LMFDB - Space of modular forms of level 1200, weight 4, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 1200 = 2^{4} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1200.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 47 $
Sturm bound:			$960$
Trace bound:			$11$
Distinguishing $T_p$:			$7$, $11$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(\Gamma_0(1200))$.

	Total	New	Old
Modular forms	756	57	699
Cusp forms	684	57	627
Eisenstein series	72	0	72

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

$2$	$3$	$5$	Fricke	Dim.
$+$	$+$	$+$	$+$	$8$
$+$	$+$	$-$	$-$	$7$
$+$	$-$	$+$	$-$	$5$
$+$	$-$	$-$	$+$	$9$
$-$	$+$	$+$	$-$	$7$
$-$	$+$	$-$	$+$	$7$
$-$	$-$	$+$	$+$	$7$
$-$	$-$	$-$	$-$	$7$
Plus space			$+$	$31$
Minus space			$-$	$26$

Trace form

Decomposition of $S_{4}^{\mathrm{new}}(\Gamma_0(1200))$ 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	5	$q$-expansion
1200.4.a.a	$1$	$70.802$	$\Q$	None	$0$	$-3$	$0$	$-28$	$-$	$+$	$+$	$q-3q^{3}-28q^{7}+9q^{9}+24q^{11}+70q^{13}+\cdots$
1200.4.a.b	$1$	$70.802$	$\Q$	None	$0$	$-3$	$0$	$-16$	$-$	$+$	$+$	$q-3q^{3}-2^{4}q^{7}+9q^{9}-12q^{11}-38q^{13}+\cdots$
1200.4.a.c	$1$	$70.802$	$\Q$	None	$0$	$-3$	$0$	$-16$	$+$	$+$	$+$	$q-3q^{3}-2^{4}q^{7}+9q^{9}+28q^{11}+26q^{13}+\cdots$
1200.4.a.d	$1$	$70.802$	$\Q$	None	$0$	$-3$	$0$	$-13$	$-$	$+$	$+$	$q-3q^{3}-13q^{7}+9q^{9}-6q^{11}-5q^{13}+\cdots$
1200.4.a.e	$1$	$70.802$	$\Q$	None	$0$	$-3$	$0$	$-10$	$+$	$+$	$-$	$q-3q^{3}-10q^{7}+9q^{9}+14q^{11}-82q^{13}+\cdots$
1200.4.a.f	$1$	$70.802$	$\Q$	None	$0$	$-3$	$0$	$-10$	$+$	$+$	$-$	$q-3q^{3}-10q^{7}+9q^{9}+46q^{11}-34q^{13}+\cdots$
1200.4.a.g	$1$	$70.802$	$\Q$	None	$0$	$-3$	$0$	$-5$	$+$	$+$	$-$	$q-3q^{3}-5q^{7}+9q^{9}-14q^{11}+q^{13}+\cdots$
1200.4.a.h	$1$	$70.802$	$\Q$	None	$0$	$-3$	$0$	$-2$	$-$	$+$	$-$	$q-3q^{3}-2q^{7}+9q^{9}-70q^{11}-54q^{13}+\cdots$
1200.4.a.i	$1$	$70.802$	$\Q$	None	$0$	$-3$	$0$	$-1$	$-$	$+$	$+$	$q-3q^{3}-q^{7}+9q^{9}-42q^{11}+67q^{13}+\cdots$
1200.4.a.j	$1$	$70.802$	$\Q$	None	$0$	$-3$	$0$	$0$	$+$	$+$	$+$	$q-3q^{3}+9q^{9}-4q^{11}-54q^{13}-114q^{17}+\cdots$
1200.4.a.k	$1$	$70.802$	$\Q$	None	$0$	$-3$	$0$	$4$	$+$	$+$	$+$	$q-3q^{3}+4q^{7}+9q^{9}-72q^{11}+6q^{13}+\cdots$
