Newform orbit 819.2.ev.a

• Label: 819.2.ev.a
• Level: $819$
• Weight: $2$
• Character orbit: 819.ev
• Analytic conductor: $6.540$
• Analytic rank: $0$
• Dimension: $432$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.ev (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.53974792554\)
Analytic rank:	\(0\)
Dimension:	\(432\)
Relative dimension:	\(108\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 432 q - 4 q^{3} - 6 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
86.1	−1.94103	+	1.94103i	−0.519949	−	1.65217i		−	5.53520i	0.494103	+	0.132394i	4.21614	+	2.19767i	0.759688	+	2.53434i	6.86194	+	6.86194i	−2.45931	+	1.71808i	−1.21605	+	0.702087i
86.2	−1.93863	+	1.93863i	1.42660	−	0.982252i		−	5.51656i	2.41180	+	0.646239i	−0.861420	+	4.66986i	−2.19913	−	1.47099i	6.81730	+	6.81730i	1.07036	−	2.80256i	−5.92840	+	3.42276i
86.3	−1.92009	+	1.92009i	−1.62932	−	0.587642i		−	5.37348i	−3.85256	−	1.03229i	4.25676	−	2.00011i	−0.179377	−	2.63966i	6.47737	+	6.47737i	2.30935	+	1.91491i	9.37935	−	5.41517i
86.4	−1.90894	+	1.90894i	−0.327729	+	1.70076i		−	5.28810i	0.893281	+	0.239354i	−2.62104	−	3.87227i	0.221778	−	2.63644i	6.27679	+	6.27679i	−2.78519	−	1.11478i	−2.16213	+	1.24831i
86.5	−1.84767	+	1.84767i	0.853624	+	1.50709i		−	4.82773i	−0.833887	−	0.223439i	−4.36181	−	1.20739i	−2.31693	+	1.27743i	5.22471	+	5.22471i	−1.54265	+	2.57298i	1.95358	−	1.12790i
86.6	−1.84534	+	1.84534i	1.58135	+	0.706643i		−	4.81059i	0.556317	+	0.149065i	−4.22213	+	1.61413i	2.63969	+	0.178986i	5.18650	+	5.18650i	2.00131	+	2.23489i	−1.30167	+	0.751520i
86.7	−1.84386	+	1.84386i	−1.65884	+	0.498260i		−	4.79963i	−1.28621	−	0.344638i	2.13994	−	3.97738i	0.567090	+	2.58426i	5.16213	+	5.16213i	2.50347	−	1.65306i	3.00705	−	1.73612i
86.8	−1.76674	+	1.76674i	−1.56499	+	0.742155i		−	4.24275i	4.13350	+	1.10757i	1.45374	−	4.07613i	−2.20049	+	1.46896i	3.96236	+	3.96236i	1.89841	−	2.32294i	−9.25962	+	5.34604i
86.9	−1.75430	+	1.75430i	1.44401	−	0.956463i		−	4.15515i	−3.43590	−	0.920646i	−0.855314	+	4.21116i	1.01432	+	2.44359i	3.78079	+	3.78079i	1.17036	−	2.76229i	7.64270	−	4.41251i
86.10	−1.69652	+	1.69652i	−0.266887	−	1.71137i		−	3.75634i	1.38065	+	0.369943i	3.35614	+	2.45058i	0.398899	−	2.61551i	2.97965	+	2.97965i	−2.85754	+	0.913482i	−2.96991	+	1.71468i
86.11	−1.65422	+	1.65422i	1.73123	+	0.0531826i		−	3.47286i	−2.89112	−	0.774674i	−2.95181	+	2.77586i	−1.72954	−	2.00217i	2.43643	+	2.43643i	2.99434	+	0.184143i	6.06402	−	3.50106i
86.12	−1.62730	+	1.62730i	0.471207	+	1.66672i		−	3.29621i	3.37035	+	0.903083i	−3.47905	−	1.94546i	1.79670	+	1.94213i	2.10933	+	2.10933i	−2.55593	+	1.57074i	−6.95417	+	4.01499i
86.13	−1.58454	+	1.58454i	0.293174	−	1.70706i		−	3.02154i	−2.12986	−	0.570693i	2.24036	+	3.16945i	2.24331	−	1.40270i	1.61868	+	1.61868i	−2.82810	−	1.00093i	4.27913	−	2.47056i
86.14	−1.58285	+	1.58285i	−0.705408	+	1.58190i		−	3.01080i	−2.69226	−	0.721389i	−1.38735	−	3.62045i	−1.87727	+	1.86436i	1.59994	+	1.59994i	−2.00480	−	2.23177i	5.40328	−	3.11958i
86.15	−1.57528	+	1.57528i	−1.29768	−	1.14718i		−	2.96299i	0.426469	+	0.114272i	3.85133	−	0.237087i	−2.56181	+	0.661158i	1.51697	+	1.51697i	0.367964	+	2.97735i	−0.851816	+	0.491796i
86.16	−1.56550	+	1.56550i	1.53367	−	0.804903i		−	2.90158i	2.68352	+	0.719047i	−1.14088	+	3.66103i	2.64413	−	0.0926122i	1.41142	+	1.41142i	1.70426	−	2.46890i	−5.32671	+	3.07538i
86.17	−1.48612	+	1.48612i	−1.73174	+	0.0330286i		−	2.41712i	1.11830	+	0.299648i	2.52449	−	2.62266i	2.41197	−	1.08738i	0.619890	+	0.619890i	2.99782	−	0.114394i	−2.10724	+	1.21662i
86.18	−1.47584	+	1.47584i	−1.65502	+	0.510786i		−	2.35620i	0.0195797	+	0.00524636i	1.68871	−	3.19639i	−1.63613	−	2.07920i	0.525701	+	0.525701i	2.47820	−	1.69072i	−0.0366393	+	0.0211537i
86.19	−1.47090	+	1.47090i	−0.558333	+	1.63959i		−	2.32708i	−3.08787	−	0.827391i	−1.59042	−	3.23292i	2.62478	−	0.332466i	0.481097	+	0.481097i	−2.37653	−	1.83088i	5.75894	−	3.32493i
86.20	−1.46644	+	1.46644i	1.20160	−	1.24746i		−	2.30087i	0.859356	+	0.230264i	0.0672495	+	3.59139i	−1.79630	+	1.94250i	0.441203	+	0.441203i	−0.112312	−	2.99790i	−1.59786	+	0.922524i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
13.d	odd	4	1	inner
63.j	odd	6	1	inner
819.ev	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	819.2.ev.a	✓	432
7.c	even	3	1		819.2.fx.a	yes	432
9.d	odd	6	1		819.2.fx.a	yes	432
13.d	odd	4	1	inner	819.2.ev.a	✓	432
63.j	odd	6	1	inner	819.2.ev.a	✓	432
91.z	odd	12	1		819.2.fx.a	yes	432
117.z	even	12	1		819.2.fx.a	yes	432
819.ev	even	12	1	inner	819.2.ev.a	✓	432

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
819.2.ev.a	✓	432	1.a	even	1	1	trivial
819.2.ev.a	✓	432	13.d	odd	4	1	inner
819.2.ev.a	✓	432	63.j	odd	6	1	inner
819.2.ev.a	✓	432	819.ev	even	12	1	inner
819.2.fx.a	yes	432	7.c	even	3	1
819.2.fx.a	yes	432	9.d	odd	6	1
819.2.fx.a	yes	432	91.z	odd	12	1
819.2.fx.a	yes	432	117.z	even	12	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(819, [\chi])\).