LMFDB - Space of modular forms of level 7280, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 7280 = 2^{4} \cdot 5 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7280.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 59 $
Sturm bound:			$2688$
Trace bound:			$23$
Distinguishing $T_p$:			$3$, $11$, $17$, $19$, $23$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(7280))$.

	Total	New	Old
Modular forms	1368	144	1224
Cusp forms	1321	144	1177
Eisenstein series	47	0	47

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

$2$	$5$	$7$	$13$	Fricke	Dim.
$+$	$+$	$+$	$+$	$+$	$10$
$+$	$+$	$+$	$-$	$-$	$8$
$+$	$+$	$-$	$+$	$-$	$10$
$+$	$+$	$-$	$-$	$+$	$8$
$+$	$-$	$+$	$+$	$-$	$8$
$+$	$-$	$+$	$-$	$+$	$10$
$+$	$-$	$-$	$+$	$+$	$8$
$+$	$-$	$-$	$-$	$-$	$10$
$-$	$+$	$+$	$+$	$-$	$11$
$-$	$+$	$+$	$-$	$+$	$8$
$-$	$+$	$-$	$+$	$+$	$5$
$-$	$+$	$-$	$-$	$-$	$12$
$-$	$-$	$+$	$+$	$+$	$8$
$-$	$-$	$+$	$-$	$-$	$11$
$-$	$-$	$-$	$+$	$-$	$12$
$-$	$-$	$-$	$-$	$+$	$5$
Plus space				$+$	$62$
Minus space				$-$	$82$

Trace form

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(7280))$ 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	5	7	13	$q$-expansion
7280.2.a.a	$1$	$58.131$	$\Q$	None	$0$	$-2$	$-1$	$-1$	$+$	$+$	$+$	$+$	$q-2q^{3}-q^{5}-q^{7}+q^{9}-6q^{11}-q^{13}+\cdots$
7280.2.a.b	$1$	$58.131$	$\Q$	None	$0$	$-2$	$-1$	$-1$	$-$	$+$	$+$	$-$	$q-2q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}+q^{13}+\cdots$
7280.2.a.c	$1$	$58.131$	$\Q$	None	$0$	$-2$	$-1$	$1$	$+$	$+$	$-$	$+$	$q-2q^{3}-q^{5}+q^{7}+q^{9}+2q^{11}-q^{13}+\cdots$
7280.2.a.d	$1$	$58.131$	$\Q$	None	$0$	$-2$	$1$	$1$	$+$	$-$	$-$	$+$	$q-2q^{3}+q^{5}+q^{7}+q^{9}-q^{13}-2q^{15}+\cdots$
7280.2.a.e	$1$	$58.131$	$\Q$	None	$0$	$-2$	$1$	$1$	$+$	$-$	$-$	$+$	$q-2q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}-q^{13}+\cdots$
7280.2.a.f	$1$	$58.131$	$\Q$	None	$0$	$-1$	$-1$	$-1$	$-$	$+$	$+$	$-$	$q-q^{3}-q^{5}-q^{7}-2q^{9}+3q^{11}+q^{13}+\cdots$
7280.2.a.g	$1$	$58.131$	$\Q$	None	$0$	$-1$	$1$	$-1$	$-$	$-$	$+$	$-$	$q-q^{3}+q^{5}-q^{7}-2q^{9}+3q^{11}+q^{13}+\cdots$
7280.2.a.h	$1$	$58.131$	$\Q$	None	$0$	$0$	$-1$	$-1$	$-$	$+$	$+$	$+$	$q-q^{5}-q^{7}-3q^{9}-4q^{11}-q^{13}+\cdots$
7280.2.a.i	$1$	$58.131$	$\Q$	None	$0$	$0$	$-1$	$-1$	$+$	$+$	$+$	$+$	$q-q^{5}-q^{7}-3q^{9}-q^{13}+6q^{17}+\cdots$
7280.2.a.j	$1$	$58.131$	$\Q$	None	$0$	$0$	$-1$	$1$	$+$	$+$	$-$	$-$	$q-q^{5}+q^{7}-3q^{9}-2q^{11}+q^{13}+\cdots$
7280.2.a.k	$1$	$58.131$	$\Q$	None	$0$	$0$	$-1$	$1$	$-$	$+$	$-$	$+$	$q-q^{5}+q^{7}-3q^{9}-q^{13}-2q^{17}+\cdots$
