Newform orbit 128.5.l.a

• Label: 128.5.l.a
• Level: $128$
• Weight: $5$
• Character orbit: 128.l
• Analytic conductor: $13.231$
• Analytic rank: $0$
• Dimension: $1008$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	128.l (of order \(32\), degree \(16\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(13.2313552747\)
Analytic rank:	\(0\)
Dimension:	\(1008\)
Relative dimension:	\(63\) over \(\Q(\zeta_{32})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1008 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3.1	−3.98767	+	0.313821i	−13.0973	+	10.7487i	15.8030	−	2.50283i	37.0978	+	11.2535i	48.8546	−	46.9724i	4.64899	+	23.3721i	−62.2319	+	14.9398i	40.2030	−	202.114i	−151.465	−	33.2332i
3.2	−3.95882	−	0.572521i	−4.36463	+	3.58196i	15.3444	+	4.53301i	2.00607	+	0.608536i	19.3295	−	11.6815i	−7.49964	−	37.7032i	−58.1506	−	26.7304i	−9.58275	+	48.1757i	−7.59328	−	3.55760i
3.3	−3.93898	+	0.696008i	6.46187	−	5.30312i	15.0311	−	5.48312i	−28.0844	−	8.51932i	−21.7622	+	25.3864i	0.922571	+	4.63808i	−55.3911	+	32.0597i	−2.16964	+	10.9075i	116.554	+	14.0104i
3.4	−3.93799	−	0.701605i	11.4156	−	9.36851i	15.0155	+	5.52582i	39.4094	+	11.9547i	−51.5273	+	28.8839i	−18.6869	−	93.9456i	−55.2539	−	32.2956i	26.7438	−	134.450i	−146.806	−	74.7273i
3.5	−3.89182	+	0.923973i	−7.47268	+	6.13267i	14.2925	−	7.19188i	−34.4748	−	10.4578i	23.4159	−	30.7718i	−4.53604	−	22.8042i	−48.9789	+	41.1954i	2.42901	−	12.2115i	143.832	+	8.84616i
3.6	−3.87913	−	0.975872i	13.1338	−	10.7787i	14.0953	+	7.57107i	−12.6494	−	3.83717i	−61.4665	+	28.9949i	15.2716	+	76.7754i	−47.2893	−	43.1245i	40.5159	−	203.687i	45.3243	+	27.2291i
3.7	−3.87689	+	0.984756i	3.81952	−	3.13460i	14.0605	−	7.63558i	27.8176	+	8.43838i	−11.7210	+	15.9138i	7.96282	+	40.0318i	−46.9918	+	43.4484i	−11.0393	+	55.4983i	−116.155	−	5.32109i
3.8	−3.86190	−	1.04198i	1.98252	−	1.62701i	13.8286	+	8.04803i	−2.07933	−	0.630759i	−9.35161	+	4.21762i	−2.78288	−	13.9905i	−45.0187	−	45.4898i	−14.5191	+	72.9924i	7.37294	+	4.60255i
3.9	−3.81656	−	1.19746i	−9.21046	+	7.55883i	13.1322	+	9.14031i	−23.7963	−	7.21854i	44.2036	−	17.8196i	16.4786	+	82.8433i	−39.1746	−	50.6098i	11.8943	−	59.7969i	82.1761	+	56.0450i
3.10	−3.38069	−	2.13798i	−2.22632	+	1.82709i	6.85808	+	14.4557i	21.3910	+	6.48890i	11.4328	−	1.41700i	12.9621	+	65.1649i	7.72094	−	63.5326i	−14.1841	+	71.3082i	−58.4433	−	67.6706i
3.11	−3.37653	+	2.14454i	−6.28903	+	5.16127i	6.80190	−	14.4822i	17.4865	+	5.30446i	10.1665	−	30.9143i	−14.2328	−	71.5529i	8.09084	+	63.4865i	−2.88917	+	14.5249i	−70.4191	+	19.5897i
3.12	−3.26315	+	2.31341i	9.84830	−	8.08229i	5.29629	−	15.0980i	−14.5438	−	4.41182i	−13.4388	+	49.1569i	−8.09349	−	40.6887i	17.6452	+	61.5195i	15.8633	−	79.7501i	57.6650	−	19.2494i
3.13	−3.25888	−	2.31942i	5.81494	−	4.77220i	5.24061	+	15.1174i	−28.0812	−	8.51835i	−30.0189	+	2.06475i	−9.11012	−	45.7997i	17.9850	−	61.4210i	−4.76266	+	23.9435i	71.7558	+	92.8924i
3.14	−3.22267	+	2.36947i	−7.20596	+	5.91378i	4.77123	−	15.2720i	2.33003	+	0.706808i	9.20993	−	36.1325i	11.1538	+	56.0737i	20.8105	+	60.5221i	1.15079	−	5.78540i	−9.18370	+	3.24313i
3.15	−3.09156	−	2.53816i	−12.3327	+	10.1212i	3.11546	+	15.6938i	−15.2168	−	4.61597i	63.8165	+	0.0121723i	−11.6720	−	58.6789i	30.2017	−	56.4257i	33.8548	−	170.200i	35.3276	+	52.8933i
3.16	−2.96812	−	2.68147i	−5.39383	+	4.42660i	1.61947	+	15.9178i	42.9519	+	13.0293i	27.8793	+	1.32469i	−8.38667	−	42.1626i	37.8764	−	51.5886i	−6.30371	+	31.6909i	−92.5487	−	153.847i
3.17	−2.80758	+	2.84912i	−0.236785	+	0.194325i	−0.235026	−	15.9983i	−27.1487	−	8.23546i	0.111138	−	1.22021i	13.1413	+	66.0660i	46.2409	+	44.2468i	−15.7840	+	79.3516i	99.6858	−	54.2283i
3.18	−2.66833	−	2.97993i	8.56994	−	7.03317i	−1.75999	+	15.9029i	16.1113	+	4.88731i	−43.8258	−	6.77100i	8.61826	+	43.3269i	52.0858	−	37.1896i	8.17609	−	41.1040i	−28.4265	−	61.0516i
3.19	−2.35233	+	3.23520i	1.64666	−	1.35138i	−4.93309	−	15.2205i	31.2429	+	9.47742i	0.498498	+	8.50617i	−6.24158	−	31.3785i	60.8458	+	19.8442i	−14.9171	+	74.9931i	−104.155	+	78.7830i
3.20	−2.15707	−	3.36854i	−1.54548	+	1.26834i	−6.69413	+	14.5323i	−43.0952	−	13.0728i	7.60615	+	2.47011i	10.6247	+	53.4142i	63.3924	−	8.79776i	−15.0225	+	75.5232i	48.9230	+	173.367i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
128.l	odd	32	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	128.5.l.a	✓	1008
128.l	odd	32	1	inner	128.5.l.a	✓	1008

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
128.5.l.a	✓	1008	1.a	even	1	1	trivial
128.5.l.a	✓	1008	128.l	odd	32	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(128, [\chi])\).