LMFDB - Space of modular forms of level 882, weight 2, and Trivial character

Defining parameters

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 15 $
Sturm bound:			$336$
Trace bound:			$13$
Distinguishing $T_p$:			$5$, $11$, $13$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(882))$.

	Total	New	Old
Modular forms	200	18	182
Cusp forms	137	18	119
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.

$2$	$3$	$7$	Fricke	Dim.
$+$	$+$	$+$	$+$	$3$
$+$	$+$	$-$	$-$	$1$
$+$	$-$	$+$	$-$	$3$
$+$	$-$	$-$	$+$	$2$
$-$	$+$	$+$	$-$	$3$
$-$	$+$	$-$	$+$	$1$
$-$	$-$	$+$	$+$	$1$
$-$	$-$	$-$	$-$	$4$
Plus space			$+$	$7$
Minus space			$-$	$11$

Trace form

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(882))$ into newform subspaces

Label	Dim.	$A$	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	2	3	7	$q$-expansion
882.2.a.a	$1$	$7.043$	$\Q$	None	$-1$	$0$	$-3$	$0$	$+$	$+$	$+$	$q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}+3q^{11}+\cdots$
882.2.a.b	$1$	$7.043$	$\Q$	None	$-1$	$0$	$-2$	$0$	$+$	$-$	$-$	$q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+4q^{11}+\cdots$
882.2.a.c	$1$	$7.043$	$\Q$	None	$-1$	$0$	$-1$	$0$	$+$	$-$	$+$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-5q^{11}+\cdots$
882.2.a.d	$1$	$7.043$	$\Q$	None	$-1$	$0$	$1$	$0$	$+$	$-$	$-$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-5q^{11}+\cdots$
882.2.a.e	$1$	$7.043$	$\Q$	None	$-1$	$0$	$3$	$0$	$+$	$+$	$-$	$q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}+3q^{11}+\cdots$
882.2.a.f	$1$	$7.043$	$\Q$	None	$1$	$0$	$-4$	$0$	$-$	$-$	$-$	$q+q^{2}+q^{4}-4q^{5}+q^{8}-4q^{10}+4q^{11}+\cdots$
882.2.a.g	$1$	$7.043$	$\Q$	None	$1$	$0$	$-3$	$0$	$-$	$-$	$+$	$q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}-3q^{11}+\cdots$
882.2.a.h	$1$	$7.043$	$\Q$	None	$1$	$0$	$-3$	$0$	$-$	$+$	$-$	$q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}-3q^{11}+\cdots$
882.2.a.i	$1$	$7.043$	$\Q$	None	$1$	$0$	$0$	$0$	$-$	$-$	$-$	$q+q^{2}+q^{4}+q^{8}+4q^{13}+q^{16}+6q^{17}+\cdots$
882.2.a.j	$1$	$7.043$	$\Q$	None	$1$	$0$	$3$	$0$	$-$	$+$	$+$	$q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-3q^{11}+\cdots$
882.2.a.k	$1$	$7.043$	$\Q$	None	$1$	$0$	$3$	$0$	$-$	$-$	$-$	$q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-3q^{11}+\cdots$
882.2.a.l	$1$	$7.043$	$\Q$	None	$1$	$0$	$4$	$0$	$-$	$-$	$-$	$q+q^{2}+q^{4}+4q^{5}+q^{8}+4q^{10}+4q^{11}+\cdots$
882.2.a.m	$2$	$7.043$	$\Q(\sqrt{2}) $	None	$-2$	$0$	$0$	$0$	$+$	$+$	$+$	$q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}-4q^{11}+\cdots$
882.2.a.n	$2$	$7.043$	$\Q(\sqrt{2}) $	None	$-2$	$0$	$0$	$0$	$+$	$-$	$+$	$q-q^{2}+q^{4}+2\beta q^{5}-q^{8}-2\beta q^{10}+\cdots$
882.2.a.o	$2$	$7.043$	$\Q(\sqrt{2}) $	None	$2$	$0$	$0$	$0$	$-$	$+$	$+$	$q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}+4q^{11}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(882))$ into lower level spaces