1200.4.a.l	$1$	$70.802$	$\Q$	None	$0$	$-3$	$0$	$4$	$+$	$+$	$-$	$q-3q^{3}+4q^{7}+9q^{9}+28q^{11}+2^{4}q^{13}+\cdots$
1200.4.a.m	$1$	$70.802$	$\Q$	None	$0$	$-3$	$0$	$7$	$-$	$+$	$-$	$q-3q^{3}+7q^{7}+9q^{9}+54q^{11}-55q^{13}+\cdots$
1200.4.a.n	$1$	$70.802$	$\Q$	None	$0$	$-3$	$0$	$19$	$+$	$+$	$-$	$q-3q^{3}+19q^{7}+9q^{9}-22q^{11}+q^{13}+\cdots$
1200.4.a.o	$1$	$70.802$	$\Q$	None	$0$	$-3$	$0$	$20$	$-$	$+$	$+$	$q-3q^{3}+20q^{7}+9q^{9}+24q^{11}-74q^{13}+\cdots$
1200.4.a.p	$1$	$70.802$	$\Q$	None	$0$	$-3$	$0$	$20$	$+$	$+$	$+$	$q-3q^{3}+20q^{7}+9q^{9}+56q^{11}+86q^{13}+\cdots$
1200.4.a.q	$1$	$70.802$	$\Q$	None	$0$	$-3$	$0$	$22$	$-$	$+$	$-$	$q-3q^{3}+22q^{7}+9q^{9}+14q^{11}+30q^{13}+\cdots$
1200.4.a.r	$1$	$70.802$	$\Q$	None	$0$	$-3$	$0$	$23$	$-$	$+$	$+$	$q-3q^{3}+23q^{7}+9q^{9}+30q^{11}-29q^{13}+\cdots$
1200.4.a.s	$1$	$70.802$	$\Q$	None	$0$	$-3$	$0$	$32$	$-$	$+$	$+$	$q-3q^{3}+2^{5}q^{7}+9q^{9}-6^{2}q^{11}+10q^{13}+\cdots$
1200.4.a.t	$1$	$70.802$	$\Q$	None	$0$	$3$	$0$	$-24$	$-$	$-$	$+$	$q+3q^{3}-24q^{7}+9q^{9}-52q^{11}-22q^{13}+\cdots$
1200.4.a.u	$1$	$70.802$	$\Q$	None	$0$	$3$	$0$	$-24$	$+$	$-$	$+$	$q+3q^{3}-24q^{7}+9q^{9}+28q^{11}+74q^{13}+\cdots$
1200.4.a.v	$1$	$70.802$	$\Q$	None	$0$	$3$	$0$	$-23$	$-$	$-$	$-$	$q+3q^{3}-23q^{7}+9q^{9}+30q^{11}+29q^{13}+\cdots$
1200.4.a.w	$1$	$70.802$	$\Q$	None	$0$	$3$	$0$	$-22$	$-$	$-$	$-$	$q+3q^{3}-22q^{7}+9q^{9}+14q^{11}-30q^{13}+\cdots$
1200.4.a.x	$1$	$70.802$	$\Q$	None	$0$	$3$	$0$	$-19$	$+$	$-$	$+$	$q+3q^{3}-19q^{7}+9q^{9}-22q^{11}-q^{13}+\cdots$
1200.4.a.y	$1$	$70.802$	$\Q$	None	$0$	$3$	$0$	$-7$	$-$	$-$	$+$	$q+3q^{3}-7q^{7}+9q^{9}+54q^{11}+55q^{13}+\cdots$
1200.4.a.z	$1$	$70.802$	$\Q$	None	$0$	$3$	$0$	$-4$	$+$	$-$	$-$	$q+3q^{3}-4q^{7}+9q^{9}+28q^{11}-2^{4}q^{13}+\cdots$
1200.4.a.ba	$1$	$70.802$	$\Q$	None	$0$	$3$	$0$	$-4$	$-$	$-$	$+$	$q+3q^{3}-4q^{7}+9q^{9}+48q^{11}-2q^{13}+\cdots$
1200.4.a.bb	$1$	$70.802$	$\Q$	None	$0$	$3$	$0$	$1$	$-$	$-$	$-$	$q+3q^{3}+q^{7}+9q^{9}-42q^{11}-67q^{13}+\cdots$
1200.4.a.bc	$1$	$70.802$	$\Q$	None	$0$	$3$	$0$	$2$	$-$	$-$	$-$	$q+3q^{3}+2q^{7}+9q^{9}-70q^{11}+54q^{13}+\cdots$
1200.4.a.bd	$1$	$70.802$	$\Q$	None	$0$	$3$	$0$	$5$	$+$	$-$	$+$	$q+3q^{3}+5q^{7}+9q^{9}-14q^{11}-q^{13}+\cdots$
