LMFDB - Space of modular forms of level 6762, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6762.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 74 $
Sturm bound:			$2688$
Trace bound:			$17$
Distinguishing $T_p$:			$5$, $11$, $13$, $17$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(6762))$.

	Total	New	Old
Modular forms	1376	150	1226
Cusp forms	1313	150	1163
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.

$2$	$3$	$7$	$23$	Fricke	Total			Cusp			Eisenstein
$2$	$3$	$7$	$23$	Fricke	All	New	Old	All	New	Old	All	New	Old
$+$	$+$	$+$	$+$	$+$	$76$	$12$	$64$	$73$	$12$	$61$	$3$	$0$	$3$
$+$	$+$	$+$	$-$	$-$	$96$	$8$	$88$	$92$	$8$	$84$	$4$	$0$	$4$
$+$	$+$	$-$	$+$	$-$	$94$	$7$	$87$	$90$	$7$	$83$	$4$	$0$	$4$
$+$	$+$	$-$	$-$	$+$	$78$	$10$	$68$	$74$	$10$	$64$	$4$	$0$	$4$
$+$	$-$	$+$	$+$	$-$	$84$	$11$	$73$	$80$	$11$	$69$	$4$	$0$	$4$
$+$	$-$	$+$	$-$	$+$	$88$	$7$	$81$	$84$	$7$	$77$	$4$	$0$	$4$
$+$	$-$	$-$	$+$	$+$	$90$	$8$	$82$	$86$	$8$	$78$	$4$	$0$	$4$
$+$	$-$	$-$	$-$	$-$	$82$	$11$	$71$	$78$	$11$	$67$	$4$	$0$	$4$
$-$	$+$	$+$	$+$	$-$	$80$	$9$	$71$	$76$	$9$	$67$	$4$	$0$	$4$
$-$	$+$	$+$	$-$	$+$	$92$	$9$	$83$	$88$	$9$	$79$	$4$	$0$	$4$
$-$	$+$	$-$	$+$	$+$	$92$	$9$	$83$	$88$	$9$	$79$	$4$	$0$	$4$
$-$	$+$	$-$	$-$	$-$	$80$	$12$	$68$	$76$	$12$	$64$	$4$	$0$	$4$
$-$	$-$	$+$	$+$	$+$	$80$	$6$	$74$	$76$	$6$	$70$	$4$	$0$	$4$
$-$	$-$	$+$	$-$	$-$	$92$	$14$	$78$	$88$	$14$	$74$	$4$	$0$	$4$
$-$	$-$	$-$	$+$	$-$	$92$	$13$	$79$	$88$	$13$	$75$	$4$	$0$	$4$
$-$	$-$	$-$	$-$	$+$	$80$	$4$	$76$	$76$	$4$	$72$	$4$	$0$	$4$
Plus space				$+$	$676$	$65$	$611$	$645$	$65$	$580$	$31$	$0$	$31$
Minus space				$-$	$700$	$85$	$615$	$668$	$85$	$583$	$32$	$0$	$32$

Trace form

$ 150 q + 2 q^{2} - 2 q^{3} + 150 q^{4} + 4 q^{5} - 2 q^{6} + 2 q^{8} + 150 q^{9} - 2 q^{12} - 4 q^{13} - 4 q^{15} + 150 q^{16} - 4 q^{17} + 2 q^{18} - 12 q^{19} + 4 q^{20} - 12 q^{22} - 2 q^{24} + 146 q^{25}+ \cdots - 12 q^{97}+O(q^{100}) $

150 * q + 2 * q^2 - 2 * q^3 + 150 * q^4 + 4 * q^5 - 2 * q^6 + 2 * q^8 + 150 * q^9 - 2 * q^12 - 4 * q^13 - 4 * q^15 + 150 * q^16 - 4 * q^17 + 2 * q^18 - 12 * q^19 + 4 * q^20 - 12 * q^22 - 2 * q^24 + 146 * q^25 + 12 * q^26 - 2 * q^27 - 4 * q^29 - 16 * q^31 + 2 * q^32 + 4 * q^33 + 12 * q^34 + 150 * q^36 + 32 * q^37 - 8 * q^38 + 36 * q^39 - 12 * q^41 + 60 * q^43 + 4 * q^45 + 4 * q^46 - 24 * q^47 - 2 * q^48 + 86 * q^50 + 8 * q^51 - 4 * q^52 + 76 * q^53 - 2 * q^54 + 16 * q^55 + 60 * q^57 + 68 * q^58 + 8 * q^59 - 4 * q^60 + 24 * q^61 + 8 * q^62 + 150 * q^64 + 40 * q^65 + 20 * q^67 - 4 * q^68 - 4 * q^69 - 40 * q^71 + 2 * q^72 + 12 * q^73 + 52 * q^74 + 2 * q^75 - 12 * q^76 - 4 * q^78 + 4 * q^80 + 150 * q^81 - 4 * q^82 + 24 * q^83 + 72 * q^85 - 16 * q^86 + 12 * q^87 - 12 * q^88 - 4 * q^89 + 32 * q^93 + 8 * q^94 - 24 * q^95 - 2 * q^96 - 12 * q^97

