LMFDB - Space of modular forms of level 6384, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 6384 = 2^{4} \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6384.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 58 $
Sturm bound:			$2560$
Trace bound:			$25$
Distinguishing $T_p$:			$5$, $11$, $13$, $17$, $23$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(6384))$.

	Total	New	Old
Modular forms	1304	108	1196
Cusp forms	1257	108	1149
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.

$2$	$3$	$7$	$19$	Fricke	Dim.
$+$	$+$	$+$	$+$	$+$	$8$
$+$	$+$	$+$	$-$	$-$	$6$
$+$	$+$	$-$	$+$	$-$	$7$
$+$	$+$	$-$	$-$	$+$	$7$
$+$	$-$	$+$	$+$	$-$	$7$
$+$	$-$	$+$	$-$	$+$	$7$
$+$	$-$	$-$	$+$	$+$	$6$
$+$	$-$	$-$	$-$	$-$	$8$
$-$	$+$	$+$	$+$	$-$	$8$
$-$	$+$	$+$	$-$	$+$	$6$
$-$	$+$	$-$	$+$	$+$	$4$
$-$	$+$	$-$	$-$	$-$	$8$
$-$	$-$	$+$	$+$	$+$	$5$
$-$	$-$	$+$	$-$	$-$	$9$
$-$	$-$	$-$	$+$	$-$	$9$
$-$	$-$	$-$	$-$	$+$	$3$
Plus space				$+$	$46$
Minus space				$-$	$62$

Trace form

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(6384))$ 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	19	$q$-expansion
6384.2.a.a	$1$	$50.976$	$\Q$	None	$0$	$-1$	$-4$	$-1$	$+$	$+$	$+$	$+$	$q-q^{3}-4q^{5}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots$
6384.2.a.b	$1$	$50.976$	$\Q$	None	$0$	$-1$	$-4$	$1$	$+$	$+$	$-$	$-$	$q-q^{3}-4q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
6384.2.a.c	$1$	$50.976$	$\Q$	None	$0$	$-1$	$-4$	$1$	$-$	$+$	$-$	$-$	$q-q^{3}-4q^{5}+q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots$
6384.2.a.d	$1$	$50.976$	$\Q$	None	$0$	$-1$	$-2$	$-1$	$-$	$+$	$+$	$+$	$q-q^{3}-2q^{5}-q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots$
6384.2.a.e	$1$	$50.976$	$\Q$	None	$0$	$-1$	$-2$	$-1$	$-$	$+$	$+$	$-$	$q-q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$
6384.2.a.f	$1$	$50.976$	$\Q$	None	$0$	$-1$	$-2$	$-1$	$+$	$+$	$+$	$-$	$q-q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
6384.2.a.g	$1$	$50.976$	$\Q$	None	$0$	$-1$	$-2$	$1$	$-$	$+$	$-$	$+$	$q-q^{3}-2q^{5}+q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots$
6384.2.a.h	$1$	$50.976$	$\Q$	None	$0$	$-1$	$-2$	$1$	$-$	$+$	$-$	$+$	$q-q^{3}-2q^{5}+q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots$
6384.2.a.i	$1$	$50.976$	$\Q$	None	$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$+$	$q-q^{3}-q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots$
6384.2.a.j	$1$	$50.976$	$\Q$	None	$0$	$-1$	$0$	$-1$	$+$	$+$	$+$	$-$	$q-q^{3}-q^{7}+q^{9}-2q^{13}-8q^{17}+\cdots$
6384.2.a.k	$1$	$50.976$	$\Q$	None	$0$	$-1$	$0$	$1$	$+$	$+$	$-$	$-$	$q-q^{3}+q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots$
6384.2.a.l	$1$	$50.976$	$\Q$	None	$0$	$-1$	$2$	$1$	$-$	$+$	$-$	$+$	$q-q^{3}+2q^{5}+q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots$
6384.2.a.m	$1$	$50.976$	$\Q$	None	$0$	$-1$	$2$	$1$	$-$	$+$	$-$	$+$	$q-q^{3}+2q^{5}+q^{7}+q^{9}+2q^{13}-2q^{15}+\cdots$
6384.2.a.n	$1$	$50.976$	$\Q$	None	$0$	$-1$	$2$	$1$	$-$	$+$	$-$	$-$	$q-q^{3}+2q^{5}+q^{7}+q^{9}+2q^{13}-2q^{15}+\cdots$
6384.2.a.o	$1$	$50.976$	$\Q$	None	$0$	$-1$	$2$	$1$	$+$	$+$	$-$	$+$	$q-q^{3}+2q^{5}+q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots$
6384.2.a.p	$1$	$50.976$	$\Q$	None	$0$	$-1$	$4$	$-1$	$-$	$+$	$+$	$+$	$q-q^{3}+4q^{5}-q^{7}+q^{9}+2q^{11}-4q^{15}+\cdots$
6384.2.a.q	$1$	$50.976$	$\Q$	None	$0$	$-1$	$4$	$1$	$-$	$+$	$-$	$-$	$q-q^{3}+4q^{5}+q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots$