1200.4.a.be	$1$	$70.802$	$\Q$	None	$0$	$3$	$0$	$8$	$-$	$-$	$+$	$q+3q^{3}+8q^{7}+9q^{9}-6^{2}q^{11}+10q^{13}+\cdots$
1200.4.a.bf	$1$	$70.802$	$\Q$	None	$0$	$3$	$0$	$8$	$+$	$-$	$+$	$q+3q^{3}+8q^{7}+9q^{9}-20q^{11}-22q^{13}+\cdots$
1200.4.a.bg	$1$	$70.802$	$\Q$	None	$0$	$3$	$0$	$10$	$+$	$-$	$-$	$q+3q^{3}+10q^{7}+9q^{9}+14q^{11}+82q^{13}+\cdots$
1200.4.a.bh	$1$	$70.802$	$\Q$	None	$0$	$3$	$0$	$10$	$+$	$-$	$-$	$q+3q^{3}+10q^{7}+9q^{9}+46q^{11}+34q^{13}+\cdots$
1200.4.a.bi	$1$	$70.802$	$\Q$	None	$0$	$3$	$0$	$13$	$-$	$-$	$-$	$q+3q^{3}+13q^{7}+9q^{9}-6q^{11}+5q^{13}+\cdots$
1200.4.a.bj	$1$	$70.802$	$\Q$	None	$0$	$3$	$0$	$20$	$+$	$-$	$+$	$q+3q^{3}+20q^{7}+9q^{9}-2^{4}q^{11}-58q^{13}+\cdots$
1200.4.a.bk	$1$	$70.802$	$\Q$	None	$0$	$3$	$0$	$32$	$-$	$-$	$+$	$q+3q^{3}+2^{5}q^{7}+9q^{9}+60q^{11}+34q^{13}+\cdots$
1200.4.a.bl	$2$	$70.802$	$\Q(\sqrt{19}) $	None	$0$	$-6$	$0$	$-26$	$-$	$+$	$-$	$q-3q^{3}+(-13+\beta )q^{7}+9q^{9}+(-14+\cdots)q^{11}+\cdots$
1200.4.a.bm	$2$	$70.802$	$\Q(\sqrt{181}) $	None	$0$	$-6$	$0$	$-6$	$+$	$+$	$+$	$q-3q^{3}+(-3-\beta )q^{7}+9q^{9}+(-4+\cdots)q^{11}+\cdots$
1200.4.a.bn	$2$	$70.802$	$\Q(\sqrt{41}) $	None	$0$	$-6$	$0$	$-6$	$-$	$+$	$-$	$q-3q^{3}+(-3-3\beta )q^{7}+9q^{9}+(21+\cdots)q^{11}+\cdots$
1200.4.a.bo	$2$	$70.802$	$\Q(\sqrt{129}) $	None	$0$	$-6$	$0$	$2$	$+$	$+$	$-$	$q-3q^{3}+(1+3\beta )q^{7}+9q^{9}+(-37+\cdots)q^{11}+\cdots$
1200.4.a.bp	$2$	$70.802$	$\Q(\sqrt{109}) $	None	$0$	$-6$	$0$	$2$	$+$	$+$	$+$	$q-3q^{3}+(1+\beta )q^{7}+9q^{9}+(8-3\beta )q^{11}+\cdots$
1200.4.a.bq	$2$	$70.802$	$\Q(\sqrt{129}) $	None	$0$	$6$	$0$	$-2$	$+$	$-$	$-$	$q+3q^{3}+(-1-3\beta )q^{7}+9q^{9}+(-37+\cdots)q^{11}+\cdots$
1200.4.a.br	$2$	$70.802$	$\Q(\sqrt{109}) $	None	$0$	$6$	$0$	$-2$	$+$	$-$	$-$	$q+3q^{3}+(-1-\beta )q^{7}+9q^{9}+(8-3\beta )q^{11}+\cdots$
1200.4.a.bs	$2$	$70.802$	$\Q(\sqrt{181}) $	None	$0$	$6$	$0$	$6$	$+$	$-$	$-$	$q+3q^{3}+(3+\beta )q^{7}+9q^{9}+(-4-\beta )q^{11}+\cdots$
1200.4.a.bt	$2$	$70.802$	$\Q(\sqrt{41}) $	None	$0$	$6$	$0$	$6$	$-$	$-$	$-$	$q+3q^{3}+(3+3\beta )q^{7}+9q^{9}+(21-3\beta )q^{11}+\cdots$
1200.4.a.bu	$2$	$70.802$	$\Q(\sqrt{19}) $	None	$0$	$6$	$0$	$26$	$-$	$-$	$+$	$q+3q^{3}+(13+\beta )q^{7}+9q^{9}+(-14+\cdots)q^{11}+\cdots$