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(6762))$ 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	23	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6762.2.a.a	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.i.e	$1$	$1$	$-1$	$-1$	$-3$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{8}+\cdots$
6762.2.a.b	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.i.g	$1$	$1$	$-1$	$-1$	$-3$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{8}+\cdots$
6762.2.a.c	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓	✓			6762.2.a.c	$1$	$1$	$-1$	$-1$	$-2$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots$
6762.2.a.d	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓	✓			6762.2.a.d	$1$	$1$	$-1$	$-1$	$-2$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots$
6762.2.a.e	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.i.f	$1$	$0$	$-1$	$-1$	$0$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
6762.2.a.f	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.a.e	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
6762.2.a.g	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				138.2.a.b	$1$	$0$	$-1$	$-1$	$0$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
6762.2.a.h	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.a.f	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
6762.2.a.i	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓	✓			6762.2.a.i	$1$	$0$	$-1$	$-1$	$1$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots$
6762.2.a.j	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓	✓			6762.2.a.j	$1$	$1$	$-1$	$-1$	$3$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}-q^{8}+\cdots$
6762.2.a.k	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓	✓			6762.2.a.j	$1$	$0$	$-1$	$1$	$-3$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{8}+\cdots$
6762.2.a.l	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.a.d	$1$	$1$	$-1$	$1$	$-3$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{8}+\cdots$
6762.2.a.m	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.a.c	$1$	$0$	$-1$	$1$	$-2$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{8}+\cdots$
6762.2.a.n	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓	✓			6762.2.a.i	$1$	$1$	$-1$	$1$	$-1$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
6762.2.a.o	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.i.f	$1$	$0$	$-1$	$1$	$0$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
6762.2.a.p	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓	✓			6762.2.a.c	$1$	$0$	$-1$	$1$	$2$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots$
6762.2.a.q	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				138.2.a.a	$1$	$1$	$-1$	$1$	$2$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots$
6762.2.a.r	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.a.b	$1$	$1$	$-1$	$1$	$2$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots$
6762.2.a.s	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓	✓			6762.2.a.d	$1$	$0$	$-1$	$1$	$2$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots$
6762.2.a.t	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.i.e	$1$	$1$	$-1$	$1$	$3$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-q^{8}+\cdots$
6762.2.a.u	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.i.g	$1$	$1$	$-1$	$1$	$3$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-q^{8}+\cdots$
6762.2.a.v	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.a.a	$1$	$0$	$-1$	$1$	$4$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{8}+\cdots$
6762.2.a.w	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.i.a	$1$	$0$	$1$	$-1$	$-4$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}+q^{8}+\cdots$
6762.2.a.x	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.i.d	$1$	$0$	$1$	$-1$	$-3$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{8}+\cdots$
6762.2.a.y	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.a.k	$1$	$0$	$1$	$-1$	$-3$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{8}+\cdots$
6762.2.a.z	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓	✓			6762.2.a.z	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
6762.2.a.ba	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.i.b	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
