Newform orbit 120.4.v.a

• Label: 120.4.v.a
• Level: $120$
• Weight: $4$
• Character orbit: 120.v
• Analytic conductor: $7.080$
• Analytic rank: $0$
• Dimension: $72$
• Inner twists: $4$

Newspace parameters

Level:	$N$	$=$	$120 = 2^{3} \cdot 3 \cdot 5$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	120.v (of order $4$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

The algebraic $q$-expansion of this newform has not been computed, but we have computed the trace expansion.

$\operatorname{Tr}(f)(q) =$ 72 * q + 12 * q^6 + 84 * q^8 - 72 * q^10 + 24 * q^12 - 20 * q^16 - 104 * q^17 + 380 * q^20 + 44 * q^22 - 88 * q^25 - 368 * q^26 - 1068 * q^28 + 408 * q^30 + 340 * q^32 + 912 * q^35 - 108 * q^36 - 40 * q^38 - 952 * q^40 - 660 * q^42 + 864 * q^43 - 2256 * q^46 + 528 * q^48 - 344 * q^50 - 1488 * q^51 + 2544 * q^52 + 2144 * q^56 + 1004 * q^58 + 420 * q^60 + 2608 * q^62 - 1048 * q^65 + 1368 * q^66 + 3696 * q^67 - 1464 * q^68 + 204 * q^70 - 756 * q^72 + 1480 * q^73 - 4016 * q^76 - 72 * q^78 - 1684 * q^80 - 5832 * q^81 - 6712 * q^82 - 5360 * q^83 - 8416 * q^86 - 404 * q^88 + 108 * q^90 + 3392 * q^91 + 8432 * q^92 + 3828 * q^96 - 328 * q^97 + 7576 * q^98

Embeddings

For each embedding $\iota_m$ of the coefficient field, the values $\iota_m(a_n)$ are shown below.

For more information on an embedded modular form you can click on its label.