7280.2.a.l	$1$	$58.131$	$\Q$	None	$0$	$0$	$-1$	$1$	$-$	$+$	$-$	$-$	$q-q^{5}+q^{7}-3q^{9}+6q^{11}+q^{13}+\cdots$
7280.2.a.m	$1$	$58.131$	$\Q$	None	$0$	$0$	$1$	$-1$	$+$	$-$	$+$	$+$	$q+q^{5}-q^{7}-3q^{9}+2q^{11}-q^{13}+\cdots$
7280.2.a.n	$1$	$58.131$	$\Q$	None	$0$	$0$	$1$	$-1$	$-$	$-$	$+$	$+$	$q+q^{5}-q^{7}-3q^{9}+2q^{11}-q^{13}+\cdots$
7280.2.a.o	$1$	$58.131$	$\Q$	None	$0$	$0$	$1$	$1$	$-$	$-$	$-$	$-$	$q+q^{5}+q^{7}-3q^{9}+q^{13}-6q^{17}+\cdots$
7280.2.a.p	$1$	$58.131$	$\Q$	None	$0$	$1$	$-1$	$-1$	$-$	$+$	$+$	$+$	$q+q^{3}-q^{5}-q^{7}-2q^{9}+5q^{11}-q^{13}+\cdots$
7280.2.a.q	$1$	$58.131$	$\Q$	None	$0$	$1$	$-1$	$1$	$+$	$+$	$-$	$+$	$q+q^{3}-q^{5}+q^{7}-2q^{9}-5q^{11}-q^{13}+\cdots$
7280.2.a.r	$1$	$58.131$	$\Q$	None	$0$	$1$	$1$	$1$	$+$	$-$	$-$	$+$	$q+q^{3}+q^{5}+q^{7}-2q^{9}+3q^{11}-q^{13}+\cdots$
7280.2.a.s	$1$	$58.131$	$\Q$	None	$0$	$2$	$-1$	$-1$	$-$	$+$	$+$	$-$	$q+2q^{3}-q^{5}-q^{7}+q^{9}+q^{13}-2q^{15}+\cdots$
7280.2.a.t	$1$	$58.131$	$\Q$	None	$0$	$2$	$-1$	$-1$	$-$	$+$	$+$	$-$	$q+2q^{3}-q^{5}-q^{7}+q^{9}+q^{13}-2q^{15}+\cdots$
7280.2.a.u	$1$	$58.131$	$\Q$	None	$0$	$2$	$1$	$-1$	$+$	$-$	$+$	$-$	$q+2q^{3}+q^{5}-q^{7}+q^{9}+2q^{11}+q^{13}+\cdots$
7280.2.a.v	$1$	$58.131$	$\Q$	None	$0$	$2$	$1$	$1$	$-$	$-$	$-$	$+$	$q+2q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}-q^{13}+\cdots$
7280.2.a.w	$1$	$58.131$	$\Q$	None	$0$	$3$	$-1$	$1$	$-$	$+$	$-$	$-$	$q+3q^{3}-q^{5}+q^{7}+6q^{9}-3q^{11}+\cdots$
7280.2.a.x	$2$	$58.131$	$\Q(\sqrt{3}) $	None	$0$	$-2$	$-2$	$-2$	$-$	$+$	$+$	$-$	$q+(-1+\beta )q^{3}-q^{5}-q^{7}+(1-2\beta )q^{9}+\cdots$
7280.2.a.y	$2$	$58.131$	$\Q(\sqrt{5}) $	None	$0$	$-2$	$-2$	$2$	$-$	$+$	$-$	$-$	$q+(-1-\beta )q^{3}-q^{5}+q^{7}+(3+2\beta )q^{9}+\cdots$
7280.2.a.z	$2$	$58.131$	$\Q(\sqrt{5}) $	None	$0$	$-1$	$2$	$-2$	$+$	$-$	$+$	$-$	$q-\beta q^{3}+q^{5}-q^{7}+(-2+\beta )q^{9}+4\beta q^{11}+\cdots$
7280.2.a.ba	$2$	$58.131$	$\Q(\sqrt{5}) $	None	$0$	$-1$	$2$	$2$	$-$	$-$	$-$	$-$	$q-\beta q^{3}+q^{5}+q^{7}+(-2+\beta )q^{9}-2\beta q^{11}+\cdots$
7280.2.a.bb	$2$	$58.131$	$\Q(\sqrt{17}) $	None	$0$	$-1$	$2$	$2$	$-$	$-$	$-$	$-$	$q-\beta q^{3}+q^{5}+q^{7}+(1+\beta )q^{9}+\beta q^{11}+\cdots$
7280.2.a.bc	$2$	$58.131$	$\Q(\sqrt{2}) $	None	$0$	$0$	$2$	$-2$	$-$	$-$	$+$	$-$	$q+\beta q^{3}+q^{5}-q^{7}+5q^{9}-4q^{11}+\cdots$
7280.2.a.bd	$2$	$58.131$	$\Q(\sqrt{2}) $	None	$0$	$0$	$2$	$2$	$+$	$-$	$-$	$-$	$q+q^{5}+q^{7}-3q^{9}+\beta q^{11}+q^{13}+\cdots$
7280.2.a.be	$2$	$58.131$	$\Q(\sqrt{13}) $	None	$0$	$1$	$-2$	$-2$	$-$	$+$	$+$	$+$	$q+\beta q^{3}-q^{5}-q^{7}+\beta q^{9}+2q^{11}+\cdots$
7280.2.a.bf	$2$	$58.131$	$\Q(\sqrt{5}) $	None	$0$	$1$	$-2$	$2$	$-$	$+$	$-$	$+$	$q+\beta q^{3}-q^{5}+q^{7}+(-2+\beta )q^{9}+2\beta q^{11}+\cdots$