6384.2.a.r	$1$	$50.976$	$\Q$	None	$0$	$1$	$-4$	$1$	$+$	$-$	$-$	$+$	$q+q^{3}-4q^{5}+q^{7}+q^{9}-2q^{13}-4q^{15}+\cdots$
6384.2.a.s	$1$	$50.976$	$\Q$	None	$0$	$1$	$-2$	$-1$	$+$	$-$	$+$	$-$	$q+q^{3}-2q^{5}-q^{7}+q^{9}-2q^{13}-2q^{15}+\cdots$
6384.2.a.t	$1$	$50.976$	$\Q$	None	$0$	$1$	$-2$	$1$	$-$	$-$	$-$	$+$	$q+q^{3}-2q^{5}+q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots$
6384.2.a.u	$1$	$50.976$	$\Q$	None	$0$	$1$	$-2$	$1$	$+$	$-$	$-$	$+$	$q+q^{3}-2q^{5}+q^{7}+q^{9}-2q^{13}-2q^{15}+\cdots$
6384.2.a.v	$1$	$50.976$	$\Q$	None	$0$	$1$	$-2$	$1$	$+$	$-$	$-$	$+$	$q+q^{3}-2q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
6384.2.a.w	$1$	$50.976$	$\Q$	None	$0$	$1$	$0$	$-1$	$+$	$-$	$+$	$+$	$q+q^{3}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots$
6384.2.a.x	$1$	$50.976$	$\Q$	None	$0$	$1$	$0$	$-1$	$-$	$-$	$+$	$+$	$q+q^{3}-q^{7}+q^{9}+2q^{11}-4q^{17}+\cdots$
6384.2.a.y	$1$	$50.976$	$\Q$	None	$0$	$1$	$0$	$-1$	$+$	$-$	$+$	$+$	$q+q^{3}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
6384.2.a.z	$1$	$50.976$	$\Q$	None	$0$	$1$	$0$	$1$	$-$	$-$	$-$	$-$	$q+q^{3}+q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots$
6384.2.a.ba	$1$	$50.976$	$\Q$	None	$0$	$1$	$0$	$1$	$-$	$-$	$-$	$-$	$q+q^{3}+q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots$
6384.2.a.bb	$1$	$50.976$	$\Q$	None	$0$	$1$	$0$	$1$	$+$	$-$	$-$	$+$	$q+q^{3}+q^{7}+q^{9}-2q^{13}-q^{19}+q^{21}+\cdots$
6384.2.a.bc	$1$	$50.976$	$\Q$	None	$0$	$1$	$0$	$1$	$-$	$-$	$-$	$-$	$q+q^{3}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots$
6384.2.a.bd	$1$	$50.976$	$\Q$	None	$0$	$1$	$0$	$1$	$-$	$-$	$-$	$+$	$q+q^{3}+q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots$
6384.2.a.be	$1$	$50.976$	$\Q$	None	$0$	$1$	$2$	$1$	$+$	$-$	$-$	$+$	$q+q^{3}+2q^{5}+q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots$
6384.2.a.bf	$1$	$50.976$	$\Q$	None	$0$	$1$	$2$	$1$	$+$	$-$	$-$	$+$	$q+q^{3}+2q^{5}+q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots$
6384.2.a.bg	$1$	$50.976$	$\Q$	None	$0$	$1$	$2$	$1$	$+$	$-$	$-$	$-$	$q+q^{3}+2q^{5}+q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots$
6384.2.a.bh	$2$	$50.976$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$-4$	$2$	$+$	$+$	$-$	$+$	$q-q^{3}+(-2+\beta )q^{5}+q^{7}+q^{9}-2\beta q^{11}+\cdots$
6384.2.a.bi	$2$	$50.976$	$\Q(\sqrt{3}) $	None	$0$	$-2$	$-2$	$-2$	$+$	$+$	$+$	$+$	$q-q^{3}+(-1+\beta )q^{5}-q^{7}+q^{9}+4q^{11}+\cdots$
6384.2.a.bj	$2$	$50.976$	$\Q(\sqrt{3}) $	None	$0$	$-2$	$-2$	$2$	$-$	$+$	$-$	$-$	$q-q^{3}+(-1+\beta )q^{5}+q^{7}+q^{9}+2\beta q^{11}+\cdots$
6384.2.a.bk	$2$	$50.976$	$\Q(\sqrt{3}) $	None	$0$	$-2$	$0$	$2$	$+$	$+$	$-$	$-$	$q-q^{3}+\beta q^{5}+q^{7}+q^{9}-2q^{13}-\beta q^{15}+\cdots$
6384.2.a.bl	$2$	$50.976$	$\Q(\sqrt{5}) $	None	$0$	$-2$	$2$	$-2$	$-$	$+$	$+$	$-$	$q-q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}-2q^{11}+\cdots$
6384.2.a.bm	$2$	$50.976$	$\Q(\sqrt{5}) $	None	$0$	$2$	$-2$	$-2$	$-$	$-$	$+$	$-$	$q+q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+2q^{11}+\cdots$
6384.2.a.bn	$2$	$50.976$	$\Q(\sqrt{5}) $	None	$0$	$2$	$-2$	$-2$	$-$	$-$	$+$	$-$	$q+q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+2q^{11}+\cdots$
6384.2.a.bo	$2$	$50.976$	$\Q(\sqrt{7}) $	None	$0$	$2$	$-2$	$2$	$-$	$-$	$-$	$+$	$q+q^{3}+(-1+\beta )q^{5}+q^{7}+q^{9}+2\beta q^{11}+\cdots$
6384.2.a.bp	$2$	$50.976$	$\Q(\sqrt{2}) $	None	$0$	$2$	$0$	$-2$	$-$	$-$	$+$	$+$	$q+q^{3}+\beta q^{5}-q^{7}+q^{9}-2q^{11}+2\beta q^{13}+\cdots$
