LMFDB - Space of modular forms of level 2070, weight 4, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2070.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 42 $
Sturm bound:			$1728$
Trace bound:			$7$
Distinguishing $T_p$:			$7$, $11$, $17$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(\Gamma_0(2070))$.

	Total	New	Old
Modular forms	1312	110	1202
Cusp forms	1280	110	1170
Eisenstein series	32	0	32

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

$2$	$3$	$5$	$23$	Fricke	Dim.
$+$	$+$	$+$	$+$	$+$	$5$
$+$	$+$	$+$	$-$	$-$	$6$
$+$	$+$	$-$	$+$	$-$	$6$
$+$	$+$	$-$	$-$	$+$	$5$
$+$	$-$	$+$	$+$	$-$	$7$
$+$	$-$	$+$	$-$	$+$	$9$
$+$	$-$	$-$	$+$	$+$	$9$
$+$	$-$	$-$	$-$	$-$	$7$
$-$	$+$	$+$	$+$	$-$	$5$
$-$	$+$	$+$	$-$	$+$	$6$
$-$	$+$	$-$	$+$	$+$	$6$
$-$	$+$	$-$	$-$	$-$	$5$
$-$	$-$	$+$	$+$	$+$	$10$
$-$	$-$	$+$	$-$	$-$	$7$
$-$	$-$	$-$	$+$	$-$	$7$
$-$	$-$	$-$	$-$	$+$	$10$
Plus space				$+$	$60$
Minus space				$-$	$50$

Trace form

$ 110 q + 4 q^{2} + 440 q^{4} - 104 q^{7} + 16 q^{8} + O(q^{10}) $

$ 110 q + 4 q^{2} + 440 q^{4} - 104 q^{7} + 16 q^{8} - 84 q^{11} - 60 q^{13} - 80 q^{14} + 1760 q^{16} - 84 q^{17} - 92 q^{19} + 40 q^{22} + 2750 q^{25} - 416 q^{28} - 248 q^{29} + 24 q^{31} + 64 q^{32} + 360 q^{34} + 100 q^{35} + 1144 q^{37} + 72 q^{38} - 268 q^{41} + 428 q^{43} - 336 q^{44} - 912 q^{47} + 6206 q^{49} + 100 q^{50} - 240 q^{52} - 872 q^{53} - 320 q^{56} - 232 q^{58} - 260 q^{59} - 3408 q^{61} + 1696 q^{62} + 7040 q^{64} - 1280 q^{65} - 1220 q^{67} - 336 q^{68} - 280 q^{70} + 792 q^{71} - 4300 q^{73} - 1664 q^{74} - 368 q^{76} + 752 q^{77} - 3088 q^{79} + 1752 q^{82} - 428 q^{83} - 1220 q^{85} - 584 q^{86} + 160 q^{88} + 1596 q^{89} + 1816 q^{91} + 3696 q^{94} + 40 q^{95} + 5612 q^{97} - 220 q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{4}^{\mathrm{new}}(\Gamma_0(2070))$ 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	23	$q$-expansion
2070.4.a.a	$1$	$122.134$	$\Q$	None	$-2$	$0$	$-5$	$-32$	$+$	$-$	$+$	$+$	$q-2q^{2}+4q^{4}-5q^{5}-2^{5}q^{7}-8q^{8}+\cdots$
2070.4.a.b	$1$	$122.134$	$\Q$	None	$-2$	$0$	$-5$	$-7$	$+$	$-$	$+$	$-$	$q-2q^{2}+4q^{4}-5q^{5}-7q^{7}-8q^{8}+\cdots$
2070.4.a.c	$1$	$122.134$	$\Q$	None	$-2$	$0$	$-5$	$2$	$+$	$+$	$+$	$-$	$q-2q^{2}+4q^{4}-5q^{5}+2q^{7}-8q^{8}+\cdots$
