	✓			5082.2.a.bg	$1$	$0$	$2$	$-2$	$4$	$-2$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(2+\beta )q^{5}-q^{6}+\cdots$
5082.2.a.br	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{5}) $	None	✓		✓		462.2.j.c	$1$	$1$	$2$	$2$	$-5$	$2$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-2-\beta )q^{5}+q^{6}+\cdots$
5082.2.a.bs	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{3}) $	None	✓	✓			5082.2.a.bi	$1$	$1$	$2$	$2$	$-4$	$-2$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-2+\beta )q^{5}+q^{6}+\cdots$
5082.2.a.bt	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{5}) $	None	✓				462.2.j.a	$1$	$1$	$2$	$2$	$-1$	$-2$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-\beta q^{5}+q^{6}-q^{7}+\cdots$
5082.2.a.bu	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{3}) $	None	✓				462.2.a.h	$1$	$0$	$2$	$2$	$0$	$-2$	$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{7}+\cdots$
5082.2.a.bv	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{5}) $	None	✓	✓			5082.2.a.bk	$1$	$0$	$2$	$2$	$2$	$2$	$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots$
5082.2.a.bw	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{33}) $	None	✓	✓			5082.2.a.bl	$1$	$0$	$2$	$2$	$3$	$-2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots$
5082.2.a.bx	$5082$	$2$	5082.a	1.a	$1$	$4$	$4$	$40.580$	4.4.8000.1	None	✓		✓		462.2.j.f	$1$	$1$	$-4$	$-4$	$2$	$4$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots$
5082.2.a.by	$5082$	$2$	5082.a	1.a	$1$	$4$	$4$	$40.580$	4.4.28400.1	None	✓		✓		462.2.j.h	$1$	$1$	$-4$	$-4$	$4$	$-4$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1+\beta _{1})q^{5}+q^{6}+\cdots$
5082.2.a.bz	$5082$	$2$	5082.a	1.a	$1$	$4$	$4$	$40.580$	$\Q(\sqrt{3}, \sqrt{5})$	None	✓		✓		462.2.j.g	$1$	$1$	$-4$	$4$	$0$	$4$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(\beta _{1}+\beta _{3})q^{5}-q^{6}+\cdots$
5082.2.a.ca	$5082$	$2$	5082.a	1.a	$1$	$4$	$4$	$40.580$	4.4.4400.1	None	✓		✓		462.2.j.e	$1$	$1$	$-4$	$4$	$2$	$-4$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots$
5082.2.a.cb	$5082$	$2$	5082.a	1.a	$1$	$4$	$4$	$40.580$	4.4.69264.1	None	✓	✓	✓		5082.2.a.cb	$1$	$0$	$-4$	$4$	$4$	$-4$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(1+\beta _{1}-\beta _{2})q^{5}+\cdots$
5082.2.a.cc	$5082$	$2$	5082.a	1.a	$1$	$4$	$4$	$40.580$	4.4.8000.1	None	✓		✓		462.2.j.f	$1$	$0$	$4$	$-4$	$2$	$-4$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots$
5082.2.a.cd	$5082$	$2$	5082.a	1.a	$1$	$4$	$4$	$40.580$	4.4.28400.1	None	✓		✓		462.2.j.h	$1$	$0$	$4$	$-4$	$4$	$4$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(1+\beta _{1})q^{5}-q^{6}+\cdots$
5082.2.a.ce	$5082$	$2$	5082.a	1.a	$1$	$4$	$4$	$40.580$	$\Q(\sqrt{3}, \sqrt{5})$	None	✓		✓		462.2.j.g	$1$	$0$	$4$	$4$	$0$	$-4$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(\beta _{1}+\beta _{3})q^{5}+q^{6}+\cdots$
5082.2.a.cf	$5082$	$2$	5082.a	1.a	$1$	$4$	$4$	$40.580$	4.4.4400.1	None	✓				462.2.j.e	$1$	$0$	$4$	$4$	$2$	$4$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots$
5082.2.a.cg	$5082$	$2$	5082.a	1.a	$1$	$4$	$4$	$40.580$	4.4.69264.1	None	✓	✓			5082.2.a.cb	$1$	$0$	$4$	$4$	$4$	$4$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(1+\beta _{1}-\beta _{2})q^{5}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(5082))$ 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:	\( N \)	\(=\)	\( 5082 = 2 \cdot 3 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5082.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 59 \)
Sturm bound:			\(2112\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(13\), \(17\), \(19\)

\(2\)	\(3\)	\(7\)	\(11\)	Fricke	Total			Cusp			Eisenstein
\(2\)	\(3\)	\(7\)	\(11\)	Fricke	All	New	Old	All	New	Old	All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(60\)	\(7\)	\(53\)	\(55\)	\(7\)	\(48\)	\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(77\)	\(6\)	\(71\)	\(71\)	\(6\)	\(65\)	\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(72\)	\(8\)	\(64\)	\(66\)	\(8\)	\(58\)	\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(66\)	\(6\)	\(60\)	\(60\)	\(6\)	\(54\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(72\)	\(8\)	\(64\)	\(66\)	\(8\)	\(58\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(67\)	\(6\)	\(61\)	\(61\)	\(6\)	\(55\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(72\)	\(7\)	\(65\)	\(66\)	\(7\)	\(59\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(66\)	\(6\)	\(60\)	\(60\)	\(6\)	\(54\)	\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(72\)	\(10\)	\(62\)	\(66\)	\(10\)	\(56\)	\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(66\)	\(4\)	\(62\)	\(60\)	\(4\)	\(56\)	\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(66\)	\(5\)	\(61\)	\(60\)	\(5\)	\(55\)	\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(73\)	\(9\)	\(64\)	\(67\)	\(9\)	\(58\)	\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(72\)	\(5\)	\(67\)	\(66\)	\(5\)	\(61\)	\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(66\)	\(9\)	\(57\)	\(60\)	\(9\)	\(51\)	\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(66\)	\(10\)	\(56\)	\(60\)	\(10\)	\(50\)	\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(71\)	\(4\)	\(67\)	\(65\)	\(4\)	\(61\)	\(6\)	\(0\)	\(6\)
Plus space				\(+\)	\(540\)	\(44\)	\(496\)	\(493\)	\(44\)	\(449\)	\(47\)	\(0\)	\(47\)
Minus space				\(-\)	\(564\)	\(66\)	\(498\)	\(516\)	\(66\)	\(450\)	\(48\)	\(0\)	\(48\)

Introduction

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Modular forms

Varieties

Fields

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5082))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5082))\) 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	5082.2.a

Level	$5082$
Weight	$2$
Character orbit	5082.a
Rep. character	$\chi_{5082}(1,\cdot)$
Character field	$\Q$
Dimension	$110$
Newform subspaces	$59$
Sturm bound	$2112$
Trace bound	$13$