6384.2.a.bq	$2$	$50.976$	$\Q(\sqrt{2}) $	None	$0$	$2$	$0$	$-2$	$-$	$-$	$+$	$+$	$q+q^{3}+\beta q^{5}-q^{7}+q^{9}-2q^{11}-\beta q^{13}+\cdots$
6384.2.a.br	$2$	$50.976$	$\Q(\sqrt{3}) $	None	$0$	$2$	$0$	$2$	$-$	$-$	$-$	$+$	$q+q^{3}+\beta q^{5}+q^{7}+q^{9}+(2-\beta )q^{11}+\cdots$
6384.2.a.bs	$2$	$50.976$	$\Q(\sqrt{3}) $	None	$0$	$2$	$2$	$-2$	$+$	$-$	$+$	$-$	$q+q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}+(-2+\cdots)q^{13}+\cdots$
6384.2.a.bt	$3$	$50.976$	3.3.1016.1	None	$0$	$-3$	$0$	$-3$	$-$	$+$	$+$	$-$	$q-q^{3}+\beta _{2}q^{5}-q^{7}+q^{9}-2q^{11}+\cdots$
6384.2.a.bu	$3$	$50.976$	3.3.404.1	None	$0$	$-3$	$0$	$3$	$-$	$+$	$-$	$-$	$q-q^{3}+\beta _{2}q^{5}+q^{7}+q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots$
6384.2.a.bv	$3$	$50.976$	3.3.316.1	None	$0$	$-3$	$0$	$3$	$+$	$+$	$-$	$-$	$q-q^{3}+q^{7}+q^{9}+(1-\beta _{1})q^{11}+(-2+\cdots)q^{13}+\cdots$
6384.2.a.bw	$3$	$50.976$	3.3.568.1	None	$0$	$3$	$0$	$3$	$+$	$-$	$-$	$-$	$q+q^{3}-\beta _{1}q^{5}+q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots$
6384.2.a.bx	$3$	$50.976$	3.3.148.1	None	$0$	$3$	$4$	$3$	$-$	$-$	$-$	$+$	$q+q^{3}+(1+\beta _{1})q^{5}+q^{7}+q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$
6384.2.a.by	$4$	$50.976$	4.4.2225.1	None	$0$	$-4$	$4$	$-4$	$+$	$+$	$+$	$-$	$q-q^{3}+(1-\beta _{2})q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
6384.2.a.bz	$4$	$50.976$	4.4.7232.1	None	$0$	$-4$	$4$	$4$	$+$	$+$	$-$	$+$	$q-q^{3}+(1-\beta _{1})q^{5}+q^{7}+q^{9}+\beta _{2}q^{11}+\cdots$
6384.2.a.ca	$4$	$50.976$	4.4.13068.1	None	$0$	$4$	$-4$	$-4$	$+$	$-$	$+$	$-$	$q+q^{3}+(-1-\beta _{2})q^{5}-q^{7}+q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$
6384.2.a.cb	$4$	$50.976$	4.4.9248.1	None	$0$	$4$	$0$	$4$	$+$	$-$	$-$	$-$	$q+q^{3}+\beta _{1}q^{5}+q^{7}+q^{9}+(\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$
6384.2.a.cc	$5$	$50.976$	5.5.1240016.1	None	$0$	$-5$	$-2$	$-5$	$-$	$+$	$+$	$+$	$q-q^{3}+\beta _{2}q^{5}-q^{7}+q^{9}+\beta _{1}q^{11}+\cdots$
6384.2.a.cd	$5$	$50.976$	5.5.401584.1	None	$0$	$-5$	$2$	$-5$	$+$	$+$	$+$	$+$	$q-q^{3}-\beta _{1}q^{5}-q^{7}+q^{9}+(-1+\beta _{2}+\cdots)q^{11}+\cdots$
6384.2.a.ce	$5$	$50.976$	5.5.135076.1	None	$0$	$5$	$2$	$-5$	$+$	$-$	$+$	$+$	$q+q^{3}+\beta _{1}q^{5}-q^{7}+q^{9}+\beta _{4}q^{11}+\cdots$
6384.2.a.cf	$5$	$50.976$	5.5.368464.1	None	$0$	$5$	$4$	$-5$	$-$	$-$	$+$	$-$	$q+q^{3}+(1+\beta _{3})q^{5}-q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(6384))$ into lower level spaces

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Level:	\( N \)	\(=\)	\( 6384 = 2^{4} \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6384.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 58 \)
Sturm bound:			\(2560\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(17\), \(23\)

\(2\)	\(3\)	\(7\)	\(19\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(8\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(6\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(7\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(7\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(7\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(7\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(6\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(8\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(8\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(4\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(8\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(5\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(9\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(9\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(3\)