2070.4.a.d	$1$	$122.134$	$\Q$	None	$-2$	$0$	$5$	$-20$	$+$	$-$	$-$	$+$	$q-2q^{2}+4q^{4}+5q^{5}-20q^{7}-8q^{8}+\cdots$
2070.4.a.e	$1$	$122.134$	$\Q$	None	$-2$	$0$	$5$	$-18$	$+$	$-$	$-$	$-$	$q-2q^{2}+4q^{4}+5q^{5}-18q^{7}-8q^{8}+\cdots$
2070.4.a.f	$1$	$122.134$	$\Q$	None	$-2$	$0$	$5$	$-5$	$+$	$-$	$-$	$+$	$q-2q^{2}+4q^{4}+5q^{5}-5q^{7}-8q^{8}+\cdots$
2070.4.a.g	$1$	$122.134$	$\Q$	None	$2$	$0$	$-5$	$-19$	$-$	$-$	$+$	$-$	$q+2q^{2}+4q^{4}-5q^{5}-19q^{7}+8q^{8}+\cdots$
2070.4.a.h	$1$	$122.134$	$\Q$	None	$2$	$0$	$-5$	$-18$	$-$	$-$	$+$	$+$	$q+2q^{2}+4q^{4}-5q^{5}-18q^{7}+8q^{8}+\cdots$
2070.4.a.i	$1$	$122.134$	$\Q$	None	$2$	$0$	$-5$	$16$	$-$	$-$	$+$	$-$	$q+2q^{2}+4q^{4}-5q^{5}+2^{4}q^{7}+8q^{8}+\cdots$
2070.4.a.j	$1$	$122.134$	$\Q$	None	$2$	$0$	$-5$	$20$	$-$	$-$	$+$	$+$	$q+2q^{2}+4q^{4}-5q^{5}+20q^{7}+8q^{8}+\cdots$
2070.4.a.k	$1$	$122.134$	$\Q$	None	$2$	$0$	$5$	$-16$	$-$	$-$	$-$	$+$	$q+2q^{2}+4q^{4}+5q^{5}-2^{4}q^{7}+8q^{8}+\cdots$
2070.4.a.l	$1$	$122.134$	$\Q$	None	$2$	$0$	$5$	$-5$	$-$	$-$	$-$	$+$	$q+2q^{2}+4q^{4}+5q^{5}-5q^{7}+8q^{8}+\cdots$
2070.4.a.m	$1$	$122.134$	$\Q$	None	$2$	$0$	$5$	$2$	$-$	$+$	$-$	$+$	$q+2q^{2}+4q^{4}+5q^{5}+2q^{7}+8q^{8}+\cdots$
2070.4.a.n	$1$	$122.134$	$\Q$	None	$2$	$0$	$5$	$3$	$-$	$-$	$-$	$+$	$q+2q^{2}+4q^{4}+5q^{5}+3q^{7}+8q^{8}+\cdots$
2070.4.a.o	$1$	$122.134$	$\Q$	None	$2$	$0$	$5$	$12$	$-$	$-$	$-$	$+$	$q+2q^{2}+4q^{4}+5q^{5}+12q^{7}+8q^{8}+\cdots$
2070.4.a.p	$2$	$122.134$	$\Q(\sqrt{41}) $	None	$-4$	$0$	$-10$	$-26$	$+$	$+$	$+$	$+$	$q-2q^{2}+4q^{4}-5q^{5}+(-13-\beta )q^{7}+\cdots$
2070.4.a.q	$2$	$122.134$	$\Q(\sqrt{14}) $	None	$-4$	$0$	$-10$	$-2$	$+$	$-$	$+$	$+$	$q-2q^{2}+4q^{4}-5q^{5}+(-1+4\beta )q^{7}+\cdots$
2070.4.a.r	$2$	$122.134$	$\Q(\sqrt{6}) $	None	$4$	$0$	$-10$	$-26$	$-$	$-$	$+$	$+$	$q+2q^{2}+4q^{4}-5q^{5}+(-13+2\beta )q^{7}+\cdots$
2070.4.a.s	$2$	$122.134$	$\Q(\sqrt{73}) $	None	$4$	$0$	$-10$	$-17$	$-$	$-$	$+$	$-$	$q+2q^{2}+4q^{4}-5q^{5}+(-8-\beta )q^{7}+\cdots$
2070.4.a.t	$2$	$122.134$	$\Q(\sqrt{41}) $	None	$4$	$0$	$10$	$-26$	$-$	$+$	$-$	$-$	$q+2q^{2}+4q^{4}+5q^{5}+(-13-\beta )q^{7}+\cdots$
2070.4.a.u	$3$	$122.134$	3.3.19544.1	None	$-6$	$0$	$-15$	$-16$	$+$	$+$	$+$	$+$	$q-2q^{2}+4q^{4}-5q^{5}+(-6+3\beta _{1}+\cdots)q^{7}+\cdots$
2070.4.a.v	$3$	$122.134$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$-6$	$0$	$15$	$-2$	$+$	$-$	$-$	$-$	$q-2q^{2}+4q^{4}+5q^{5}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots$