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	($ 1 + T $)($ 1 + T $)($ 1 + T $)($ 1 + T $)($ 1 + T $)($ 1 - T $)($ 1 - T $)($ 1 - T $)($ 1 - T $)($ 1 - T $)($ 1 - T $)($ 1 - T $)($ ( 1 + T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 - T )^{2} $)
$3$	1
$5$	($ 1 + 3 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + T + 5 T^{2} $)($ 1 - T + 5 T^{2} $)($ 1 - 3 T + 5 T^{2} $)($ 1 + 4 T + 5 T^{2} $)($ 1 + 3 T + 5 T^{2} $)($ 1 + 3 T + 5 T^{2} $)($ 1 + 5 T^{2} $)($ 1 - 3 T + 5 T^{2} $)($ 1 - 3 T + 5 T^{2} $)($ 1 - 4 T + 5 T^{2} $)($ 1 + 8 T^{2} + 25 T^{4} $)($ 1 + 2 T^{2} + 25 T^{4} $)($ 1 + 8 T^{2} + 25 T^{4} $)
$7$	1
$11$	($ 1 - 3 T + 11 T^{2} $)($ 1 - 4 T + 11 T^{2} $)($ 1 + 5 T + 11 T^{2} $)($ 1 + 5 T + 11 T^{2} $)($ 1 - 3 T + 11 T^{2} $)($ 1 - 4 T + 11 T^{2} $)($ 1 + 3 T + 11 T^{2} $)($ 1 + 3 T + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 3 T + 11 T^{2} $)($ 1 + 3 T + 11 T^{2} $)($ 1 - 4 T + 11 T^{2} $)($ ( 1 + 4 T + 11 T^{2} )^{2} $)($ ( 1 - 2 T + 11 T^{2} )^{2} $)($ ( 1 - 4 T + 11 T^{2} )^{2} $)
$13$	($ 1 - 2 T + 13 T^{2} $)($ 1 + 6 T + 13 T^{2} $)($ 1 + 13 T^{2} $)($ 1 + 13 T^{2} $)($ 1 + 2 T + 13 T^{2} $)($ 1 - 4 T + 13 T^{2} $)($ 1 + 4 T + 13 T^{2} $)($ 1 + 2 T + 13 T^{2} $)($ 1 - 4 T + 13 T^{2} $)($ 1 - 2 T + 13 T^{2} $)($ 1 - 4 T + 13 T^{2} $)($ 1 + 4 T + 13 T^{2} $)($ 1 + 8 T^{2} + 169 T^{4} $)($ ( 1 + 13 T^{2} )^{2} $)($ 1 + 8 T^{2} + 169 T^{4} $)
$17$	($ 1 + 6 T + 17 T^{2} $)($ 1 - 2 T + 17 T^{2} $)($ 1 - 4 T + 17 T^{2} $)($ 1 + 4 T + 17 T^{2} $)($ 1 - 6 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 + 6 T + 17 T^{2} $)($ 1 - 6 T + 17 T^{2} $)($ 1 - 6 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 - 16 T^{2} + 289 T^{4} $)($ 1 + 32 T^{2} + 289 T^{4} $)($ 1 - 16 T^{2} + 289 T^{4} $)
$19$	($ 1 - 2 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 - 8 T + 19 T^{2} $)($ 1 + 8 T + 19 T^{2} $)($ 1 + 2 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 + 2 T + 19 T^{2} $)($ 1 + 2 T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 + 6 T^{2} + 361 T^{4} $)($ 1 - 12 T^{2} + 361 T^{4} $)($ 1 + 6 T^{2} + 361 T^{4} $)