7280.2.a.bg	$2$	$58.131$	$\Q(\sqrt{17}) $	None	$0$	$1$	$-2$	$2$	$-$	$+$	$-$	$+$	$q+\beta q^{3}-q^{5}+q^{7}+(1+\beta )q^{9}-\beta q^{11}+\cdots$
7280.2.a.bh	$2$	$58.131$	$\Q(\sqrt{13}) $	None	$0$	$1$	$2$	$-2$	$+$	$-$	$+$	$+$	$q+\beta q^{3}+q^{5}-q^{7}+\beta q^{9}+(2-2\beta )q^{11}+\cdots$
7280.2.a.bi	$2$	$58.131$	$\Q(\sqrt{5}) $	None	$0$	$1$	$2$	$2$	$+$	$-$	$-$	$+$	$q+\beta q^{3}+q^{5}+q^{7}+(-2+\beta )q^{9}-q^{13}+\cdots$
7280.2.a.bj	$2$	$58.131$	$\Q(\sqrt{13}) $	None	$0$	$3$	$-2$	$-2$	$-$	$+$	$+$	$-$	$q+(1+\beta )q^{3}-q^{5}-q^{7}+(1+3\beta )q^{9}+\cdots$
7280.2.a.bk	$2$	$58.131$	$\Q(\sqrt{5}) $	None	$0$	$3$	$2$	$-2$	$-$	$-$	$+$	$-$	$q+(1+\beta )q^{3}+q^{5}-q^{7}+(-1+3\beta )q^{9}+\cdots$
7280.2.a.bl	$3$	$58.131$	3.3.229.1	None	$0$	$-1$	$3$	$-3$	$-$	$-$	$+$	$+$	$q+\beta _{2}q^{3}+q^{5}-q^{7}+(1-\beta _{1})q^{9}+(-2+\cdots)q^{11}+\cdots$
7280.2.a.bm	$3$	$58.131$	3.3.1573.1	None	$0$	$-1$	$3$	$3$	$+$	$-$	$-$	$+$	$q-\beta _{1}q^{3}+q^{5}+q^{7}+(2+\beta _{1}+\beta _{2})q^{9}+\cdots$
7280.2.a.bn	$3$	$58.131$	3.3.1101.1	None	$0$	$1$	$-3$	$-3$	$+$	$+$	$+$	$+$	$q+\beta _{1}q^{3}-q^{5}-q^{7}+(4-\beta _{1}+\beta _{2})q^{9}+\cdots$
7280.2.a.bo	$3$	$58.131$	3.3.568.1	None	$0$	$1$	$3$	$3$	$-$	$-$	$-$	$+$	$q-\beta _{2}q^{3}+q^{5}+q^{7}+(3-\beta _{1})q^{9}+(-2+\cdots)q^{11}+\cdots$
7280.2.a.bp	$3$	$58.131$	3.3.229.1	None	$0$	$2$	$-3$	$3$	$+$	$+$	$-$	$-$	$q+(1+\beta _{2})q^{3}-q^{5}+q^{7}+(1+\beta _{1})q^{9}+\cdots$
7280.2.a.bq	$4$	$58.131$	4.4.1957.1	None	$0$	$-4$	$4$	$4$	$-$	$-$	$-$	$+$	$q+(-1+\beta _{2})q^{3}+q^{5}+q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots$
7280.2.a.br	$4$	$58.131$	4.4.4913.1	None	$0$	$-3$	$-4$	$4$	$+$	$+$	$-$	$-$	$q+(-1+\beta _{1})q^{3}-q^{5}+q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
7280.2.a.bs	$4$	$58.131$	4.4.23724.1	None	$0$	$-1$	$-4$	$-4$	$+$	$+$	$+$	$-$	$q+\beta _{1}q^{3}-q^{5}-q^{7}+(1+\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots$
7280.2.a.bt	$4$	$58.131$	4.4.2225.1	None	$0$	$-1$	$-4$	$4$	$+$	$+$	$-$	$+$	$q-\beta _{1}q^{3}-q^{5}+q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots$
7280.2.a.bu	$4$	$58.131$	4.4.50908.1	None	$0$	$-1$	$4$	$-4$	$-$	$-$	$+$	$+$	$q-\beta _{3}q^{3}+q^{5}-q^{7}+(2-\beta _{1}+\beta _{3})q^{9}+\cdots$
7280.2.a.bv	$4$	$58.131$	4.4.24197.1	None	$0$	$0$	$-4$	$-4$	$+$	$+$	$+$	$-$	$q-\beta _{1}q^{3}-q^{5}-q^{7}+\beta _{2}q^{9}+(\beta _{2}-\beta _{3})q^{11}+\cdots$
7280.2.a.bw	$4$	$58.131$	4.4.12197.1	None	$0$	$0$	$-4$	$4$	$-$	$+$	$-$	$-$	$q+\beta _{1}q^{3}-q^{5}+q^{7}+(2-\beta _{3})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$