2070.4.a.w	$3$	$122.134$	3.3.162793.1	None	$-6$	$0$	$15$	$3$	$+$	$-$	$-$	$+$	$q-2q^{2}+4q^{4}+5q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+\cdots$
2070.4.a.x	$3$	$122.134$	3.3.396732.1	None	$-6$	$0$	$15$	$12$	$+$	$-$	$-$	$-$	$q-2q^{2}+4q^{4}+5q^{5}+(4-\beta _{1}+\beta _{2})q^{7}+\cdots$
2070.4.a.y	$3$	$122.134$	3.3.460593.1	None	$6$	$0$	$-15$	$-3$	$-$	$-$	$+$	$-$	$q+2q^{2}+4q^{4}-5q^{5}+(-1+\beta _{2})q^{7}+\cdots$
2070.4.a.z	$3$	$122.134$	3.3.931848.1	None	$6$	$0$	$-15$	$6$	$-$	$-$	$+$	$+$	$q+2q^{2}+4q^{4}-5q^{5}+(1+2\beta _{1}-\beta _{2})q^{7}+\cdots$
2070.4.a.ba	$3$	$122.134$	3.3.318165.1	None	$6$	$0$	$-15$	$7$	$-$	$-$	$+$	$+$	$q+2q^{2}+4q^{4}-5q^{5}+(1+3\beta _{1}-\beta _{2})q^{7}+\cdots$
2070.4.a.bb	$3$	$122.134$	3.3.471057.3	None	$6$	$0$	$15$	$-35$	$-$	$-$	$-$	$+$	$q+2q^{2}+4q^{4}+5q^{5}+(-12-\beta _{1}+\cdots)q^{7}+\cdots$
2070.4.a.bc	$3$	$122.134$	3.3.19544.1	None	$6$	$0$	$15$	$-16$	$-$	$+$	$-$	$-$	$q+2q^{2}+4q^{4}+5q^{5}+(-6+3\beta _{1}+\cdots)q^{7}+\cdots$
2070.4.a.bd	$3$	$122.134$	3.3.207308.1	None	$6$	$0$	$15$	$2$	$-$	$-$	$-$	$-$	$q+2q^{2}+4q^{4}+5q^{5}+(1-2\beta _{1}+\beta _{2})q^{7}+\cdots$
2070.4.a.be	$3$	$122.134$	3.3.617756.1	None	$6$	$0$	$15$	$30$	$-$	$-$	$-$	$-$	$q+2q^{2}+4q^{4}+5q^{5}+(10+\beta _{2})q^{7}+\cdots$
2070.4.a.bf	$4$	$122.134$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$-8$	$0$	$-20$	$7$	$+$	$-$	$+$	$-$	$q-2q^{2}+4q^{4}-5q^{5}+(2-\beta _{1})q^{7}+\cdots$
2070.4.a.bg	$4$	$122.134$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$-8$	$0$	$-20$	$8$	$+$	$-$	$+$	$-$	$q-2q^{2}+4q^{4}-5q^{5}+(1+\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots$
2070.4.a.bh	$4$	$122.134$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$-8$	$0$	$-20$	$26$	$+$	$-$	$+$	$+$	$q-2q^{2}+4q^{4}-5q^{5}+(6-\beta _{1})q^{7}+\cdots$
2070.4.a.bi	$4$	$122.134$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$-8$	$0$	$20$	$26$	$+$	$-$	$-$	$+$	$q-2q^{2}+4q^{4}+5q^{5}+(6-\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots$
2070.4.a.bj	$4$	$122.134$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$8$	$0$	$20$	$-1$	$-$	$-$	$-$	$-$	$q+2q^{2}+4q^{4}+5q^{5}+(2\beta _{1}+\beta _{2})q^{7}+\cdots$