6762.2.a.bb	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.i.c	$1$	$1$	$1$	$-1$	$1$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
6762.2.a.bc	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.a.j	$1$	$0$	$1$	$-1$	$2$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots$
6762.2.a.bd	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.a.i	$1$	$1$	$1$	$-1$	$3$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+q^{8}+\cdots$
6762.2.a.be	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓	✓			6762.2.a.be	$1$	$0$	$1$	$-1$	$3$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+q^{8}+\cdots$
6762.2.a.bf	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓	✓			6762.2.a.be	$1$	$1$	$1$	$1$	$-3$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{8}+\cdots$
6762.2.a.bg	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				138.2.a.c	$1$	$0$	$1$	$1$	$-2$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots$
6762.2.a.bh	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.i.c	$1$	$1$	$1$	$1$	$-1$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
6762.2.a.bi	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.a.h	$1$	$1$	$1$	$1$	$-1$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
6762.2.a.bj	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓	✓			6762.2.a.z	$1$	$1$	$1$	$1$	$0$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
6762.2.a.bk	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.i.b	$1$	$0$	$1$	$1$	$0$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
6762.2.a.bl	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.a.g	$1$	$0$	$1$	$1$	$2$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{8}+\cdots$
6762.2.a.bm	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.i.d	$1$	$0$	$1$	$1$	$3$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{8}+\cdots$
6762.2.a.bn	$6762$	$2$	6762.a	1.a	$1$	$1$	$1$	$53.995$	$\Q$	None	✓				966.2.i.a	$1$	$0$	$1$	$1$	$4$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+q^{8}+\cdots$
6762.2.a.bo	$6762$	$2$	6762.a	1.a	$1$	$2$	$2$	$53.995$	$\Q(\sqrt{41}) $	None	✓				966.2.a.n	$1$	$1$	$-2$	$-2$	$-1$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-\beta q^{5}+q^{6}-q^{8}+\cdots$
6762.2.a.bp	$6762$	$2$	6762.a	1.a	$1$	$2$	$2$	$53.995$	$\Q(\sqrt{2}) $	None	✓	✓			6762.2.a.bp	$1$	$0$	$-2$	$-2$	$0$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{8}+\cdots$
6762.2.a.bq	$6762$	$2$	6762.a	1.a	$1$	$2$	$2$	$53.995$	$\Q(\sqrt{41}) $	None	✓				966.2.a.m	$1$	$0$	$-2$	$-2$	$1$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{8}+\cdots$
6762.2.a.br	$6762$	$2$	6762.a	1.a	$1$	$2$	$2$	$53.995$	$\Q(\sqrt{17}) $	None	✓				966.2.i.i	$1$	$0$	$-2$	$-2$	$1$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{8}+\cdots$
6762.2.a.bs	$6762$	$2$	6762.a	1.a	$1$	$2$	$2$	$53.995$	$\Q(\sqrt{2}) $	None	✓	✓			6762.2.a.bs	$1$	$0$	$-2$	$-2$	$2$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots$
6762.2.a.bt	$6762$	$2$	6762.a	1.a	$1$	$2$	$2$	$53.995$	$\Q(\sqrt{2}) $	None	✓				966.2.i.j	$1$	$1$	$-2$	$-2$	$2$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots$
6762.2.a.bu	$6762$	$2$	6762.a	1.a	$1$	$2$	$2$	$53.995$	$\Q(\sqrt{2}) $	None	✓	✓			6762.2.a.bs	$1$	$1$	$-2$	$2$	$-2$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(-1+\beta )q^{5}-q^{6}+\cdots$
6762.2.a.bv	$6762$	$2$	6762.a	1.a	$1$	$2$	$2$	$53.995$	$\Q(\sqrt{2}) $	None	✓				966.2.i.j	$1$	$1$	$-2$	$2$	$-2$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(-1+\beta )q^{5}-q^{6}+\cdots$
6762.2.a.bw	$6762$	$2$	6762.a	1.a	$1$	$2$	$2$	$53.995$	$\Q(\sqrt{17}) $	None	✓				966.2.a.l	$1$	$0$	$-2$	$2$	$-1$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}-q^{8}+\cdots$
6762.2.a.bx	$6762$	$2$	6762.a	1.a	$1$	$2$	$2$	$53.995$	$\Q(\sqrt{17}) $	None	✓				966.2.i.i	$1$	$0$	$-2$	$2$	$-1$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}-q^{8}+\cdots$
6762.2.a.by	$6762$	$2$	6762.a	1.a	$1$	$2$	$2$	$53.995$	$\Q(\sqrt{2}) $	None	✓	✓			6762.2.a.bp	$1$	$1$	$-2$	$2$	$0$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{8}+\cdots$
6762.2.a.bz	$6762$	$2$	6762.a	1.a	$1$	$2$	$2$	$53.995$	$\Q(\sqrt{5}) $	None	✓				966.2.a.p	$1$	$1$	$2$	$-2$	$-4$	$0$	$-$	$+$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots$
6762.2.a.ca	$6762$	$2$	6762.a	1.a	$1$	$2$	$2$	$53.995$	$\Q(\sqrt{2}) $	None	✓				966.2.i.h	$1$	$1$	$2$	$-2$	$2$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