7280.2.a.bx	$4$	$58.131$	4.4.24197.1	None	$0$	$0$	$4$	$4$	$+$	$-$	$-$	$-$	$q-\beta _{2}q^{3}+q^{5}+q^{7}+(4+\beta _{1})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$
7280.2.a.by	$4$	$58.131$	4.4.30972.1	None	$0$	$1$	$-4$	$4$	$-$	$+$	$-$	$-$	$q+\beta _{1}q^{3}-q^{5}+q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
7280.2.a.bz	$4$	$58.131$	4.4.13676.1	None	$0$	$1$	$-4$	$4$	$+$	$+$	$-$	$+$	$q+\beta _{1}q^{3}-q^{5}+q^{7}+(3+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots$
7280.2.a.ca	$4$	$58.131$	4.4.2225.1	None	$0$	$1$	$4$	$4$	$+$	$-$	$-$	$-$	$q+\beta _{1}q^{3}+q^{5}+q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots$
7280.2.a.cb	$4$	$58.131$	4.4.27004.1	None	$0$	$3$	$4$	$4$	$-$	$-$	$-$	$+$	$q+(1-\beta _{1})q^{3}+q^{5}+q^{7}+(1-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
7280.2.a.cc	$5$	$58.131$	5.5.1194649.1	None	$0$	$0$	$-5$	$-5$	$+$	$+$	$+$	$+$	$q+\beta _{1}q^{3}-q^{5}-q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots$
7280.2.a.cd	$5$	$58.131$	5.5.2112217.1	None	$0$	$0$	$5$	$-5$	$+$	$-$	$+$	$+$	$q+\beta _{1}q^{3}+q^{5}-q^{7}+(1+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots$
7280.2.a.ce	$6$	$58.131$	6.6.45853772.1	None	$0$	$0$	$6$	$-6$	$-$	$-$	$+$	$-$	$q-\beta _{5}q^{3}+q^{5}-q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
7280.2.a.cf	$7$	$58.131$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$0$	$-4$	$7$	$-7$	$+$	$-$	$+$	$-$	$q+(-1+\beta _{1})q^{3}+q^{5}-q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots$
7280.2.a.cg	$7$	$58.131$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$0$	$0$	$-7$	$-7$	$-$	$+$	$+$	$+$	$q-\beta _{5}q^{3}-q^{5}-q^{7}+(3-\beta _{4})q^{9}+(-1+\cdots)q^{11}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(7280))$ 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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 7280 = 2^{4} \cdot 5 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7280.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 59 \)
Sturm bound:			\(2688\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(3\), \(11\), \(17\), \(19\), \(23\)