2070.4.a.bk	$5$	$122.134$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	$-10$	$0$	$-25$	$12$	$+$	$+$	$+$	$-$	$q-2q^{2}+4q^{4}-5q^{5}+(2-\beta _{2})q^{7}+\cdots$
2070.4.a.bl	$5$	$122.134$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	$-10$	$0$	$25$	$0$	$+$	$+$	$-$	$-$	$q-2q^{2}+4q^{4}+5q^{5}+(-\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots$
2070.4.a.bm	$5$	$122.134$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	$10$	$0$	$-25$	$0$	$-$	$+$	$+$	$+$	$q+2q^{2}+4q^{4}-5q^{5}+(-\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots$
2070.4.a.bn	$5$	$122.134$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	$10$	$0$	$25$	$12$	$-$	$+$	$-$	$+$	$q+2q^{2}+4q^{4}+5q^{5}+(2-\beta _{2})q^{7}+\cdots$
2070.4.a.bo	$6$	$122.134$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$-12$	$0$	$30$	$0$	$+$	$+$	$-$	$+$	$q-2q^{2}+4q^{4}+5q^{5}-\beta _{1}q^{7}-8q^{8}+\cdots$
2070.4.a.bp	$6$	$122.134$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$12$	$0$	$-30$	$0$	$-$	$+$	$+$	$-$	$q+2q^{2}+4q^{4}-5q^{5}-\beta _{1}q^{7}+8q^{8}+\cdots$

Decomposition of $S_{4}^{\mathrm{old}}(\Gamma_0(2070))$ into lower level spaces

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Level:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2070.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 42 \)
Sturm bound:			\(1728\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\), \(11\), \(17\)

\(2\)	\(3\)	\(5\)	\(23\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(5\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(6\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(6\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(5\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(7\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(9\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(9\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(7\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(5\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(6\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(5\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(10\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(7\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(7\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(10\)
Plus space				\(+\)	\(60\)