6762.2.a.cb	$6762$	$2$	6762.a	1.a	$1$	$2$	$2$	$53.995$	$\Q(\sqrt{5}) $	None	✓				138.2.a.d	$1$	$0$	$2$	$-2$	$2$	$0$	$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots$
6762.2.a.cc	$6762$	$2$	6762.a	1.a	$1$	$2$	$2$	$53.995$	$\Q(\sqrt{2}) $	None	✓				966.2.i.h	$1$	$1$	$2$	$2$	$-2$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
6762.2.a.cd	$6762$	$2$	6762.a	1.a	$1$	$2$	$2$	$53.995$	$\Q(\sqrt{33}) $	None	✓				966.2.a.o	$1$	$0$	$2$	$2$	$3$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots$
6762.2.a.ce	$6762$	$2$	6762.a	1.a	$1$	$3$	$3$	$53.995$	3.3.3132.1	None	✓				966.2.i.k	$1$	$1$	$-3$	$-3$	$3$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots$
6762.2.a.cf	$6762$	$2$	6762.a	1.a	$1$	$3$	$3$	$53.995$	3.3.3132.1	None	✓		✓		966.2.i.k	$1$	$1$	$-3$	$3$	$-3$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
6762.2.a.cg	$6762$	$2$	6762.a	1.a	$1$	$4$	$4$	$53.995$	$\Q(\sqrt{25 +8 \sqrt{7}})$	None	✓		✓		966.2.i.n	$1$	$0$	$-4$	$-4$	$2$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}-q^{8}+\cdots$
6762.2.a.ch	$6762$	$2$	6762.a	1.a	$1$	$4$	$4$	$53.995$	$\Q(\sqrt{25 +8 \sqrt{7}})$	None	✓		✓		966.2.i.n	$1$	$0$	$-4$	$4$	$-2$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}-q^{8}+\cdots$
6762.2.a.ci	$6762$	$2$	6762.a	1.a	$1$	$4$	$4$	$53.995$	$\Q(\sqrt{7 +2 \sqrt{2}})$	None	✓	✓			6762.2.a.ci	$1$	$1$	$4$	$-4$	$-8$	$0$	$-$	$+$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-2-\beta _{1})q^{5}-q^{6}+\cdots$
6762.2.a.cj	$6762$	$2$	6762.a	1.a	$1$	$4$	$4$	$53.995$	4.4.23252.1	None	✓	✓	✓		6762.2.a.cj	$1$	$1$	$4$	$-4$	$-3$	$0$	$-$	$+$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-1+\beta _{3})q^{5}-q^{6}+\cdots$
6762.2.a.ck	$6762$	$2$	6762.a	1.a	$1$	$4$	$4$	$53.995$	$\Q(\sqrt{17 +8 \sqrt{2}})$	None	✓	✓			6762.2.a.ck	$1$	$1$	$4$	$-4$	$2$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}-q^{6}+\cdots$
6762.2.a.cl	$6762$	$2$	6762.a	1.a	$1$	$4$	$4$	$53.995$	4.4.473376.1	None	✓				966.2.i.m	$1$	$0$	$4$	$-4$	$2$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}-q^{6}+\cdots$
6762.2.a.cm	$6762$	$2$	6762.a	1.a	$1$	$4$	$4$	$53.995$	$\Q(\sqrt{27 +6 \sqrt{2}})$	None	✓		✓		966.2.i.l	$1$	$0$	$4$	$-4$	$4$	$0$	$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(1-\beta _{2})q^{5}-q^{6}+\cdots$
6762.2.a.cn	$6762$	$2$	6762.a	1.a	$1$	$4$	$4$	$53.995$	$\Q(\sqrt{17 +4 \sqrt{2}})$	None	✓	✓			6762.2.a.cn	$1$	$0$	$4$	$-4$	$6$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(1+\beta _{1})q^{5}-q^{6}+\cdots$
6762.2.a.co	$6762$	$2$	6762.a	1.a	$1$	$4$	$4$	$53.995$	$\Q(\sqrt{17 +4 \sqrt{2}})$	None	✓	✓	✓		6762.2.a.cn	$1$	$1$	$4$	$4$	$-6$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-1-\beta _{1})q^{5}+q^{6}+\cdots$
6762.2.a.cp	$6762$	$2$	6762.a	1.a	$1$	$4$	$4$	$53.995$	$\Q(\sqrt{27 +6 \sqrt{2}})$	None	✓				966.2.i.l	$1$	$0$	$4$	$4$	$-4$	$0$	$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-1+\beta _{2})q^{5}+q^{6}+\cdots$
6762.2.a.cq	$6762$	$2$	6762.a	1.a	$1$	$4$	$4$	$53.995$	$\Q(\sqrt{17 +8 \sqrt{2}})$	None	✓	✓			6762.2.a.ck	$1$	$0$	$4$	$4$	$-2$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots$
6762.2.a.cr	$6762$	$2$	6762.a	1.a	$1$	$4$	$4$	$53.995$	4.4.473376.1	None	✓				966.2.i.m	$1$	$0$	$4$	$4$	$-2$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}+q^{6}+\cdots$
6762.2.a.cs	$6762$	$2$	6762.a	1.a	$1$	$4$	$4$	$53.995$	4.4.23252.1	None	✓	✓			6762.2.a.cj	$1$	$0$	$4$	$4$	$3$	$0$	$-$	$-$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(1-\beta _{3})q^{5}+q^{6}+\cdots$
6762.2.a.ct	$6762$	$2$	6762.a	1.a	$1$	$4$	$4$	$53.995$	$\Q(\sqrt{7 +2 \sqrt{2}})$	None	✓	✓			6762.2.a.ci	$1$	$0$	$4$	$4$	$8$	$0$	$-$	$-$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(2+\beta _{1})q^{5}+q^{6}+\cdots$
6762.2.a.cu	$6762$	$2$	6762.a	1.a	$1$	$8$	$8$	$53.995$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓		6762.2.a.cu	$1$	$1$	$-8$	$-8$	$-2$	$0$	$+$	$+$	$+$	$+$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-\beta _{7}q^{5}+q^{6}-q^{8}+\cdots$
6762.2.a.cv	$6762$	$2$	6762.a	1.a	$1$	$8$	$8$	$53.995$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓		6762.2.a.cu	$1$	$0$	$-8$	$8$	$2$	$0$	$+$	$-$	$+$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+\beta _{7}q^{5}-q^{6}-q^{8}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(6762))$ into lower level spaces