\(2\)	\(5\)	\(7\)	\(13\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(10\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(8\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(10\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(8\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(8\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(10\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(8\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(10\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(11\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(8\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(5\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(12\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(8\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(11\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(12\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(5\)
Plus space				\(+\)	\(62\)
Minus space				\(-\)	\(82\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7280))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7280))\) 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	7280.2.a

Level	$7280$
Weight	$2$
Character orbit	7280.a
Rep. character	$\chi_{7280}(1,\cdot)$
Character field	$\Q$
Dimension	$144$
Newform subspaces	$59$
Sturm bound	$2688$
Trace bound	$23$

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	5	7	13	$q$-expansion
7280.2.a.a	$1$	$58.131$	\(\Q\)	None	\(0\)	\(-2\)	\(-1\)	\(-1\)	$+$	$+$	$+$	$+$	\(q-2q^{3}-q^{5}-q^{7}+q^{9}-6q^{11}-q^{13}+\cdots\)
7280.2.a.b	$1$	$58.131$	\(\Q\)	None	\(0\)	\(-2\)	\(-1\)	\(-1\)	$-$	$+$	$+$	$-$	\(q-2q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}+q^{13}+\cdots\)
7280.2.a.c	$1$	$58.131$	\(\Q\)	None	\(0\)	\(-2\)	\(-1\)	\(1\)	$+$	$+$	$-$	$+$	\(q-2q^{3}-q^{5}+q^{7}+q^{9}+2q^{11}-q^{13}+\cdots\)
7280.2.a.d	$1$	$58.131$	\(\Q\)	None	\(0\)	\(-2\)	\(1\)	\(1\)	$+$	$-$	$-$	$+$	\(q-2q^{3}+q^{5}+q^{7}+q^{9}-q^{13}-2q^{15}+\cdots\)
7280.2.a.e	$1$	$58.131$	\(\Q\)	None	\(0\)	\(-2\)	\(1\)	\(1\)	$+$	$-$	$-$	$+$	\(q-2q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
7280.2.a.f	$1$	$58.131$	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(-1\)	$-$	$+$	$+$	$-$	\(q-q^{3}-q^{5}-q^{7}-2q^{9}+3q^{11}+q^{13}+\cdots\)
7280.2.a.g	$1$	$58.131$	\(\Q\)	None	\(0\)	\(-1\)	\(1\)	\(-1\)	$-$	$-$	$+$	$-$	\(q-q^{3}+q^{5}-q^{7}-2q^{9}+3q^{11}+q^{13}+\cdots\)
7280.2.a.h	$1$	$58.131$	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(-1\)	$-$	$+$	$+$	$+$	\(q-q^{5}-q^{7}-3q^{9}-4q^{11}-q^{13}+\cdots\)
7280.2.a.i	$1$	$58.131$	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(-1\)	$+$	$+$	$+$	$+$	\(q-q^{5}-q^{7}-3q^{9}-q^{13}+6q^{17}+\cdots\)
7280.2.a.j	$1$	$58.131$	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(1\)	$+$	$+$	$-$	$-$	\(q-q^{5}+q^{7}-3q^{9}-2q^{11}+q^{13}+\cdots\)