Minus space				\(-\)	\(50\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2070))\) into newform subspaces

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2070))\) 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	2070.4.a

Level	$2070$
Weight	$4$
Character orbit	2070.a
Rep. character	$\chi_{2070}(1,\cdot)$
Character field	$\Q$
Dimension	$110$
Newform subspaces	$42$
Sturm bound	$1728$
Trace bound	$7$

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	23	$q$-expansion
2070.4.a.a	$1$	$122.134$	\(\Q\)	None	\(-2\)	\(0\)	\(-5\)	\(-32\)	$+$	$-$	$+$	$+$	\(q-2q^{2}+4q^{4}-5q^{5}-2^{5}q^{7}-8q^{8}+\cdots\)
2070.4.a.b	$1$	$122.134$	\(\Q\)	None	\(-2\)	\(0\)	\(-5\)	\(-7\)	$+$	$-$	$+$	$-$	\(q-2q^{2}+4q^{4}-5q^{5}-7q^{7}-8q^{8}+\cdots\)
2070.4.a.c	$1$	$122.134$	\(\Q\)	None	\(-2\)	\(0\)	\(-5\)	\(2\)	$+$	$+$	$+$	$-$	\(q-2q^{2}+4q^{4}-5q^{5}+2q^{7}-8q^{8}+\cdots\)
2070.4.a.d	$1$	$122.134$	\(\Q\)	None	\(-2\)	\(0\)	\(5\)	\(-20\)	$+$	$-$	$-$	$+$	\(q-2q^{2}+4q^{4}+5q^{5}-20q^{7}-8q^{8}+\cdots\)
2070.4.a.e	$1$	$122.134$	\(\Q\)	None	\(-2\)	\(0\)	\(5\)	\(-18\)	$+$	$-$	$-$	$-$	\(q-2q^{2}+4q^{4}+5q^{5}-18q^{7}-8q^{8}+\cdots\)
2070.4.a.f	$1$	$122.134$	\(\Q\)	None	\(-2\)	\(0\)	\(5\)	\(-5\)	$+$	$-$	$-$	$+$	\(q-2q^{2}+4q^{4}+5q^{5}-5q^{7}-8q^{8}+\cdots\)
2070.4.a.g	$1$	$122.134$	\(\Q\)	None	\(2\)	\(0\)	\(-5\)	\(-19\)	$-$	$-$	$+$	$-$	\(q+2q^{2}+4q^{4}-5q^{5}-19q^{7}+8q^{8}+\cdots\)
2070.4.a.h	$1$	$122.134$	\(\Q\)	None	\(2\)	\(0\)	\(-5\)	\(-18\)	$-$	$-$	$+$	$+$	\(q+2q^{2}+4q^{4}-5q^{5}-18q^{7}+8q^{8}+\cdots\)
2070.4.a.i	$1$	$122.134$	\(\Q\)	None	\(2\)	\(0\)	\(-5\)	\(16\)	$-$	$-$	$+$	$-$	\(q+2q^{2}+4q^{4}-5q^{5}+2^{4}q^{7}+8q^{8}+\cdots\)
2070.4.a.j	$1$	$122.134$	\(\Q\)	None	\(2\)	\(0\)	\(-5\)	\(20\)	$-$	$-$	$+$	$+$	\(q+2q^{2}+4q^{4}-5q^{5}+20q^{7}+8q^{8}+\cdots\)
2070.4.a.k	$1$	$122.134$	\(\Q\)	None	\(2\)	\(0\)	\(5\)	\(-16\)	$-$	$-$	$-$	$+$	\(q+2q^{2}+4q^{4}+5q^{5}-2^{4}q^{7}+8q^{8}+\cdots\)
2070.4.a.l	$1$	$122.134$	\(\Q\)	None	\(2\)	\(0\)	\(5\)	\(-5\)	$-$	$-$	$-$	$+$	\(q+2q^{2}+4q^{4}+5q^{5}-5q^{7}+8q^{8}+\cdots\)
2070.4.a.m	$1$	$122.134$	\(\Q\)	None	\(2\)	\(0\)	\(5\)	\(2\)	$-$	$+$	$-$	$+$	\(q+2q^{2}+4q^{4}+5q^{5}+2q^{7}+8q^{8}+\cdots\)
2070.4.a.n	$1$	$122.134$	\(\Q\)	None	\(2\)	\(0\)	\(5\)	\(3\)	$-$	$-$	$-$	$+$	\(q+2q^{2}+4q^{4}+5q^{5}+3q^{7}+8q^{8}+\cdots\)