$23$	($ 1 - 6 T + 23 T^{2} $)($ 1 + 8 T + 23 T^{2} $)($ 1 - 4 T + 23 T^{2} $)($ 1 - 4 T + 23 T^{2} $)($ 1 - 6 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 + 6 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 + 6 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 + 23 T^{2} $)($ ( 1 + 8 T + 23 T^{2} )^{2} $)($ ( 1 - 4 T + 23 T^{2} )^{2} $)($ ( 1 - 8 T + 23 T^{2} )^{2} $)
$29$	($ 1 + 9 T + 29 T^{2} $)($ 1 - 2 T + 29 T^{2} $)($ 1 - 5 T + 29 T^{2} $)($ 1 - 5 T + 29 T^{2} $)($ 1 + 9 T + 29 T^{2} $)($ 1 + 2 T + 29 T^{2} $)($ 1 + 9 T + 29 T^{2} $)($ 1 - 9 T + 29 T^{2} $)($ 1 - 6 T + 29 T^{2} $)($ 1 - 9 T + 29 T^{2} $)($ 1 + 9 T + 29 T^{2} $)($ 1 + 2 T + 29 T^{2} $)($ ( 1 + 2 T + 29 T^{2} )^{2} $)($ ( 1 + 2 T + 29 T^{2} )^{2} $)($ ( 1 - 2 T + 29 T^{2} )^{2} $)
$31$	($ 1 + 7 T + 31 T^{2} $)($ 1 + 31 T^{2} $)($ 1 - 3 T + 31 T^{2} $)($ 1 + 3 T + 31 T^{2} $)($ 1 - 7 T + 31 T^{2} $)($ 1 - 8 T + 31 T^{2} $)($ 1 + T + 31 T^{2} $)($ 1 - 7 T + 31 T^{2} $)($ 1 - 4 T + 31 T^{2} $)($ 1 + 7 T + 31 T^{2} $)($ 1 - T + 31 T^{2} $)($ 1 + 8 T + 31 T^{2} $)($ ( 1 + 31 T^{2} )^{2} $)($ 1 - 10 T^{2} + 961 T^{4} $)($ ( 1 + 31 T^{2} )^{2} $)
$37$	($ 1 + 10 T + 37 T^{2} $)($ 1 + 10 T + 37 T^{2} $)($ 1 + 4 T + 37 T^{2} $)($ 1 + 4 T + 37 T^{2} $)($ 1 + 10 T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ 1 - 8 T + 37 T^{2} $)($ 1 + 10 T + 37 T^{2} $)($ 1 - 2 T + 37 T^{2} $)($ 1 + 10 T + 37 T^{2} $)($ 1 - 8 T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ ( 1 - 4 T + 37 T^{2} )^{2} $)($ ( 1 - 10 T + 37 T^{2} )^{2} $)($ ( 1 - 4 T + 37 T^{2} )^{2} $)
$41$	($ 1 + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 - 16 T^{2} + 1681 T^{4} $)($ 1 - 16 T^{2} + 1681 T^{4} $)($ 1 - 16 T^{2} + 1681 T^{4} $)
$43$	($ 1 + 4 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 - 2 T + 43 T^{2} $)($ 1 - 2 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ 1 + 10 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 - 8 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 + 10 T + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ ( 1 + 4 T + 43 T^{2} )^{2} $)($ ( 1 - 2 T + 43 T^{2} )^{2} $)($ ( 1 + 4 T + 43 T^{2} )^{2} $)
