Newform orbit 245.4.p.a

• Label: 245.4.p.a
• Level: $245$
• Weight: $4$
• Character orbit: 245.p
• Analytic conductor: $14.455$
• Analytic rank: $0$
• Dimension: $492$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.p (of order \(14\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.4554679514\)
Analytic rank:	\(0\)
Dimension:	\(492\)
Relative dimension:	\(82\) over \(\Q(\zeta_{14})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 492 q + 310 q^{4} - 13 q^{5} + 2 q^{6} + 762 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
29.1	−2.41989	+	5.02494i	3.86232	−	0.881549i	−14.4063	−	18.0649i	8.90073	−	6.76588i	−4.91663	+	21.5412i	−14.3875	−	11.6619i	82.1373	−	18.7473i	−10.1858	+	4.90521i	12.4594	+	61.0983i
29.2	−2.38797	+	4.95867i	−7.02754	+	1.60399i	−13.8981	−	17.4277i	9.44731	+	5.97899i	8.82789	−	38.6775i	17.7965	+	5.12697i	76.6805	−	17.5018i	22.4874	−	10.8294i	−52.2077	+	32.5685i
29.3	−2.29227	+	4.75995i	2.40449	−	0.548810i	−12.4147	−	15.5676i	−8.77705	+	6.92556i	−2.89944	+	12.7033i	2.34028	+	18.3718i	61.3534	−	14.0035i	−18.8458	+	9.07564i	−12.8459	−	57.6536i
29.4	−2.28400	+	4.74277i	−6.22063	+	1.41982i	−12.2893	−	15.4103i	−4.20310	−	10.3602i	7.47403	−	32.7459i	−5.72337	+	17.6137i	60.0992	−	13.7173i	12.3542	−	5.94948i	58.7359	+	3.72836i
29.5	−2.17075	+	4.50760i	0.0817869	−	0.0186673i	−10.6184	−	13.3151i	−7.76294	−	8.04591i	−0.0933938	+	0.409185i	11.9279	−	14.1678i	44.0480	−	10.0537i	−24.3198	+	11.7118i	53.1192	−	17.5266i
29.6	−2.13233	+	4.42783i	−6.88919	+	1.57241i	−10.0709	−	12.6285i	−8.41310	+	7.36341i	7.72765	−	33.8570i	−17.0683	−	7.18840i	39.0610	−	8.91542i	20.6623	−	9.95042i	−14.6644	−	52.9530i
29.7	−2.12106	+	4.40442i	9.54073	−	2.17761i	−9.91211	−	12.4294i	−11.0821	+	1.47897i	−10.6453	+	46.6402i	−16.2250	−	8.93021i	37.6407	−	8.59124i	61.9574	−	29.8371i	16.9917	−	51.9471i
29.8	−2.08071	+	4.32063i	−0.285912	+	0.0652575i	−9.35058	−	11.7253i	4.63335	+	10.1751i	0.312945	−	1.37110i	−0.129846	−	18.5198i	32.7139	−	7.46672i	−24.2487	+	11.6775i	−53.6033	−	1.15236i
29.9	−2.07030	+	4.29903i	5.94088	−	1.35597i	−9.20756	−	11.5459i	10.9961	+	2.02110i	−6.47007	+	28.3472i	4.02917	+	18.0767i	31.4832	−	7.18584i	9.12920	−	4.39639i	−31.4541	+	43.0884i
29.10	−2.07014	+	4.29870i	8.41445	−	1.92054i	−9.20537	−	11.5432i	−0.766011	−	11.1541i	−9.16328	+	40.1470i	18.3205	+	2.71266i	31.4645	−	7.18156i	42.7884	−	20.6058i	49.5337	+	19.7977i
29.11	−1.85464	+	3.85120i	−8.81980	+	2.01306i	−6.40412	−	8.03051i	0.568569	−	11.1659i	8.60484	−	37.7003i	2.92308	−	18.2881i	9.46571	−	2.16049i	49.4102	−	23.7947i	41.9475	+	22.8983i
29.12	−1.84044	+	3.82172i	−2.19121	+	0.500129i	−6.23041	−	7.81268i	7.10765	−	8.63026i	2.12144	−	9.29464i	−15.8083	+	9.64870i	8.24109	−	1.88098i	−19.7749	+	9.52309i	19.9012	+	43.0470i
29.13	−1.78650	+	3.70970i	4.58203	−	1.04582i	−5.58237	−	7.00007i	−5.51515	+	9.72539i	−4.30611	+	18.8663i	17.6513	−	5.60629i	3.82725	−	0.873546i	−4.42490	+	2.13092i	−26.2254	−	37.8339i
29.14	−1.78596	+	3.70859i	−4.18825	+	0.955941i	−5.57605	−	6.99214i	6.14328	+	9.34131i	3.93486	−	17.2398i	−14.8996	+	11.0001i	3.78543	−	0.864000i	−7.69855	+	3.70742i	−45.6147	+	6.09965i
29.15	−1.76565	+	3.66642i	−2.69814	+	0.615833i	−5.33717	−	6.69260i	10.1487	−	4.69087i	2.50608	−	10.9799i	18.4674	+	1.39853i	2.22234	−	0.507234i	−17.4254	+	8.39165i	−0.720368	+	45.4918i
29.16	−1.76111	+	3.65698i	6.94373	−	1.58486i	−5.28407	−	6.62601i	4.88405	+	10.0571i	−6.43285	+	28.1842i	−18.5094	+	0.635085i	1.87960	−	0.429005i	21.3775	−	10.2948i	−45.3801	+	0.149153i
29.17	−1.70345	+	3.53724i	−8.51858	+	1.94431i	−4.62243	−	5.79635i	−8.61817	+	7.12230i	7.63345	−	33.4443i	18.4109	+	2.00978i	−2.24372	+	0.512115i	44.4598	−	21.4107i	−10.5127	−	42.6170i
29.18	−1.55547	+	3.22997i	−0.929412	+	0.212132i	−3.02532	−	3.79363i	−10.6812	−	3.30331i	0.760494	−	3.33194i	−15.3850	−	10.3102i	−11.0018	+	2.51109i	−23.5074	+	11.3205i	27.2839	−	29.3618i
29.19	−1.48031	+	3.07389i	5.59079	−	1.27606i	−2.26955	−	2.84592i	−5.49423	−	9.73722i	−4.35361	+	19.0744i	−4.91890	+	17.8551i	−14.5021	+	3.31000i	5.30242	−	2.55351i	38.0642	−	2.47458i
29.20	−1.41469	+	2.93763i	−4.04505	+	0.923256i	−1.64039	−	2.05698i	−10.9376	−	2.31695i	3.01029	−	13.1890i	12.3058	+	13.8408i	−17.0669	+	3.89541i	−8.81612	+	4.24562i	22.2796	−	28.8529i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
49.e	even	7	1	inner
245.p	even	14	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	245.4.p.a	✓	492
5.b	even	2	1	inner	245.4.p.a	✓	492
49.e	even	7	1	inner	245.4.p.a	✓	492
245.p	even	14	1	inner	245.4.p.a	✓	492

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
245.4.p.a	✓	492	1.a	even	1	1	trivial
245.4.p.a	✓	492	5.b	even	2	1	inner
245.4.p.a	✓	492	49.e	even	7	1	inner
245.4.p.a	✓	492	245.p	even	14	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(245, [\chi])\).