Newform orbit 152.4.p.a

• Label: 152.4.p.a
• Level: $152$
• Weight: $4$
• Character orbit: 152.p
• Analytic conductor: $8.968$
• Analytic rank: $0$
• Dimension: $116$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	152.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.96829032087\)
Analytic rank:	\(0\)
Dimension:	\(116\)
Relative dimension:	\(58\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 116 q - q^{2} - 7 q^{4} - 11 q^{6} - 8 q^{7} - 46 q^{8} + 484 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
45.1	−2.82711	−	0.0864225i	4.26220	−	2.46078i	7.98506	+	0.488651i	−8.57414	+	4.95028i	−12.2624	+	6.58855i	24.1590			−22.5324	−	2.07156i	−1.38908	+	2.40596i	24.6678	−	13.2540i
45.2	−2.82486	+	0.142059i	−7.04526	+	4.06758i	7.95964	−	0.802590i	−4.40862	+	2.54532i	19.3240	−	12.4912i	19.7207			−22.3708	+	3.39794i	19.5905	−	33.9317i	12.0922	−	7.81645i
45.3	−2.82331	−	0.170085i	−5.08710	+	2.93704i	7.94214	+	0.960407i	17.9631	−	10.3710i	14.8620	−	7.42692i	−14.4987			−22.2598	−	4.06237i	3.75238	−	6.49931i	−52.4794	+	26.2253i
45.4	−2.81727	+	0.250933i	8.39713	−	4.84809i	7.87406	−	1.41390i	−7.24805	+	4.18466i	−22.4405	+	15.7655i	−14.4081			−21.8286	+	5.95920i	33.5079	−	58.0374i	19.3697	−	13.6081i
45.5	−2.74034	−	0.700393i	1.33173	−	0.768876i	7.01890	+	3.83863i	−0.690311	+	0.398551i	−4.18791	+	1.17424i	−7.42713			−16.5456	−	15.4351i	−12.3177	+	21.3348i	2.17083	−	0.608676i
45.6	−2.73439	−	0.723246i	−5.03629	+	2.90770i	6.95383	+	3.95528i	−17.1051	+	9.87563i	15.8742	−	4.30833i	−30.7136			−16.1539	−	15.8446i	3.40947	−	5.90537i	53.9146	−	14.6327i
45.7	−2.66177	+	0.956557i	3.22382	−	1.86127i	6.17000	−	5.09226i	15.4187	−	8.90199i	−6.80063	+	8.03803i	36.5436			−11.5520	+	19.4564i	−6.57134	+	11.3819i	−32.5257	+	38.4439i
45.8	−2.61512	+	1.07757i	2.09100	−	1.20724i	5.67769	−	5.63594i	3.32294	−	1.91850i	−4.16734	+	5.41028i	−25.0171			−8.77472	+	20.8568i	−10.5851	+	18.3340i	−6.62257	+	8.59781i
45.9	−2.55889	+	1.20502i	−4.74696	+	2.74066i	5.09583	−	6.16705i	2.75286	−	1.58936i	8.84438	−	12.7332i	6.39182			−5.60823	+	21.9214i	1.52239	−	2.63686i	−5.12904	+	7.38426i
45.10	−2.41786	−	1.46764i	6.82189	−	3.93862i	3.69206	+	7.09709i	12.0425	−	6.95276i	−22.2748	−	0.489060i	3.48301			1.48909	−	22.5784i	17.5255	−	30.3550i	−39.3213	−	0.863327i
45.11	−2.38043	−	1.52759i	−1.64191	+	0.947957i	3.33293	+	7.27266i	7.43335	−	4.29165i	5.35655	+	0.251620i	3.63601			3.17585	−	22.4034i	−11.7028	+	20.2698i	−24.2505	−	1.13915i
45.12	−2.37410	+	1.53742i	−0.934984	+	0.539813i	3.27269	−	7.29997i	−16.9708	+	9.79810i	1.38982	−	2.71903i	1.96699			3.45341	+	22.3623i	−12.9172	+	22.3733i	25.2266	−	49.3529i
45.13	−2.06790	−	1.92971i	−7.17990	+	4.14532i	0.552429	+	7.98090i	−0.378089	+	0.218290i	22.8466	+	5.28303i	17.0792			14.2585	−	17.5697i	20.8673	−	36.1433i	1.20309	+	0.278201i
45.14	−1.96964	+	2.02991i	7.73504	−	4.46582i	−0.241064	−	7.99637i	8.20718	−	4.73842i	−6.16999	+	24.4975i	−1.12317			16.7067	+	15.2606i	26.3872	−	45.7039i	−6.54660	+	25.9928i
45.15	−1.95037	−	2.04843i	−0.706252	+	0.407755i	−0.392134	+	7.99038i	−12.8180	+	7.40046i	2.21271	+	0.651437i	26.8247			17.1326	−	14.7809i	−13.1675	+	22.8067i	40.1591	+	11.8231i
45.16	−1.90949	−	2.08659i	6.11810	−	3.53229i	−0.707710	+	7.96864i	−15.3833	+	8.88152i	−19.0529	−	6.02110i	−5.95523			17.9786	−	13.7393i	11.4541	−	19.8390i	47.9062	+	15.1394i
45.17	−1.85453	+	2.13558i	−8.17248	+	4.71838i	−1.12144	−	7.92101i	0.978198	−	0.564763i	5.07960	−	26.2034i	−30.0678			18.9957	+	12.2948i	31.0262	−	53.7390i	−0.607999	+	3.13639i
45.18	−1.57710	+	2.34792i	5.02331	−	2.90021i	−3.02550	−	7.40583i	−10.8661	+	6.27356i	−1.11280	+	16.3683i	0.00550543			22.1599	+	4.57612i	3.32241	−	5.75457i	2.40715	−	35.4069i
45.19	−1.53199	+	2.37761i	−3.41182	+	1.96982i	−3.30604	−	7.28492i	2.11879	−	1.22328i	0.543410	−	11.1297i	20.3570			22.3855	+	3.29993i	−5.73966	+	9.94138i	−0.337465	+	6.91169i
45.20	−1.45458	−	2.42574i	3.96852	−	2.29123i	−3.76842	+	7.05684i	3.72792	−	2.15232i	−11.3304	−	6.29383i	−30.2215			22.5995	−	1.12350i	−3.00057	+	5.19714i	−10.6435	−	5.91226i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
8.b	even	2	1	inner
19.c	even	3	1	inner
152.p	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	152.4.p.a	✓	116
8.b	even	2	1	inner	152.4.p.a	✓	116
19.c	even	3	1	inner	152.4.p.a	✓	116
152.p	even	6	1	inner	152.4.p.a	✓	116

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
152.4.p.a	✓	116	1.a	even	1	1	trivial
152.4.p.a	✓	116	8.b	even	2	1	inner
152.4.p.a	✓	116	19.c	even	3	1	inner
152.4.p.a	✓	116	152.p	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(152, [\chi])\).