$47$	($ 1 + 12 T + 47 T^{2} $)($ 1 + 47 T^{2} $)($ 1 - 6 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 - 12 T + 47 T^{2} $)($ 1 - 8 T + 47 T^{2} $)($ 1 - 6 T + 47 T^{2} $)($ 1 + 12 T + 47 T^{2} $)($ 1 + 12 T + 47 T^{2} $)($ 1 - 12 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 + 8 T + 47 T^{2} $)($ 1 + 62 T^{2} + 2209 T^{4} $)($ 1 + 86 T^{2} + 2209 T^{4} $)($ 1 + 62 T^{2} + 2209 T^{4} $)
$53$	($ 1 - 3 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 - 9 T + 53 T^{2} $)($ 1 - 9 T + 53 T^{2} $)($ 1 - 3 T + 53 T^{2} $)($ 1 - 10 T + 53 T^{2} $)($ 1 - 3 T + 53 T^{2} $)($ 1 + 3 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 + 3 T + 53 T^{2} $)($ 1 - 3 T + 53 T^{2} $)($ 1 - 10 T + 53 T^{2} $)($ ( 1 + 4 T + 53 T^{2} )^{2} $)($ ( 1 - 2 T + 53 T^{2} )^{2} $)($ ( 1 - 4 T + 53 T^{2} )^{2} $)
$59$	($ 1 - 3 T + 59 T^{2} $)($ 1 - 4 T + 59 T^{2} $)($ 1 - 11 T + 59 T^{2} $)($ 1 + 11 T + 59 T^{2} $)($ 1 + 3 T + 59 T^{2} $)($ 1 + 4 T + 59 T^{2} $)($ 1 + 3 T + 59 T^{2} $)($ 1 - 3 T + 59 T^{2} $)($ 1 + 6 T + 59 T^{2} $)($ 1 + 3 T + 59 T^{2} $)($ 1 - 3 T + 59 T^{2} $)($ 1 - 4 T + 59 T^{2} $)($ 1 - 10 T^{2} + 3481 T^{4} $)($ 1 + 116 T^{2} + 3481 T^{4} $)($ 1 - 10 T^{2} + 3481 T^{4} $)
$61$	($ 1 + 4 T + 61 T^{2} $)($ 1 + 6 T + 61 T^{2} $)($ 1 + 6 T + 61 T^{2} $)($ 1 - 6 T + 61 T^{2} $)($ 1 - 4 T + 61 T^{2} $)($ 1 + 4 T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 - 4 T + 61 T^{2} $)($ 1 + 8 T + 61 T^{2} $)($ 1 + 4 T + 61 T^{2} $)($ 1 - 10 T + 61 T^{2} $)($ 1 - 4 T + 61 T^{2} $)($ 1 + 120 T^{2} + 3721 T^{4} $)($ 1 + 114 T^{2} + 3721 T^{4} $)($ 1 + 120 T^{2} + 3721 T^{4} $)
$67$	($ 1 - 2 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 + 2 T + 67 T^{2} $)($ 1 + 2 T + 67 T^{2} $)($ 1 - 2 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 + 10 T + 67 T^{2} $)($ 1 - 2 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 - 2 T + 67 T^{2} $)($ 1 + 10 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ ( 1 + 12 T + 67 T^{2} )^{2} $)($ ( 1 - 12 T + 67 T^{2} )^{2} $)($ ( 1 + 12 T + 67 T^{2} )^{2} $)
$71$	($ 1 + 71 T^{2} $)($ 1 + 8 T + 71 T^{2} $)($ 1 + 2 T + 71 T^{2} $)($ 1 + 2 T + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 + 8 T + 71 T^{2} $)($ 1 - 6 T + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 - 6 T + 71 T^{2} $)($ 1 + 8 T + 71 T^{2} $)($ ( 1 + 71 T^{2} )^{2} $)($ ( 1 - 12 T + 71 T^{2} )^{2} $)($ ( 1 + 71 T^{2} )^{2} $)