2070.4.a.o	$1$	$122.134$	\(\Q\)	None	\(2\)	\(0\)	\(5\)	\(12\)	$-$	$-$	$-$	$+$	\(q+2q^{2}+4q^{4}+5q^{5}+12q^{7}+8q^{8}+\cdots\)
2070.4.a.p	$2$	$122.134$	\(\Q(\sqrt{41}) \)	None	\(-4\)	\(0\)	\(-10\)	\(-26\)	$+$	$+$	$+$	$+$	\(q-2q^{2}+4q^{4}-5q^{5}+(-13-\beta )q^{7}+\cdots\)
2070.4.a.q	$2$	$122.134$	\(\Q(\sqrt{14}) \)	None	\(-4\)	\(0\)	\(-10\)	\(-2\)	$+$	$-$	$+$	$+$	\(q-2q^{2}+4q^{4}-5q^{5}+(-1+4\beta )q^{7}+\cdots\)
2070.4.a.r	$2$	$122.134$	\(\Q(\sqrt{6}) \)	None	\(4\)	\(0\)	\(-10\)	\(-26\)	$-$	$-$	$+$	$+$	\(q+2q^{2}+4q^{4}-5q^{5}+(-13+2\beta )q^{7}+\cdots\)
2070.4.a.s	$2$	$122.134$	\(\Q(\sqrt{73}) \)	None	\(4\)	\(0\)	\(-10\)	\(-17\)	$-$	$-$	$+$	$-$	\(q+2q^{2}+4q^{4}-5q^{5}+(-8-\beta )q^{7}+\cdots\)
2070.4.a.t	$2$	$122.134$	\(\Q(\sqrt{41}) \)	None	\(4\)	\(0\)	\(10\)	\(-26\)	$-$	$+$	$-$	$-$	\(q+2q^{2}+4q^{4}+5q^{5}+(-13-\beta )q^{7}+\cdots\)
2070.4.a.u	$3$	$122.134$	3.3.19544.1	None	\(-6\)	\(0\)	\(-15\)	\(-16\)	$+$	$+$	$+$	$+$	\(q-2q^{2}+4q^{4}-5q^{5}+(-6+3\beta _{1}+\cdots)q^{7}+\cdots\)
2070.4.a.v	$3$	$122.134$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(-6\)	\(0\)	\(15\)	\(-2\)	$+$	$-$	$-$	$-$	\(q-2q^{2}+4q^{4}+5q^{5}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
2070.4.a.w	$3$	$122.134$	3.3.162793.1	None	\(-6\)	\(0\)	\(15\)	\(3\)	$+$	$-$	$-$	$+$	\(q-2q^{2}+4q^{4}+5q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
2070.4.a.x	$3$	$122.134$	3.3.396732.1	None	\(-6\)	\(0\)	\(15\)	\(12\)	$+$	$-$	$-$	$-$	\(q-2q^{2}+4q^{4}+5q^{5}+(4-\beta _{1}+\beta _{2})q^{7}+\cdots\)
2070.4.a.y	$3$	$122.134$	3.3.460593.1	None	\(6\)	\(0\)	\(-15\)	\(-3\)	$-$	$-$	$+$	$-$	\(q+2q^{2}+4q^{4}-5q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
2070.4.a.z	$3$	$122.134$	3.3.931848.1	None	\(6\)	\(0\)	\(-15\)	\(6\)	$-$	$-$	$+$	$+$	\(q+2q^{2}+4q^{4}-5q^{5}+(1+2\beta _{1}-\beta _{2})q^{7}+\cdots\)
2070.4.a.ba	$3$	$122.134$	3.3.318165.1	None	\(6\)	\(0\)	\(-15\)	\(7\)	$-$	$-$	$+$	$+$	\(q+2q^{2}+4q^{4}-5q^{5}+(1+3\beta _{1}-\beta _{2})q^{7}+\cdots\)
2070.4.a.bb	$3$	$122.134$	3.3.471057.3	None	\(6\)	\(0\)	\(15\)	\(-35\)	$-$	$-$	$-$	$+$	\(q+2q^{2}+4q^{4}+5q^{5}+(-12-\beta _{1}+\cdots)q^{7}+\cdots\)
2070.4.a.bc	$3$	$122.134$	3.3.19544.1	None	\(6\)	\(0\)	\(15\)	\(-16\)	$-$	$+$	$-$	$-$	\(q+2q^{2}+4q^{4}+5q^{5}+(-6+3\beta _{1}+\cdots)q^{7}+\cdots\)