Decomposition of $S_{4}^{\mathrm{old}}(\Gamma_0(1200))$ into lower level spaces

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Level:	\( N \)	\(=\)	\( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1200.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 47 \)
Sturm bound:			\(960\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\)

\(2\)	\(3\)	\(5\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(8\)
\(+\)	\(+\)	\(-\)	\(-\)	\(7\)
\(+\)	\(-\)	\(+\)	\(-\)	\(5\)
\(+\)	\(-\)	\(-\)	\(+\)	\(9\)
\(-\)	\(+\)	\(+\)	\(-\)	\(7\)
\(-\)	\(+\)	\(-\)	\(+\)	\(7\)
\(-\)	\(-\)	\(+\)	\(+\)	\(7\)
\(-\)	\(-\)	\(-\)	\(-\)	\(7\)
Plus space			\(+\)	\(31\)
Minus space			\(-\)	\(26\)

Introduction

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Modular forms

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1200))\) into newform subspaces

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1200))\) 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	1200.4.a

Level	$1200$
Weight	$4$
Character orbit	1200.a
Rep. character	$\chi_{1200}(1,\cdot)$
Character field	$\Q$
Dimension	$57$
Newform subspaces	$47$
Sturm bound	$960$
Trace bound	$11$

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	5	$q$-expansion
1200.4.a.a	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(-3\)	\(0\)	\(-28\)	\(-\)	\(+\)	\(+\)	\(q-3q^{3}-28q^{7}+9q^{9}+24q^{11}+70q^{13}+\cdots\)
1200.4.a.b	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(-3\)	\(0\)	\(-16\)	\(-\)	\(+\)	\(+\)	\(q-3q^{3}-2^{4}q^{7}+9q^{9}-12q^{11}-38q^{13}+\cdots\)
1200.4.a.c	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(-3\)	\(0\)	\(-16\)	\(+\)	\(+\)	\(+\)	\(q-3q^{3}-2^{4}q^{7}+9q^{9}+28q^{11}+26q^{13}+\cdots\)
1200.4.a.d	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(-3\)	\(0\)	\(-13\)	\(-\)	\(+\)	\(+\)	\(q-3q^{3}-13q^{7}+9q^{9}-6q^{11}-5q^{13}+\cdots\)
1200.4.a.e	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(-3\)	\(0\)	\(-10\)	\(+\)	\(+\)	\(-\)	\(q-3q^{3}-10q^{7}+9q^{9}+14q^{11}-82q^{13}+\cdots\)
1200.4.a.f	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(-3\)	\(0\)	\(-10\)	\(+\)	\(+\)	\(-\)	\(q-3q^{3}-10q^{7}+9q^{9}+46q^{11}-34q^{13}+\cdots\)
1200.4.a.g	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(-3\)	\(0\)	\(-5\)	\(+\)	\(+\)	\(-\)	\(q-3q^{3}-5q^{7}+9q^{9}-14q^{11}+q^{13}+\cdots\)
1200.4.a.h	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(-3\)	\(0\)	\(-2\)	\(-\)	\(+\)	\(-\)	\(q-3q^{3}-2q^{7}+9q^{9}-70q^{11}-54q^{13}+\cdots\)
1200.4.a.i	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(-3\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(q-3q^{3}-q^{7}+9q^{9}-42q^{11}+67q^{13}+\cdots\)
1200.4.a.j	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(-3\)	\(0\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q-3q^{3}+9q^{9}-4q^{11}-54q^{13}-114q^{17}+\cdots\)