Plus space				\(+\)	\(46\)
Minus space				\(-\)	\(62\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6384))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6384))\) 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	6384.2.a

Level	$6384$
Weight	$2$
Character orbit	6384.a
Rep. character	$\chi_{6384}(1,\cdot)$
Character field	$\Q$
Dimension	$108$
Newform subspaces	$58$
Sturm bound	$2560$
Trace bound	$25$

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	19	$q$-expansion
6384.2.a.a	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(-1\)	\(-4\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-4q^{5}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
6384.2.a.b	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(-1\)	\(-4\)	\(1\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}-4q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6384.2.a.c	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(-1\)	\(-4\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}-4q^{5}+q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots\)
6384.2.a.d	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-2q^{5}-q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots\)
6384.2.a.e	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
6384.2.a.f	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6384.2.a.g	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(1\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}-2q^{5}+q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
6384.2.a.h	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(1\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}-2q^{5}+q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
6384.2.a.i	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots\)
6384.2.a.j	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-q^{7}+q^{9}-2q^{13}-8q^{17}+\cdots\)
6384.2.a.k	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(1\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots\)
6384.2.a.l	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(1\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}+2q^{5}+q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots\)
6384.2.a.m	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(1\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}+2q^{5}+q^{7}+q^{9}+2q^{13}-2q^{15}+\cdots\)
6384.2.a.n	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+2q^{5}+q^{7}+q^{9}+2q^{13}-2q^{15}+\cdots\)
6384.2.a.o	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(1\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}+2q^{5}+q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
6384.2.a.p	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(-1\)	\(4\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+4q^{5}-q^{7}+q^{9}+2q^{11}-4q^{15}+\cdots\)
6384.2.a.q	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(-1\)	\(4\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+4q^{5}+q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots\)
6384.2.a.r	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(1\)	\(-4\)	\(1\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}-4q^{5}+q^{7}+q^{9}-2q^{13}-4q^{15}+\cdots\)