$73$	($ 1 - 2 T + 73 T^{2} $)($ 1 + 10 T + 73 T^{2} $)($ 1 - 10 T + 73 T^{2} $)($ 1 + 10 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 + 16 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 - 16 T + 73 T^{2} $)($ 1 - 96 T^{2} + 5329 T^{4} $)($ 1 + 144 T^{2} + 5329 T^{4} $)($ 1 - 96 T^{2} + 5329 T^{4} $)
$79$	($ 1 - 5 T + 79 T^{2} $)($ 1 + 79 T^{2} $)($ 1 - 3 T + 79 T^{2} $)($ 1 - 3 T + 79 T^{2} $)($ 1 - 5 T + 79 T^{2} $)($ 1 + 8 T + 79 T^{2} $)($ 1 + T + 79 T^{2} $)($ 1 - 5 T + 79 T^{2} $)($ 1 - 8 T + 79 T^{2} $)($ 1 - 5 T + 79 T^{2} $)($ 1 + T + 79 T^{2} $)($ 1 + 8 T + 79 T^{2} $)($ ( 1 + 16 T + 79 T^{2} )^{2} $)($ ( 1 + 4 T + 79 T^{2} )^{2} $)($ ( 1 + 16 T + 79 T^{2} )^{2} $)
$83$	($ 1 + 9 T + 83 T^{2} $)($ 1 + 4 T + 83 T^{2} $)($ 1 - 7 T + 83 T^{2} $)($ 1 + 7 T + 83 T^{2} $)($ 1 - 9 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 - 9 T + 83 T^{2} $)($ 1 + 9 T + 83 T^{2} $)($ 1 + 6 T + 83 T^{2} $)($ 1 - 9 T + 83 T^{2} $)($ 1 + 9 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 + 134 T^{2} + 6889 T^{4} $)($ 1 + 68 T^{2} + 6889 T^{4} $)($ 1 + 134 T^{2} + 6889 T^{4} $)
$89$	($ 1 - 6 T + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 - 6 T + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 + 8 T + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 - 6 T + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 - 6 T + 89 T^{2} $)($ 1 - 8 T + 89 T^{2} $)($ 1 + 128 T^{2} + 7921 T^{4} $)($ 1 + 128 T^{2} + 7921 T^{4} $)($ 1 + 128 T^{2} + 7921 T^{4} $)
$97$	($ 1 + 13 T + 97 T^{2} $)($ 1 - 14 T + 97 T^{2} $)($ 1 - 7 T + 97 T^{2} $)($ 1 + 7 T + 97 T^{2} $)($ 1 - 13 T + 97 T^{2} $)($ 1 - 8 T + 97 T^{2} $)($ 1 + T + 97 T^{2} $)($ 1 - 13 T + 97 T^{2} $)($ 1 - 10 T + 97 T^{2} $)($ 1 + 13 T + 97 T^{2} $)($ 1 - T + 97 T^{2} $)($ 1 + 8 T + 97 T^{2} $)($ 1 + 144 T^{2} + 9409 T^{4} $)($ 1 + 96 T^{2} + 9409 T^{4} $)($ 1 + 144 T^{2} + 9409 T^{4} $)
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Overview	Features
Universe	Knowledge