1200.4.a.k	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(-3\)	\(0\)	\(4\)	\(+\)	\(+\)	\(+\)	\(q-3q^{3}+4q^{7}+9q^{9}-72q^{11}+6q^{13}+\cdots\)
1200.4.a.l	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(-3\)	\(0\)	\(4\)	\(+\)	\(+\)	\(-\)	\(q-3q^{3}+4q^{7}+9q^{9}+28q^{11}+2^{4}q^{13}+\cdots\)
1200.4.a.m	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(-3\)	\(0\)	\(7\)	\(-\)	\(+\)	\(-\)	\(q-3q^{3}+7q^{7}+9q^{9}+54q^{11}-55q^{13}+\cdots\)
1200.4.a.n	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(-3\)	\(0\)	\(19\)	\(+\)	\(+\)	\(-\)	\(q-3q^{3}+19q^{7}+9q^{9}-22q^{11}+q^{13}+\cdots\)
1200.4.a.o	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(-3\)	\(0\)	\(20\)	\(-\)	\(+\)	\(+\)	\(q-3q^{3}+20q^{7}+9q^{9}+24q^{11}-74q^{13}+\cdots\)
1200.4.a.p	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(-3\)	\(0\)	\(20\)	\(+\)	\(+\)	\(+\)	\(q-3q^{3}+20q^{7}+9q^{9}+56q^{11}+86q^{13}+\cdots\)
1200.4.a.q	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(-3\)	\(0\)	\(22\)	\(-\)	\(+\)	\(-\)	\(q-3q^{3}+22q^{7}+9q^{9}+14q^{11}+30q^{13}+\cdots\)
1200.4.a.r	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(-3\)	\(0\)	\(23\)	\(-\)	\(+\)	\(+\)	\(q-3q^{3}+23q^{7}+9q^{9}+30q^{11}-29q^{13}+\cdots\)
1200.4.a.s	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(-3\)	\(0\)	\(32\)	\(-\)	\(+\)	\(+\)	\(q-3q^{3}+2^{5}q^{7}+9q^{9}-6^{2}q^{11}+10q^{13}+\cdots\)
1200.4.a.t	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(3\)	\(0\)	\(-24\)	\(-\)	\(-\)	\(+\)	\(q+3q^{3}-24q^{7}+9q^{9}-52q^{11}-22q^{13}+\cdots\)
1200.4.a.u	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(3\)	\(0\)	\(-24\)	\(+\)	\(-\)	\(+\)	\(q+3q^{3}-24q^{7}+9q^{9}+28q^{11}+74q^{13}+\cdots\)
1200.4.a.v	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(3\)	\(0\)	\(-23\)	\(-\)	\(-\)	\(-\)	\(q+3q^{3}-23q^{7}+9q^{9}+30q^{11}+29q^{13}+\cdots\)
1200.4.a.w	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(3\)	\(0\)	\(-22\)	\(-\)	\(-\)	\(-\)	\(q+3q^{3}-22q^{7}+9q^{9}+14q^{11}-30q^{13}+\cdots\)
1200.4.a.x	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(3\)	\(0\)	\(-19\)	\(+\)	\(-\)	\(+\)	\(q+3q^{3}-19q^{7}+9q^{9}-22q^{11}-q^{13}+\cdots\)
1200.4.a.y	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(3\)	\(0\)	\(-7\)	\(-\)	\(-\)	\(+\)	\(q+3q^{3}-7q^{7}+9q^{9}+54q^{11}+55q^{13}+\cdots\)
1200.4.a.z	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(3\)	\(0\)	\(-4\)	\(+\)	\(-\)	\(-\)	\(q+3q^{3}-4q^{7}+9q^{9}+28q^{11}-2^{4}q^{13}+\cdots\)
1200.4.a.ba	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(3\)	\(0\)	\(-4\)	\(-\)	\(-\)	\(+\)	\(q+3q^{3}-4q^{7}+9q^{9}+48q^{11}-2q^{13}+\cdots\)
1200.4.a.bb	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(3\)	\(0\)	\(1\)	\(-\)	\(-\)	\(-\)	\(q+3q^{3}+q^{7}+9q^{9}-42q^{11}-67q^{13}+\cdots\)
1200.4.a.bc	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(3\)	\(0\)	\(2\)	\(-\)	\(-\)	\(-\)	\(q+3q^{3}+2q^{7}+9q^{9}-70q^{11}+54q^{13}+\cdots\)