7280.2.a.k	$1$	$58.131$	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(1\)	$-$	$+$	$-$	$+$	\(q-q^{5}+q^{7}-3q^{9}-q^{13}-2q^{17}+\cdots\)
7280.2.a.l	$1$	$58.131$	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(1\)	$-$	$+$	$-$	$-$	\(q-q^{5}+q^{7}-3q^{9}+6q^{11}+q^{13}+\cdots\)
7280.2.a.m	$1$	$58.131$	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(-1\)	$+$	$-$	$+$	$+$	\(q+q^{5}-q^{7}-3q^{9}+2q^{11}-q^{13}+\cdots\)
7280.2.a.n	$1$	$58.131$	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(-1\)	$-$	$-$	$+$	$+$	\(q+q^{5}-q^{7}-3q^{9}+2q^{11}-q^{13}+\cdots\)
7280.2.a.o	$1$	$58.131$	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(1\)	$-$	$-$	$-$	$-$	\(q+q^{5}+q^{7}-3q^{9}+q^{13}-6q^{17}+\cdots\)
7280.2.a.p	$1$	$58.131$	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(-1\)	$-$	$+$	$+$	$+$	\(q+q^{3}-q^{5}-q^{7}-2q^{9}+5q^{11}-q^{13}+\cdots\)
7280.2.a.q	$1$	$58.131$	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(1\)	$+$	$+$	$-$	$+$	\(q+q^{3}-q^{5}+q^{7}-2q^{9}-5q^{11}-q^{13}+\cdots\)
7280.2.a.r	$1$	$58.131$	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(1\)	$+$	$-$	$-$	$+$	\(q+q^{3}+q^{5}+q^{7}-2q^{9}+3q^{11}-q^{13}+\cdots\)
7280.2.a.s	$1$	$58.131$	\(\Q\)	None	\(0\)	\(2\)	\(-1\)	\(-1\)	$-$	$+$	$+$	$-$	\(q+2q^{3}-q^{5}-q^{7}+q^{9}+q^{13}-2q^{15}+\cdots\)
7280.2.a.t	$1$	$58.131$	\(\Q\)	None	\(0\)	\(2\)	\(-1\)	\(-1\)	$-$	$+$	$+$	$-$	\(q+2q^{3}-q^{5}-q^{7}+q^{9}+q^{13}-2q^{15}+\cdots\)
7280.2.a.u	$1$	$58.131$	\(\Q\)	None	\(0\)	\(2\)	\(1\)	\(-1\)	$+$	$-$	$+$	$-$	\(q+2q^{3}+q^{5}-q^{7}+q^{9}+2q^{11}+q^{13}+\cdots\)
7280.2.a.v	$1$	$58.131$	\(\Q\)	None	\(0\)	\(2\)	\(1\)	\(1\)	$-$	$-$	$-$	$+$	\(q+2q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
7280.2.a.w	$1$	$58.131$	\(\Q\)	None	\(0\)	\(3\)	\(-1\)	\(1\)	$-$	$+$	$-$	$-$	\(q+3q^{3}-q^{5}+q^{7}+6q^{9}-3q^{11}+\cdots\)
7280.2.a.x	$2$	$58.131$	\(\Q(\sqrt{3}) \)	None	\(0\)	\(-2\)	\(-2\)	\(-2\)	$-$	$+$	$+$	$-$	\(q+(-1+\beta )q^{3}-q^{5}-q^{7}+(1-2\beta )q^{9}+\cdots\)
7280.2.a.y	$2$	$58.131$	\(\Q(\sqrt{5}) \)	None	\(0\)	\(-2\)	\(-2\)	\(2\)	$-$	$+$	$-$	$-$	\(q+(-1-\beta )q^{3}-q^{5}+q^{7}+(3+2\beta )q^{9}+\cdots\)
7280.2.a.z	$2$	$58.131$	\(\Q(\sqrt{5}) \)	None	\(0\)	\(-1\)	\(2\)	\(-2\)	$+$	$-$	$+$	$-$	\(q-\beta q^{3}+q^{5}-q^{7}+(-2+\beta )q^{9}+4\beta q^{11}+\cdots\)
7280.2.a.ba	$2$	$58.131$	\(\Q(\sqrt{5}) \)	None	\(0\)	\(-1\)	\(2\)	\(2\)	$-$	$-$	$-$	$-$	\(q-\beta q^{3}+q^{5}+q^{7}+(-2+\beta )q^{9}-2\beta q^{11}+\cdots\)
7280.2.a.bb	$2$	$58.131$	\(\Q(\sqrt{17}) \)	None	\(0\)	\(-1\)	\(2\)	\(2\)	$-$	$-$	$-$	$-$	\(q-\beta q^{3}+q^{5}+q^{7}+(1+\beta )q^{9}+\beta q^{11}+\cdots\)