Degree 1	Degree 2
Degree 3	Degree 4
$\zeta$ zeros

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 15 \)
Sturm bound:			\(336\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\)

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Properties

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(882))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(882))\) into lower level spaces

Hecke characteristic polynomials

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	882.2.a

Level	882
Weight	2
Character orbit	a
Rep. character	\(\chi_{882}(1,\cdot)\)
Character field	\(\Q\)
Dimension	18
Newform subspaces	15
Sturm bound	336
Trace bound	13

\(2\)	\(3\)	\(7\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)	\(4\)
Plus space			\(+\)	\(7\)
Minus space			\(-\)	\(11\)

Label	Dim.	\(A\)	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	2	3	7	$q$-expansion
882.2.a.a	\(1\)	\(7.043\)	\(\Q\)	None	\(-1\)	\(0\)	\(-3\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}+3q^{11}+\cdots\)
882.2.a.b	\(1\)	\(7.043\)	\(\Q\)	None	\(-1\)	\(0\)	\(-2\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+4q^{11}+\cdots\)
882.2.a.c	\(1\)	\(7.043\)	\(\Q\)	None	\(-1\)	\(0\)	\(-1\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-5q^{11}+\cdots\)
882.2.a.d	\(1\)	\(7.043\)	\(\Q\)	None	\(-1\)	\(0\)	\(1\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-5q^{11}+\cdots\)
882.2.a.e	\(1\)	\(7.043\)	\(\Q\)	None	\(-1\)	\(0\)	\(3\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}+3q^{11}+\cdots\)
882.2.a.f	\(1\)	\(7.043\)	\(\Q\)	None	\(1\)	\(0\)	\(-4\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}-4q^{5}+q^{8}-4q^{10}+4q^{11}+\cdots\)
882.2.a.g	\(1\)	\(7.043\)	\(\Q\)	None	\(1\)	\(0\)	\(-3\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}-3q^{11}+\cdots\)
882.2.a.h	\(1\)	\(7.043\)	\(\Q\)	None	\(1\)	\(0\)	\(-3\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}-3q^{11}+\cdots\)
882.2.a.i	\(1\)	\(7.043\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{8}+4q^{13}+q^{16}+6q^{17}+\cdots\)
882.2.a.j	\(1\)	\(7.043\)	\(\Q\)	None	\(1\)	\(0\)	\(3\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-3q^{11}+\cdots\)
882.2.a.k	\(1\)	\(7.043\)	\(\Q\)	None	\(1\)	\(0\)	\(3\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-3q^{11}+\cdots\)
882.2.a.l	\(1\)	\(7.043\)	\(\Q\)	None	\(1\)	\(0\)	\(4\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+4q^{5}+q^{8}+4q^{10}+4q^{11}+\cdots\)
882.2.a.m	\(2\)	\(7.043\)	\(\Q(\sqrt{2}) \)	None	\(-2\)	\(0\)	\(0\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}-4q^{11}+\cdots\)
882.2.a.n	\(2\)	\(7.043\)	\(\Q(\sqrt{2}) \)	None	\(-2\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}+2\beta q^{5}-q^{8}-2\beta q^{10}+\cdots\)
882.2.a.o	\(2\)	\(7.043\)	\(\Q(\sqrt{2}) \)	None	\(2\)	\(0\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}+4q^{11}+\cdots\)