1200.4.a.bd	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(3\)	\(0\)	\(5\)	\(+\)	\(-\)	\(+\)	\(q+3q^{3}+5q^{7}+9q^{9}-14q^{11}-q^{13}+\cdots\)
1200.4.a.be	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(3\)	\(0\)	\(8\)	\(-\)	\(-\)	\(+\)	\(q+3q^{3}+8q^{7}+9q^{9}-6^{2}q^{11}+10q^{13}+\cdots\)
1200.4.a.bf	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(3\)	\(0\)	\(8\)	\(+\)	\(-\)	\(+\)	\(q+3q^{3}+8q^{7}+9q^{9}-20q^{11}-22q^{13}+\cdots\)
1200.4.a.bg	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(3\)	\(0\)	\(10\)	\(+\)	\(-\)	\(-\)	\(q+3q^{3}+10q^{7}+9q^{9}+14q^{11}+82q^{13}+\cdots\)
1200.4.a.bh	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(3\)	\(0\)	\(10\)	\(+\)	\(-\)	\(-\)	\(q+3q^{3}+10q^{7}+9q^{9}+46q^{11}+34q^{13}+\cdots\)
1200.4.a.bi	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(3\)	\(0\)	\(13\)	\(-\)	\(-\)	\(-\)	\(q+3q^{3}+13q^{7}+9q^{9}-6q^{11}+5q^{13}+\cdots\)
1200.4.a.bj	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(3\)	\(0\)	\(20\)	\(+\)	\(-\)	\(+\)	\(q+3q^{3}+20q^{7}+9q^{9}-2^{4}q^{11}-58q^{13}+\cdots\)
1200.4.a.bk	\(1\)	\(70.802\)	\(\Q\)	None	\(0\)	\(3\)	\(0\)	\(32\)	\(-\)	\(-\)	\(+\)	\(q+3q^{3}+2^{5}q^{7}+9q^{9}+60q^{11}+34q^{13}+\cdots\)
1200.4.a.bl	\(2\)	\(70.802\)	\(\Q(\sqrt{19}) \)	None	\(0\)	\(-6\)	\(0\)	\(-26\)	\(-\)	\(+\)	\(-\)	\(q-3q^{3}+(-13+\beta )q^{7}+9q^{9}+(-14+\cdots)q^{11}+\cdots\)
1200.4.a.bm	\(2\)	\(70.802\)	\(\Q(\sqrt{181}) \)	None	\(0\)	\(-6\)	\(0\)	\(-6\)	\(+\)	\(+\)	\(+\)	\(q-3q^{3}+(-3-\beta )q^{7}+9q^{9}+(-4+\cdots)q^{11}+\cdots\)
1200.4.a.bn	\(2\)	\(70.802\)	\(\Q(\sqrt{41}) \)	None	\(0\)	\(-6\)	\(0\)	\(-6\)	\(-\)	\(+\)	\(-\)	\(q-3q^{3}+(-3-3\beta )q^{7}+9q^{9}+(21+\cdots)q^{11}+\cdots\)
1200.4.a.bo	\(2\)	\(70.802\)	\(\Q(\sqrt{129}) \)	None	\(0\)	\(-6\)	\(0\)	\(2\)	\(+\)	\(+\)	\(-\)	\(q-3q^{3}+(1+3\beta )q^{7}+9q^{9}+(-37+\cdots)q^{11}+\cdots\)
1200.4.a.bp	\(2\)	\(70.802\)	\(\Q(\sqrt{109}) \)	None	\(0\)	\(-6\)	\(0\)	\(2\)	\(+\)	\(+\)	\(+\)	\(q-3q^{3}+(1+\beta )q^{7}+9q^{9}+(8-3\beta )q^{11}+\cdots\)
1200.4.a.bq	\(2\)	\(70.802\)	\(\Q(\sqrt{129}) \)	None	\(0\)	\(6\)	\(0\)	\(-2\)	\(+\)	\(-\)	\(-\)	\(q+3q^{3}+(-1-3\beta )q^{7}+9q^{9}+(-37+\cdots)q^{11}+\cdots\)
1200.4.a.br	\(2\)	\(70.802\)	\(\Q(\sqrt{109}) \)	None	\(0\)	\(6\)	\(0\)	\(-2\)	\(+\)	\(-\)	\(-\)	\(q+3q^{3}+(-1-\beta )q^{7}+9q^{9}+(8-3\beta )q^{11}+\cdots\)
1200.4.a.bs	\(2\)	\(70.802\)	\(\Q(\sqrt{181}) \)	None	\(0\)	\(6\)	\(0\)	\(6\)	\(+\)	\(-\)	\(-\)	\(q+3q^{3}+(3+\beta )q^{7}+9q^{9}+(-4-\beta )q^{11}+\cdots\)
1200.4.a.bt	\(2\)	\(70.802\)	\(\Q(\sqrt{41}) \)	None	\(0\)	\(6\)	\(0\)	\(6\)	\(-\)	\(-\)	\(-\)	\(q+3q^{3}+(3+3\beta )q^{7}+9q^{9}+(21-3\beta )q^{11}+\cdots\)
1200.4.a.bu	\(2\)	\(70.802\)	\(\Q(\sqrt{19}) \)	None	\(0\)	\(6\)	\(0\)	\(26\)	\(-\)	\(-\)	\(+\)	\(q+3q^{3}+(13+\beta )q^{7}+9q^{9}+(-14+\cdots)q^{11}+\cdots\)