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6762.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 74 \)
Sturm bound:			\(2688\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(17\)

\(2\)	\(3\)	\(7\)	\(23\)	Fricke	Total			Cusp			Eisenstein
\(2\)	\(3\)	\(7\)	\(23\)	Fricke	All	New	Old	All	New	Old	All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(76\)	\(12\)	\(64\)	\(73\)	\(12\)	\(61\)	\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(96\)	\(8\)	\(88\)	\(92\)	\(8\)	\(84\)	\(4\)	\(0\)	\(4\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(94\)	\(7\)	\(87\)	\(90\)	\(7\)	\(83\)	\(4\)	\(0\)	\(4\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(78\)	\(10\)	\(68\)	\(74\)	\(10\)	\(64\)	\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(84\)	\(11\)	\(73\)	\(80\)	\(11\)	\(69\)	\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(88\)	\(7\)	\(81\)	\(84\)	\(7\)	\(77\)	\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(90\)	\(8\)	\(82\)	\(86\)	\(8\)	\(78\)	\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(82\)	\(11\)	\(71\)	\(78\)	\(11\)	\(67\)	\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(80\)	\(9\)	\(71\)	\(76\)	\(9\)	\(67\)	\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(92\)	\(9\)	\(83\)	\(88\)	\(9\)	\(79\)	\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(92\)	\(9\)	\(83\)	\(88\)	\(9\)	\(79\)	\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(80\)	\(12\)	\(68\)	\(76\)	\(12\)	\(64\)	\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(80\)	\(6\)	\(74\)	\(76\)	\(6\)	\(70\)	\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(92\)	\(14\)	\(78\)	\(88\)	\(14\)	\(74\)	\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(92\)	\(13\)	\(79\)	\(88\)	\(13\)	\(75\)	\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(80\)	\(4\)	\(76\)	\(76\)	\(4\)	\(72\)	\(4\)	\(0\)	\(4\)
Plus space				\(+\)	\(676\)	\(65\)	\(611\)	\(645\)	\(65\)	\(580\)	\(31\)	\(0\)	\(31\)
Minus space				\(-\)	\(700\)	\(85\)	\(615\)	\(668\)	\(85\)	\(583\)	\(32\)	\(0\)	\(32\)

Introduction

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Modular forms

Varieties

Fields

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Groups

Database

Properties

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6762))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6762))\) 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	6762.2.a

Level	$6762$
Weight	$2$
Character orbit	6762.a
Rep. character	$\chi_{6762}(1,\cdot)$
Character field	$\Q$
Dimension	$150$
Newform subspaces	$74$
Sturm bound	$2688$
Trace bound	$17$