6384.2.a.s	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}-2q^{5}-q^{7}+q^{9}-2q^{13}-2q^{15}+\cdots\)
6384.2.a.t	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(1\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}-2q^{5}+q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots\)
6384.2.a.u	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(1\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}-2q^{5}+q^{7}+q^{9}-2q^{13}-2q^{15}+\cdots\)
6384.2.a.v	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(1\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}-2q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6384.2.a.w	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
6384.2.a.x	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}-q^{7}+q^{9}+2q^{11}-4q^{17}+\cdots\)
6384.2.a.y	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6384.2.a.z	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(1\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
6384.2.a.ba	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(1\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
6384.2.a.bb	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(1\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+q^{7}+q^{9}-2q^{13}-q^{19}+q^{21}+\cdots\)
6384.2.a.bc	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(1\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
6384.2.a.bd	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(1\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots\)
6384.2.a.be	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(1\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+2q^{5}+q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
6384.2.a.bf	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(1\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+2q^{5}+q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
6384.2.a.bg	\(1\)	\(50.976\)	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(1\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+2q^{5}+q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
6384.2.a.bh	\(2\)	\(50.976\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(-4\)	\(2\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}+(-2+\beta )q^{5}+q^{7}+q^{9}-2\beta q^{11}+\cdots\)
6384.2.a.bi	\(2\)	\(50.976\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(-2\)	\(-2\)	\(-2\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+(-1+\beta )q^{5}-q^{7}+q^{9}+4q^{11}+\cdots\)
6384.2.a.bj	\(2\)	\(50.976\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(-2\)	\(-2\)	\(2\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+(-1+\beta )q^{5}+q^{7}+q^{9}+2\beta q^{11}+\cdots\)
6384.2.a.bk	\(2\)	\(50.976\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(-2\)	\(0\)	\(2\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+\beta q^{5}+q^{7}+q^{9}-2q^{13}-\beta q^{15}+\cdots\)
6384.2.a.bl	\(2\)	\(50.976\)	\(\Q(\sqrt{5}) \)	None	\(0\)	\(-2\)	\(2\)	\(-2\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}-2q^{11}+\cdots\)
6384.2.a.bm	\(2\)	\(50.976\)	\(\Q(\sqrt{5}) \)	None	\(0\)	\(2\)	\(-2\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+2q^{11}+\cdots\)
6384.2.a.bn	\(2\)	\(50.976\)	\(\Q(\sqrt{5}) \)	None	\(0\)	\(2\)	\(-2\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+2q^{11}+\cdots\)