$p$	$F_p(T)$
$2$	(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))
$3$	1
$5$	(\( 1 + 3 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 + 4 T + 5 T^{2} \))(\( 1 + 3 T + 5 T^{2} \))(\( 1 + 3 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + 8 T^{2} + 25 T^{4} \))(\( 1 + 2 T^{2} + 25 T^{4} \))(\( 1 + 8 T^{2} + 25 T^{4} \))
$7$	1
$11$	(\( 1 - 3 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + 5 T + 11 T^{2} \))(\( 1 + 5 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( ( 1 + 4 T + 11 T^{2} )^{2} \))(\( ( 1 - 2 T + 11 T^{2} )^{2} \))(\( ( 1 - 4 T + 11 T^{2} )^{2} \))
$13$	(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 8 T^{2} + 169 T^{4} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( 1 + 8 T^{2} + 169 T^{4} \))
$17$	(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 16 T^{2} + 289 T^{4} \))(\( 1 + 32 T^{2} + 289 T^{4} \))(\( 1 - 16 T^{2} + 289 T^{4} \))
$19$	(\( 1 - 2 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 6 T^{2} + 361 T^{4} \))(\( 1 - 12 T^{2} + 361 T^{4} \))(\( 1 + 6 T^{2} + 361 T^{4} \))
$23$	(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( ( 1 + 8 T + 23 T^{2} )^{2} \))(\( ( 1 - 4 T + 23 T^{2} )^{2} \))(\( ( 1 - 8 T + 23 T^{2} )^{2} \))
$29$	(\( 1 + 9 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 - 5 T + 29 T^{2} \))(\( 1 - 5 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))
$31$	(\( 1 + 7 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 3 T + 31 T^{2} \))(\( 1 + 3 T + 31 T^{2} \))(\( 1 - 7 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + T + 31 T^{2} \))(\( 1 - 7 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 7 T + 31 T^{2} \))(\( 1 - T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( 1 - 10 T^{2} + 961 T^{4} \))(\( ( 1 + 31 T^{2} )^{2} \))
$37$	(\( 1 + 10 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( ( 1 - 4 T + 37 T^{2} )^{2} \))(\( ( 1 - 10 T + 37 T^{2} )^{2} \))(\( ( 1 - 4 T + 37 T^{2} )^{2} \))
$41$	(\( 1 + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 16 T^{2} + 1681 T^{4} \))(\( 1 - 16 T^{2} + 1681 T^{4} \))(\( 1 - 16 T^{2} + 1681 T^{4} \))
$43$	(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 2 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))
$47$	(\( 1 + 12 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 62 T^{2} + 2209 T^{4} \))(\( 1 + 86 T^{2} + 2209 T^{4} \))(\( 1 + 62 T^{2} + 2209 T^{4} \))
$53$	(\( 1 - 3 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 9 T + 53 T^{2} \))(\( 1 - 9 T + 53 T^{2} \))(\( 1 - 3 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 - 3 T + 53 T^{2} \))(\( 1 + 3 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 3 T + 53 T^{2} \))(\( 1 - 3 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( ( 1 + 4 T + 53 T^{2} )^{2} \))(\( ( 1 - 2 T + 53 T^{2} )^{2} \))(\( ( 1 - 4 T + 53 T^{2} )^{2} \))
$59$	(\( 1 - 3 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 11 T + 59 T^{2} \))(\( 1 + 11 T + 59 T^{2} \))(\( 1 + 3 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 3 T + 59 T^{2} \))(\( 1 - 3 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 3 T + 59 T^{2} \))(\( 1 - 3 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 10 T^{2} + 3481 T^{4} \))(\( 1 + 116 T^{2} + 3481 T^{4} \))(\( 1 - 10 T^{2} + 3481 T^{4} \))
$61$	(\( 1 + 4 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 + 120 T^{2} + 3721 T^{4} \))(\( 1 + 114 T^{2} + 3721 T^{4} \))(\( 1 + 120 T^{2} + 3721 T^{4} \))
$67$	(\( 1 - 2 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 10 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 + 10 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( ( 1 + 12 T + 67 T^{2} )^{2} \))(\( ( 1 - 12 T + 67 T^{2} )^{2} \))(\( ( 1 + 12 T + 67 T^{2} )^{2} \))
$71$	(\( 1 + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 + 2 T + 71 T^{2} \))(\( 1 + 2 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))
$73$	(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 16 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 - 96 T^{2} + 5329 T^{4} \))(\( 1 + 144 T^{2} + 5329 T^{4} \))(\( 1 - 96 T^{2} + 5329 T^{4} \))
$79$	(\( 1 - 5 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 - 3 T + 79 T^{2} \))(\( 1 - 3 T + 79 T^{2} \))(\( 1 - 5 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + T + 79 T^{2} \))(\( 1 - 5 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 - 5 T + 79 T^{2} \))(\( 1 + T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( ( 1 + 16 T + 79 T^{2} )^{2} \))(\( ( 1 + 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 16 T + 79 T^{2} )^{2} \))
$83$	(\( 1 + 9 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 7 T + 83 T^{2} \))(\( 1 + 7 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 134 T^{2} + 6889 T^{4} \))(\( 1 + 68 T^{2} + 6889 T^{4} \))(\( 1 + 134 T^{2} + 6889 T^{4} \))
$89$	(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 8 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 8 T + 89 T^{2} \))(\( 1 + 128 T^{2} + 7921 T^{4} \))(\( 1 + 128 T^{2} + 7921 T^{4} \))(\( 1 + 128 T^{2} + 7921 T^{4} \))
$97$	(\( 1 + 13 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 - 7 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 - 13 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 + T + 97 T^{2} \))(\( 1 - 13 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 13 T + 97 T^{2} \))(\( 1 - T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 + 144 T^{2} + 9409 T^{4} \))(\( 1 + 96 T^{2} + 9409 T^{4} \))(\( 1 + 144 T^{2} + 9409 T^{4} \))
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