Newform orbit 384.2.v.a

• Label: 384.2.v.a
• Level: $384$
• Weight: $2$
• Character orbit: 384.v
• Analytic conductor: $3.066$
• Analytic rank: $0$
• Dimension: $512$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.06625543762\)
Analytic rank:	\(0\)
Dimension:	\(512\)
Relative dimension:	\(32\) over \(\Q(\zeta_{32})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \)

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	−1.40051	−	0.196427i	0.290285	+	0.956940i	1.92283	+	0.550195i	0.0502132	+	0.509823i	−0.218576	−	1.39722i	−1.66106	+	2.48595i	−2.58487	−	1.14825i	−0.831470	+	0.555570i	0.0298193	−	0.723874i
13.2	−1.39658	−	0.222610i	−0.290285	−	0.956940i	1.90089	+	0.621788i	0.0409738	+	0.416014i	0.192382	+	1.40107i	−0.338624	+	0.506787i	−2.51633	−	1.29154i	−0.831470	+	0.555570i	0.0353857	−	0.590120i
13.3	−1.34449	+	0.438569i	−0.290285	−	0.956940i	1.61531	−	1.17931i	0.414961	+	4.21317i	0.809970	+	1.15929i	−0.841223	+	1.25898i	−1.65457	+	2.29399i	−0.831470	+	0.555570i	−2.40568	−	5.48258i
13.4	−1.30780	−	0.538203i	0.290285	+	0.956940i	1.42068	+	1.40772i	0.403677	+	4.09860i	0.135394	−	1.40772i	2.40587	−	3.60064i	−1.10032	−	2.60563i	−0.831470	+	0.555570i	1.67795	−	5.57741i
13.5	−1.26580	+	0.630679i	0.290285	+	0.956940i	1.20449	−	1.59662i	−0.0580215	−	0.589102i	−0.970964	−	1.02822i	0.672130	−	1.00591i	−0.517679	+	2.78065i	−0.831470	+	0.555570i	0.444978	+	0.709091i
13.6	−1.21456	+	0.724467i	−0.290285	−	0.956940i	0.950294	−	1.75981i	−0.290371	−	2.94818i	1.04584	+	0.951956i	1.76246	−	2.63771i	0.120741	+	2.82585i	−0.831470	+	0.555570i	2.48853	+	3.37037i
13.7	−1.06403	−	0.931580i	0.290285	+	0.956940i	0.264317	+	1.98246i	−0.231940	−	2.35493i	0.582595	−	1.28864i	0.430118	−	0.643717i	1.56558	−	2.35563i	−0.831470	+	0.555570i	−1.94701	+	2.72179i
13.8	−1.06073	−	0.935332i	−0.290285	−	0.956940i	0.250309	+	1.98427i	−0.385901	−	3.91812i	−0.587142	+	1.28657i	−2.38112	+	3.56360i	1.59044	−	2.33891i	−0.831470	+	0.555570i	−3.25540	+	4.51703i
13.9	−0.922626	+	1.07180i	−0.290285	−	0.956940i	−0.297523	−	1.97775i	−0.0692954	−	0.703568i	1.29348	+	0.571770i	−2.09840	+	3.14048i	2.39426	+	1.50583i	−0.831470	+	0.555570i	0.818020	+	0.574859i
13.10	−0.870630	+	1.11445i	0.290285	+	0.956940i	−0.484007	−	1.94055i	−0.328555	−	3.33588i	−1.31919	−	0.509633i	−1.53196	+	2.29274i	2.58404	+	1.15010i	−0.831470	+	0.555570i	4.00372	+	2.53816i
13.11	−0.612256	−	1.27481i	−0.290285	−	0.956940i	−1.25028	+	1.56102i	0.189500	+	1.92402i	−1.04219	+	0.955951i	0.476963	−	0.713825i	2.75550	+	0.638130i	−0.831470	+	0.555570i	2.33674	−	1.41957i
13.12	−0.607361	+	1.27715i	−0.290285	−	0.956940i	−1.26223	−	1.55138i	0.269039	+	2.73160i	1.39846	+	0.210471i	0.857384	−	1.28317i	2.74797	−	0.669804i	−0.831470	+	0.555570i	−3.65206	−	1.31546i
13.13	−0.542361	−	1.30608i	0.290285	+	0.956940i	−1.41169	+	1.41673i	0.155407	+	1.57788i	1.09240	−	0.898142i	0.0321569	−	0.0481261i	2.61601	+	1.07540i	−0.831470	+	0.555570i	1.97655	−	1.05875i
13.14	−0.283082	+	1.38559i	0.290285	+	0.956940i	−1.83973	−	0.784471i	−0.166665	−	1.69218i	−1.40810	+	0.131324i	1.76235	−	2.63755i	1.60775	−	2.32704i	−0.831470	+	0.555570i	2.39185	+	0.248095i
13.15	−0.229611	−	1.39545i	0.290285	+	0.956940i	−1.89456	+	0.640821i	−0.159671	−	1.62116i	1.26871	−	0.624802i	−2.66520	+	3.98875i	1.32924	+	2.49662i	−0.831470	+	0.555570i	−2.22559	+	0.595050i
13.16	−0.162120	−	1.40489i	−0.290285	−	0.956940i	−1.94743	+	0.455521i	−0.344842	−	3.50124i	−1.29734	+	0.562957i	1.89335	−	2.83360i	0.955675	+	2.66208i	−0.831470	+	0.555570i	−4.86295	+	1.05208i
13.17	−0.156266	+	1.40555i	−0.290285	−	0.956940i	−1.95116	−	0.439279i	−0.103867	−	1.05457i	1.39039	−	0.258474i	−0.0783117	+	0.117202i	0.922330	−	2.67382i	−0.831470	+	0.555570i	1.49849	+	0.0188036i
13.18	0.147414	−	1.40651i	−0.290285	−	0.956940i	−1.95654	−	0.414679i	0.138503	+	1.40624i	−1.38874	+	0.267222i	−1.77662	+	2.65890i	−0.871671	+	2.69076i	−0.831470	+	0.555570i	1.99831	+	0.0124945i
13.19	0.246397	+	1.39258i	0.290285	+	0.956940i	−1.87858	+	0.686257i	0.267357	+	2.71452i	−1.26109	+	0.640033i	−0.343422	+	0.513967i	−1.41855	−	2.44698i	−0.831470	+	0.555570i	−3.71432	+	1.04117i
13.20	0.320440	−	1.37743i	0.290285	+	0.956940i	−1.79464	−	0.882769i	−0.362380	−	3.67931i	1.41114	−	0.0932050i	1.08924	−	1.63016i	−1.79103	+	2.18911i	−0.831470	+	0.555570i	−5.18411	−	0.679844i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	384.2.v.a	✓	512
128.k	even	32	1	inner	384.2.v.a	✓	512

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
384.2.v.a	✓	512	1.a	even	1	1	trivial
384.2.v.a	✓	512	128.k	even	32	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(384, [\chi])\).