6384.2.a.bo	\(2\)	\(50.976\)	\(\Q(\sqrt{7}) \)	None	\(0\)	\(2\)	\(-2\)	\(2\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+(-1+\beta )q^{5}+q^{7}+q^{9}+2\beta q^{11}+\cdots\)
6384.2.a.bp	\(2\)	\(50.976\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(0\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}+\beta q^{5}-q^{7}+q^{9}-2q^{11}+2\beta q^{13}+\cdots\)
6384.2.a.bq	\(2\)	\(50.976\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(0\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}+\beta q^{5}-q^{7}+q^{9}-2q^{11}-\beta q^{13}+\cdots\)
6384.2.a.br	\(2\)	\(50.976\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(2\)	\(0\)	\(2\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+\beta q^{5}+q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
6384.2.a.bs	\(2\)	\(50.976\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(2\)	\(2\)	\(-2\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}+(-2+\cdots)q^{13}+\cdots\)
6384.2.a.bt	\(3\)	\(50.976\)	3.3.1016.1	None	\(0\)	\(-3\)	\(0\)	\(-3\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+\beta _{2}q^{5}-q^{7}+q^{9}-2q^{11}+\cdots\)
6384.2.a.bu	\(3\)	\(50.976\)	3.3.404.1	None	\(0\)	\(-3\)	\(0\)	\(3\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+\beta _{2}q^{5}+q^{7}+q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
6384.2.a.bv	\(3\)	\(50.976\)	3.3.316.1	None	\(0\)	\(-3\)	\(0\)	\(3\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+q^{7}+q^{9}+(1-\beta _{1})q^{11}+(-2+\cdots)q^{13}+\cdots\)
6384.2.a.bw	\(3\)	\(50.976\)	3.3.568.1	None	\(0\)	\(3\)	\(0\)	\(3\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}-\beta _{1}q^{5}+q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
6384.2.a.bx	\(3\)	\(50.976\)	3.3.148.1	None	\(0\)	\(3\)	\(4\)	\(3\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+(1+\beta _{1})q^{5}+q^{7}+q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
6384.2.a.by	\(4\)	\(50.976\)	4.4.2225.1	None	\(0\)	\(-4\)	\(4\)	\(-4\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+(1-\beta _{2})q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
6384.2.a.bz	\(4\)	\(50.976\)	4.4.7232.1	None	\(0\)	\(-4\)	\(4\)	\(4\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}+(1-\beta _{1})q^{5}+q^{7}+q^{9}+\beta _{2}q^{11}+\cdots\)
6384.2.a.ca	\(4\)	\(50.976\)	4.4.13068.1	None	\(0\)	\(4\)	\(-4\)	\(-4\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}+(-1-\beta _{2})q^{5}-q^{7}+q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
6384.2.a.cb	\(4\)	\(50.976\)	4.4.9248.1	None	\(0\)	\(4\)	\(0\)	\(4\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+\beta _{1}q^{5}+q^{7}+q^{9}+(\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
6384.2.a.cc	\(5\)	\(50.976\)	5.5.1240016.1	None	\(0\)	\(-5\)	\(-2\)	\(-5\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+\beta _{2}q^{5}-q^{7}+q^{9}+\beta _{1}q^{11}+\cdots\)
6384.2.a.cd	\(5\)	\(50.976\)	5.5.401584.1	None	\(0\)	\(-5\)	\(2\)	\(-5\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-\beta _{1}q^{5}-q^{7}+q^{9}+(-1+\beta _{2}+\cdots)q^{11}+\cdots\)
6384.2.a.ce	\(5\)	\(50.976\)	5.5.135076.1	None	\(0\)	\(5\)	\(2\)	\(-5\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}+\beta _{1}q^{5}-q^{7}+q^{9}+\beta _{4}q^{11}+\cdots\)
6384.2.a.cf	\(5\)	\(50.976\)	5.5.368464.1	None	\(0\)	\(5\)	\(4\)	\(-5\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}+(1+\beta _{3})q^{5}-q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)