Label	$a_{2}$			$a_{3}$			$a_{4}$			$a_{5}$			$a_{6}$			$a_{7}$			$a_{8}$			$a_{9}$			$a_{10}$
43.1	−2.80887	+	0.332069i	−2.12132	−	2.12132i	7.77946	−	1.86547i	11.1658	−	0.570174i	6.66293	+	5.25408i	−5.65722	−	5.65722i	−21.2320	+	7.82318i			9.00000i	−31.1739	+	5.30935i
43.2	−2.77605	+	0.541804i	−2.12132	−	2.12132i	7.41290	−	3.00815i	−9.61270	−	5.70930i	7.03823	+	4.73955i	−7.34859	−	7.34859i	−18.9487	+	12.3671i			9.00000i	29.7786	+	10.6411i
43.3	−2.71261	−	0.801077i	2.12132	+	2.12132i	6.71655	+	4.34603i	11.0300	+	1.82735i	−4.05498	−	7.45366i	11.6097	+	11.6097i	−14.7379	−	17.1696i			9.00000i	−28.4563	−	13.7928i
43.4	−2.65758	−	0.968140i	2.12132	+	2.12132i	6.12541	+	5.14581i	−8.21764	+	7.58092i	−3.58383	−	7.69130i	−21.7697	−	21.7697i	−11.2969	−	19.6056i			9.00000i	29.1784	−	12.1910i
43.5	−2.62410	+	1.05551i	2.12132	+	2.12132i	5.77179	−	5.53954i	4.33793	−	10.3045i	−7.80563	−	3.32747i	−15.3854	−	15.3854i	−9.29869	+	20.6285i			9.00000i	−0.506636	+	31.6187i
43.6	−2.47537	+	1.36841i	2.12132	+	2.12132i	4.25492	−	6.77464i	3.59302	+	10.5873i	−8.15389	−	2.34822i	−3.55795	−	3.55795i	−1.26202	+	22.5922i			9.00000i	−23.3818	−	21.2907i
43.7	−2.33617	−	1.59446i	−2.12132	−	2.12132i	2.91539	+	7.44987i	−0.0435396	−	11.1803i	1.57341	+	8.33813i	23.8377	+	23.8377i	5.06766	−	22.0526i			9.00000i	−17.7248	+	26.1884i
43.8	−2.17261	+	1.81101i	−2.12132	−	2.12132i	1.44051	−	7.86924i	1.41154	+	11.0909i	8.45054	+	0.767086i	−8.12099	−	8.12099i	11.1216	+	19.7056i			9.00000i	−23.1524	−	21.5399i
43.9	−1.97204	−	2.02758i	2.12132	+	2.12132i	−0.222122	+	7.99692i	−8.64040	−	7.09531i	0.117809	−	8.48446i	4.53056	+	4.53056i	16.6524	−	15.3199i			9.00000i	2.65294	+	31.5113i
43.10	−1.89618	−	2.09869i	−2.12132	−	2.12132i	−0.808999	+	7.95899i	11.1181	+	1.17809i	−0.429587	+	8.47440i	−18.4060	−	18.4060i	18.2375	−	13.3938i			9.00000i	−18.6095	−	25.5673i
43.11	−1.81101	+	2.17261i	−2.12132	−	2.12132i	−1.44051	−	7.86924i	−1.41154	−	11.0909i	8.45054	−	0.767086i	8.12099	+	8.12099i	19.7056	+	11.1216i			9.00000i	26.6525	+	17.0189i
43.12	−1.60248	−	2.33068i	−2.12132	−	2.12132i	−2.86414	+	7.46972i	−9.22898	+	6.31077i	−1.54475	+	8.34348i	−4.23024	−	4.23024i	21.9992	−	5.29467i			9.00000i	29.4976	+	11.3969i
43.13	−1.36841	+	2.47537i	2.12132	+	2.12132i	−4.25492	−	6.77464i	−3.59302	−	10.5873i	−8.15389	+	2.34822i	3.55795	+	3.55795i	22.5922	−	1.26202i			9.00000i	31.1241	+	5.59364i
43.14	−1.05551	+	2.62410i	2.12132	+	2.12132i	−5.77179	−	5.53954i	−4.33793	+	10.3045i	−7.80563	+	3.32747i	15.3854	+	15.3854i	20.6285	−	9.29869i			9.00000i	−22.4612	−	22.2597i
43.15	−0.866614	−	2.69239i	2.12132	+	2.12132i	−6.49796	+	4.66653i	8.74847	−	6.96163i	3.87306	−	7.54979i	−1.78469	−	1.78469i	18.1954	+	13.4510i			9.00000i	−26.3250	−	17.5213i
43.16	−0.541804	+	2.77605i	−2.12132	−	2.12132i	−7.41290	−	3.00815i	9.61270	+	5.70930i	7.03823	−	4.73955i	7.34859	+	7.34859i	12.3671	−	18.9487i			9.00000i	−21.0575	+	23.5920i
43.17	−0.332069	+	2.80887i	−2.12132	−	2.12132i	−7.77946	−	1.86547i	−11.1658	+	0.570174i	6.66293	−	5.25408i	5.65722	+	5.65722i	7.82318	−	21.2320i			9.00000i	2.10627	−	31.5526i
43.18	−0.0857827	−	2.82713i	2.12132	+	2.12132i	−7.98528	+	0.485037i	0.507948	+	11.1688i	5.81527	−	6.17921i	−17.5600	−	17.5600i	2.05626	+	22.5338i			9.00000i	31.5320	−	2.39412i
43.19	−0.0403611	−	2.82814i	−2.12132	−	2.12132i	−7.99674	+	0.228293i	8.79326	+	6.90497i	−5.91377	+	6.08501i	24.3320	+	24.3320i	0.968403	+	22.6067i			9.00000i	19.1733	−	25.1472i
43.20	−0.00187419	−	2.82843i	−2.12132	−	2.12132i	−7.99999	+	0.0106020i	−1.00793	−	11.1348i	−5.99602	+	6.00397i	−9.44565	−	9.44565i	0.0449806	+	22.6274i			9.00000i	−31.4921	+	2.87171i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
8.d	odd	2	1	inner
40.k	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	120.4.v.a	✓	72
4.b	odd	2	1		480.4.bh.a		72
5.c	odd	4	1	inner	120.4.v.a	✓	72
8.b	even	2	1		480.4.bh.a		72
8.d	odd	2	1	inner	120.4.v.a	✓	72
20.e	even	4	1		480.4.bh.a		72
40.i	odd	4	1		480.4.bh.a		72
40.k	even	4	1	inner	120.4.v.a	✓	72

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
120.4.v.a	✓	72	1.a	even	1	1	trivial
120.4.v.a	✓	72	5.c	odd	4	1	inner
120.4.v.a	✓	72	8.d	odd	2	1	inner
120.4.v.a	✓	72	40.k	even	4	1	inner
480.4.bh.a		72	4.b	odd	2	1
480.4.bh.a		72	8.b	even	2	1
480.4.bh.a		72	20.e	even	4	1
480.4.bh.a		72	40.i	odd	4	1

Hecke kernels

This newform subspace is the entire newspace $S_{4}^{\mathrm{new}}(120, [\chi])$.