Newform orbit 152.5.s.a

• Label: 152.5.s.a
• Level: $152$
• Weight: $5$
• Character orbit: 152.s
• Analytic conductor: $15.712$
• Analytic rank: $0$
• Dimension: $468$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	152.s (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(15.7122343887\)
Analytic rank:	\(0\)
Dimension:	\(468\)
Relative dimension:	\(78\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 468 q - 6 q^{2} + 36 q^{4} - 60 q^{6} - 6 q^{7} - 9 q^{8} - 12 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
13.1	−3.99995	+	0.0208133i	1.45607	+	0.529968i	15.9991	−	0.166505i	10.3751	−	1.82941i	−5.83525	−	2.08954i	42.4700	−	73.5603i	−63.9922	+	0.999005i	−60.2103	−	50.5225i	−41.4618	+	7.53348i
13.2	−3.98189	−	0.380165i	15.0788	+	5.48824i	15.7109	+	3.02755i	5.43997	−	0.959214i	−57.9558	−	27.5860i	1.05650	−	1.82991i	−61.4084	−	18.0281i	135.200	+	113.446i	−22.0260	+	1.75140i
13.3	−3.98023	−	0.397248i	−5.92960	−	2.15820i	15.6844	+	3.16227i	−34.2302	+	6.03571i	22.7438	+	10.9456i	1.05836	−	1.83313i	−61.1712	−	18.8172i	−31.5473	−	26.4713i	138.642	−	10.4256i
13.4	−3.97290	−	0.464799i	−9.67720	−	3.52221i	15.5679	+	3.69321i	2.38082	−	0.419802i	36.8095	+	18.4914i	−20.2990	+	35.1590i	−60.1333	−	21.9087i	19.1927	+	16.1045i	−9.65388	+	0.561232i
13.5	−3.96753	+	0.508611i	7.08196	+	2.57762i	15.4826	−	4.03586i	22.8280	−	4.02519i	−29.4089	−	6.62483i	−26.9729	+	46.7184i	−59.3751	+	23.8871i	−18.5396	−	15.5566i	−88.5235	+	27.5806i
13.6	−3.94439	−	0.664645i	−15.4607	−	5.62723i	15.1165	+	5.24325i	32.5259	−	5.73520i	57.2430	+	32.4719i	18.5074	−	32.0558i	−56.1405	−	30.7285i	145.318	+	121.936i	−132.107	+	1.00369i
13.7	−3.83950	+	1.12173i	7.82356	+	2.84754i	13.4834	−	8.61375i	−46.2942	+	8.16292i	−33.2327	−	2.15721i	−45.9519	+	79.5910i	−42.1073	+	48.1972i	−8.95007	−	7.51000i	168.590	−	83.2711i
13.8	−3.64849	+	1.63967i	−8.56380	−	3.11697i	10.6230	−	11.9646i	30.0571	−	5.29988i	36.3558	−	2.66959i	−23.3516	+	40.4462i	−19.1397	+	61.0710i	1.57364	+	1.32044i	−100.973	+	68.6203i
13.9	−3.64398	+	1.64968i	8.69823	+	3.16590i	10.5571	−	12.0228i	2.07092	−	0.365160i	−36.9188	+	2.81285i	14.9691	−	25.9272i	−18.6361	+	61.2266i	3.58669	+	3.00959i	−6.94399	+	4.74699i
13.10	−3.64006	+	1.65831i	−2.87463	−	1.04628i	10.5000	−	12.0727i	−15.6740	+	2.76376i	12.1989	−	0.958504i	14.5510	−	25.2031i	−18.2005	+	61.3575i	−54.8808	−	46.0504i	52.4712	−	36.0526i
13.11	−3.63036	−	1.67943i	3.49687	+	1.27276i	10.3591	+	12.1938i	45.5320	−	8.02853i	−10.5574	−	10.4933i	11.8587	−	20.5399i	−17.1285	−	61.6653i	−51.4414	−	43.1645i	−178.781	−	47.3212i
13.12	−3.58925	−	1.76559i	11.6272	+	4.23196i	9.76540	+	12.6743i	−24.7546	+	4.36490i	−34.2610	−	35.7184i	3.02794	−	5.24454i	−12.6729	−	62.7327i	55.2328	+	46.3458i	96.5570	+	28.0397i
13.13	−3.58038	+	1.78351i	−16.2185	−	5.90306i	9.63820	−	12.7713i	−31.8333	+	5.61306i	68.5965	−	7.79068i	18.3098	−	31.7134i	−11.7307	+	62.9157i	166.145	+	139.412i	103.964	−	76.8717i
13.14	−3.45217	−	2.02053i	3.15525	+	1.14842i	7.83495	+	13.9504i	−23.3786	+	4.12228i	−8.57205	−	10.3398i	2.11397	−	3.66150i	1.13956	−	63.9899i	−53.4129	−	44.8187i	89.0361	+	33.0063i
13.15	−3.39655	−	2.11269i	0.467674	+	0.170219i	7.07311	+	14.3517i	18.9056	−	3.33356i	−1.22886	−	1.56621i	−38.8619	+	67.3107i	6.29644	−	63.6895i	−61.8599	−	51.9066i	−71.2565	−	28.6189i
13.16	−3.18711	+	2.41709i	14.3854	+	5.23585i	4.31532	−	15.4071i	−35.1611	+	6.19986i	−58.5033	+	18.0836i	35.0856	−	60.7701i	23.4870	+	59.5346i	117.475	+	98.5735i	97.0767	−	104.747i
13.17	−3.02797	−	2.61369i	−7.69958	−	2.80242i	2.33721	+	15.8284i	19.4221	−	3.42464i	15.9894	+	28.6100i	4.62478	−	8.01036i	34.2935	−	54.0366i	−10.6196	−	8.91089i	−67.7606	−	40.3938i
13.18	−2.94098	+	2.71121i	12.5500	+	4.56784i	1.29872	−	15.9472i	47.9861	−	8.46125i	−49.2938	+	20.5918i	3.78445	−	6.55486i	39.4166	+	50.4215i	74.5886	+	62.5873i	−118.186	+	154.985i
13.19	−2.92926	−	2.72386i	−11.0360	−	4.01676i	1.16117	+	15.9578i	−21.3343	+	3.76181i	21.3861	+	41.8266i	46.9329	−	81.2902i	40.0655	−	49.9075i	43.6085	+	36.5919i	72.7403	+	47.0922i
13.20	−2.91221	+	2.74209i	−9.87394	−	3.59382i	0.961920	−	15.9711i	−13.5121	+	2.38255i	38.6095	−	16.6092i	−33.6415	+	58.2689i	40.9927	+	49.1487i	22.5295	+	18.9045i	32.8169	−	43.9899i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
8.b	even	2	1	inner
19.f	odd	18	1	inner
152.s	odd	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	152.5.s.a	✓	468
8.b	even	2	1	inner	152.5.s.a	✓	468
19.f	odd	18	1	inner	152.5.s.a	✓	468
152.s	odd	18	1	inner	152.5.s.a	✓	468

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
152.5.s.a	✓	468	1.a	even	1	1	trivial
152.5.s.a	✓	468	8.b	even	2	1	inner
152.5.s.a	✓	468	19.f	odd	18	1	inner
152.5.s.a	✓	468	152.s	odd	18	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(152, [\chi])\).