7280.2.a.bc	$2$	$58.131$	\(\Q(\sqrt{2}) \)	None	\(0\)	\(0\)	\(2\)	\(-2\)	$-$	$-$	$+$	$-$	\(q+\beta q^{3}+q^{5}-q^{7}+5q^{9}-4q^{11}+\cdots\)
7280.2.a.bd	$2$	$58.131$	\(\Q(\sqrt{2}) \)	None	\(0\)	\(0\)	\(2\)	\(2\)	$+$	$-$	$-$	$-$	\(q+q^{5}+q^{7}-3q^{9}+\beta q^{11}+q^{13}+\cdots\)
7280.2.a.be	$2$	$58.131$	\(\Q(\sqrt{13}) \)	None	\(0\)	\(1\)	\(-2\)	\(-2\)	$-$	$+$	$+$	$+$	\(q+\beta q^{3}-q^{5}-q^{7}+\beta q^{9}+2q^{11}+\cdots\)
7280.2.a.bf	$2$	$58.131$	\(\Q(\sqrt{5}) \)	None	\(0\)	\(1\)	\(-2\)	\(2\)	$-$	$+$	$-$	$+$	\(q+\beta q^{3}-q^{5}+q^{7}+(-2+\beta )q^{9}+2\beta q^{11}+\cdots\)
7280.2.a.bg	$2$	$58.131$	\(\Q(\sqrt{17}) \)	None	\(0\)	\(1\)	\(-2\)	\(2\)	$-$	$+$	$-$	$+$	\(q+\beta q^{3}-q^{5}+q^{7}+(1+\beta )q^{9}-\beta q^{11}+\cdots\)
7280.2.a.bh	$2$	$58.131$	\(\Q(\sqrt{13}) \)	None	\(0\)	\(1\)	\(2\)	\(-2\)	$+$	$-$	$+$	$+$	\(q+\beta q^{3}+q^{5}-q^{7}+\beta q^{9}+(2-2\beta )q^{11}+\cdots\)
7280.2.a.bi	$2$	$58.131$	\(\Q(\sqrt{5}) \)	None	\(0\)	\(1\)	\(2\)	\(2\)	$+$	$-$	$-$	$+$	\(q+\beta q^{3}+q^{5}+q^{7}+(-2+\beta )q^{9}-q^{13}+\cdots\)
7280.2.a.bj	$2$	$58.131$	\(\Q(\sqrt{13}) \)	None	\(0\)	\(3\)	\(-2\)	\(-2\)	$-$	$+$	$+$	$-$	\(q+(1+\beta )q^{3}-q^{5}-q^{7}+(1+3\beta )q^{9}+\cdots\)
7280.2.a.bk	$2$	$58.131$	\(\Q(\sqrt{5}) \)	None	\(0\)	\(3\)	\(2\)	\(-2\)	$-$	$-$	$+$	$-$	\(q+(1+\beta )q^{3}+q^{5}-q^{7}+(-1+3\beta )q^{9}+\cdots\)
7280.2.a.bl	$3$	$58.131$	3.3.229.1	None	\(0\)	\(-1\)	\(3\)	\(-3\)	$-$	$-$	$+$	$+$	\(q+\beta _{2}q^{3}+q^{5}-q^{7}+(1-\beta _{1})q^{9}+(-2+\cdots)q^{11}+\cdots\)
7280.2.a.bm	$3$	$58.131$	3.3.1573.1	None	\(0\)	\(-1\)	\(3\)	\(3\)	$+$	$-$	$-$	$+$	\(q-\beta _{1}q^{3}+q^{5}+q^{7}+(2+\beta _{1}+\beta _{2})q^{9}+\cdots\)
7280.2.a.bn	$3$	$58.131$	3.3.1101.1	None	\(0\)	\(1\)	\(-3\)	\(-3\)	$+$	$+$	$+$	$+$	\(q+\beta _{1}q^{3}-q^{5}-q^{7}+(4-\beta _{1}+\beta _{2})q^{9}+\cdots\)
7280.2.a.bo	$3$	$58.131$	3.3.568.1	None	\(0\)	\(1\)	\(3\)	\(3\)	$-$	$-$	$-$	$+$	\(q-\beta _{2}q^{3}+q^{5}+q^{7}+(3-\beta _{1})q^{9}+(-2+\cdots)q^{11}+\cdots\)
7280.2.a.bp	$3$	$58.131$	3.3.229.1	None	\(0\)	\(2\)	\(-3\)	\(3\)	$+$	$+$	$-$	$-$	\(q+(1+\beta _{2})q^{3}-q^{5}+q^{7}+(1+\beta _{1})q^{9}+\cdots\)
7280.2.a.bq	$4$	$58.131$	4.4.1957.1	None	\(0\)	\(-4\)	\(4\)	\(4\)	$-$	$-$	$-$	$+$	\(q+(-1+\beta _{2})q^{3}+q^{5}+q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots\)
7280.2.a.br	$4$	$58.131$	4.4.4913.1	None	\(0\)	\(-3\)	\(-4\)	\(4\)	$+$	$+$	$-$	$-$	\(q+(-1+\beta _{1})q^{3}-q^{5}+q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