2070.4.a.bd	$3$	$122.134$	3.3.207308.1	None	\(6\)	\(0\)	\(15\)	\(2\)	$-$	$-$	$-$	$-$	\(q+2q^{2}+4q^{4}+5q^{5}+(1-2\beta _{1}+\beta _{2})q^{7}+\cdots\)
2070.4.a.be	$3$	$122.134$	3.3.617756.1	None	\(6\)	\(0\)	\(15\)	\(30\)	$-$	$-$	$-$	$-$	\(q+2q^{2}+4q^{4}+5q^{5}+(10+\beta _{2})q^{7}+\cdots\)
2070.4.a.bf	$4$	$122.134$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(-8\)	\(0\)	\(-20\)	\(7\)	$+$	$-$	$+$	$-$	\(q-2q^{2}+4q^{4}-5q^{5}+(2-\beta _{1})q^{7}+\cdots\)
2070.4.a.bg	$4$	$122.134$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(-8\)	\(0\)	\(-20\)	\(8\)	$+$	$-$	$+$	$-$	\(q-2q^{2}+4q^{4}-5q^{5}+(1+\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)
2070.4.a.bh	$4$	$122.134$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(-8\)	\(0\)	\(-20\)	\(26\)	$+$	$-$	$+$	$+$	\(q-2q^{2}+4q^{4}-5q^{5}+(6-\beta _{1})q^{7}+\cdots\)
2070.4.a.bi	$4$	$122.134$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(-8\)	\(0\)	\(20\)	\(26\)	$+$	$-$	$-$	$+$	\(q-2q^{2}+4q^{4}+5q^{5}+(6-\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
2070.4.a.bj	$4$	$122.134$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(8\)	\(0\)	\(20\)	\(-1\)	$-$	$-$	$-$	$-$	\(q+2q^{2}+4q^{4}+5q^{5}+(2\beta _{1}+\beta _{2})q^{7}+\cdots\)
2070.4.a.bk	$5$	$122.134$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	\(-10\)	\(0\)	\(-25\)	\(12\)	$+$	$+$	$+$	$-$	\(q-2q^{2}+4q^{4}-5q^{5}+(2-\beta _{2})q^{7}+\cdots\)
2070.4.a.bl	$5$	$122.134$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	\(-10\)	\(0\)	\(25\)	\(0\)	$+$	$+$	$-$	$-$	\(q-2q^{2}+4q^{4}+5q^{5}+(-\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
2070.4.a.bm	$5$	$122.134$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	\(10\)	\(0\)	\(-25\)	\(0\)	$-$	$+$	$+$	$+$	\(q+2q^{2}+4q^{4}-5q^{5}+(-\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
2070.4.a.bn	$5$	$122.134$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	\(10\)	\(0\)	\(25\)	\(12\)	$-$	$+$	$-$	$+$	\(q+2q^{2}+4q^{4}+5q^{5}+(2-\beta _{2})q^{7}+\cdots\)
2070.4.a.bo	$6$	$122.134$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(-12\)	\(0\)	\(30\)	\(0\)	$+$	$+$	$-$	$+$	\(q-2q^{2}+4q^{4}+5q^{5}-\beta _{1}q^{7}-8q^{8}+\cdots\)
2070.4.a.bp	$6$	$122.134$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(12\)	\(0\)	\(-30\)	\(0\)	$-$	$+$	$+$	$-$	\(q+2q^{2}+4q^{4}-5q^{5}-\beta _{1}q^{7}+8q^{8}+\cdots\)