7280.2.a.bs	$4$	$58.131$	4.4.23724.1	None	\(0\)	\(-1\)	\(-4\)	\(-4\)	$+$	$+$	$+$	$-$	\(q+\beta _{1}q^{3}-q^{5}-q^{7}+(1+\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots\)
7280.2.a.bt	$4$	$58.131$	4.4.2225.1	None	\(0\)	\(-1\)	\(-4\)	\(4\)	$+$	$+$	$-$	$+$	\(q-\beta _{1}q^{3}-q^{5}+q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
7280.2.a.bu	$4$	$58.131$	4.4.50908.1	None	\(0\)	\(-1\)	\(4\)	\(-4\)	$-$	$-$	$+$	$+$	\(q-\beta _{3}q^{3}+q^{5}-q^{7}+(2-\beta _{1}+\beta _{3})q^{9}+\cdots\)
7280.2.a.bv	$4$	$58.131$	4.4.24197.1	None	\(0\)	\(0\)	\(-4\)	\(-4\)	$+$	$+$	$+$	$-$	\(q-\beta _{1}q^{3}-q^{5}-q^{7}+\beta _{2}q^{9}+(\beta _{2}-\beta _{3})q^{11}+\cdots\)
7280.2.a.bw	$4$	$58.131$	4.4.12197.1	None	\(0\)	\(0\)	\(-4\)	\(4\)	$-$	$+$	$-$	$-$	\(q+\beta _{1}q^{3}-q^{5}+q^{7}+(2-\beta _{3})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
7280.2.a.bx	$4$	$58.131$	4.4.24197.1	None	\(0\)	\(0\)	\(4\)	\(4\)	$+$	$-$	$-$	$-$	\(q-\beta _{2}q^{3}+q^{5}+q^{7}+(4+\beta _{1})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
7280.2.a.by	$4$	$58.131$	4.4.30972.1	None	\(0\)	\(1\)	\(-4\)	\(4\)	$-$	$+$	$-$	$-$	\(q+\beta _{1}q^{3}-q^{5}+q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7280.2.a.bz	$4$	$58.131$	4.4.13676.1	None	\(0\)	\(1\)	\(-4\)	\(4\)	$+$	$+$	$-$	$+$	\(q+\beta _{1}q^{3}-q^{5}+q^{7}+(3+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots\)
7280.2.a.ca	$4$	$58.131$	4.4.2225.1	None	\(0\)	\(1\)	\(4\)	\(4\)	$+$	$-$	$-$	$-$	\(q+\beta _{1}q^{3}+q^{5}+q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
7280.2.a.cb	$4$	$58.131$	4.4.27004.1	None	\(0\)	\(3\)	\(4\)	\(4\)	$-$	$-$	$-$	$+$	\(q+(1-\beta _{1})q^{3}+q^{5}+q^{7}+(1-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7280.2.a.cc	$5$	$58.131$	5.5.1194649.1	None	\(0\)	\(0\)	\(-5\)	\(-5\)	$+$	$+$	$+$	$+$	\(q+\beta _{1}q^{3}-q^{5}-q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
7280.2.a.cd	$5$	$58.131$	5.5.2112217.1	None	\(0\)	\(0\)	\(5\)	\(-5\)	$+$	$-$	$+$	$+$	\(q+\beta _{1}q^{3}+q^{5}-q^{7}+(1+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
7280.2.a.ce	$6$	$58.131$	6.6.45853772.1	None	\(0\)	\(0\)	\(6\)	\(-6\)	$-$	$-$	$+$	$-$	\(q-\beta _{5}q^{3}+q^{5}-q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7280.2.a.cf	$7$	$58.131$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(0\)	\(-4\)	\(7\)	\(-7\)	$+$	$-$	$+$	$-$	\(q+(-1+\beta _{1})q^{3}+q^{5}-q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots\)
7280.2.a.cg	$7$	$58.131$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(0\)	\(0\)	\(-7\)	\(-7\)	$-$	$+$	$+$	$+$	\(q-\beta _{5}q^{3}-q^{5}-q^{7}+(3-\beta _{4})q^{9}+(-1+\cdots)q^{11}+\cdots\)