Newform orbit 927.2.y.a

• Label: 927.2.y.a
• Level: $927$
• Weight: $2$
• Character orbit: 927.y
• Analytic conductor: $7.402$
• Analytic rank: $0$
• Dimension: $3264$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 927 = 3^{2} \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	927.y (of order \(51\), degree \(32\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.40213226737\)
Analytic rank:	\(0\)
Dimension:	\(3264\)
Relative dimension:	\(102\) over \(\Q(\zeta_{51})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{51}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 3264 q - 15 q^{2} - 29 q^{3} - 215 q^{4} - 11 q^{5} - 29 q^{6} - 17 q^{7} - 56 q^{8} - 19 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
4.1	−1.65657	−	2.19365i	0.449617	+	1.67268i	−1.52056	+	5.34420i	−0.164302	+	1.77310i	2.92444	−	3.75720i	1.49261	−	1.20110i	9.11569	−	3.53144i	−2.59569	+	1.50413i	4.16175	−	2.57684i
4.2	−1.65356	−	2.18967i	−1.26327	−	1.18497i	−1.51306	+	5.31784i	−0.376687	+	4.06510i	−0.505796	+	4.72556i	2.48574	−	2.00026i	9.02903	−	3.49786i	0.191698	+	2.99387i	9.52409	−	5.89707i
4.3	−1.63521	−	2.16536i	−0.859199	−	1.50392i	−1.46757	+	5.15799i	0.227552	−	2.45568i	−1.85157	+	4.31970i	−1.75197	+	1.40980i	8.50831	−	3.29614i	−1.52355	+	2.58433i	−5.68954	+	3.52281i
4.4	−1.61795	−	2.14251i	−1.66968	+	0.460607i	−1.42526	+	5.00928i	−0.0358909	+	0.387324i	3.68831	+	2.83207i	−2.86622	+	2.30643i	8.03144	−	3.11139i	2.57568	−	1.53813i	0.887914	−	0.549773i
4.5	−1.57206	−	2.08175i	1.63580	−	0.569346i	−1.31497	+	4.62164i	−0.183379	+	1.97897i	−3.75682	−	2.51028i	−1.31862	+	1.06109i	6.82332	−	2.64337i	2.35169	−	1.86267i	4.40801	−	2.72932i
4.6	−1.56009	−	2.06590i	0.700229	−	1.58420i	−1.28671	+	4.52233i	−0.00445989	+	0.0481299i	−4.36521	+	1.02489i	−1.33487	+	1.07416i	6.52211	−	2.52668i	−2.01936	−	2.21860i	0.106389	−	0.0658735i
4.7	−1.52334	−	2.01722i	1.73205	+	0.00418268i	−1.20131	+	4.22217i	0.377962	−	4.07886i	−2.63005	−	3.50029i	−2.52536	+	2.03215i	5.63285	−	2.18218i	2.99997	+	0.0144892i	−8.80374	+	5.45105i
4.8	−1.51282	−	2.00329i	0.726646	+	1.57226i	−1.17724	+	4.13758i	0.346915	−	3.74381i	2.05041	−	3.83422i	1.37312	−	1.10495i	5.38809	−	2.08736i	−1.94397	+	2.28494i	−8.02476	+	4.96872i
4.9	−1.48598	−	1.96776i	−1.40540	+	1.01235i	−1.11660	+	3.92444i	−0.00974536	+	0.105169i	4.08046	+	1.26114i	2.51367	−	2.02274i	4.78299	−	1.85294i	0.950283	−	2.84552i	0.221429	−	0.137103i
4.10	−1.48281	−	1.96356i	0.575755	−	1.63356i	−1.10950	+	3.89950i	0.230116	−	2.48335i	−4.06131	+	1.29172i	3.01420	−	2.42552i	4.71330	−	1.82594i	−2.33701	−	1.88106i	−5.21741	+	3.23048i
4.11	−1.45756	−	1.93012i	−0.427483	+	1.67847i	−1.05357	+	3.70290i	0.115538	−	1.24686i	3.86274	−	1.62138i	−1.28764	+	1.03616i	4.17206	−	1.61626i	−2.63452	−	1.43503i	−2.57499	+	1.59437i
4.12	−1.39280	−	1.84436i	1.64989	+	0.527114i	−0.914463	+	3.21400i	−0.0502347	+	0.542119i	−1.32578	−	3.77717i	1.08419	−	0.872445i	2.89123	−	1.12007i	2.44430	+	1.73937i	1.06983	−	0.662411i
4.13	−1.38046	−	1.82802i	−0.488358	+	1.66178i	−0.888673	+	3.12336i	−0.328895	+	3.54934i	3.71192	−	1.40128i	−3.53273	+	2.84277i	2.66431	−	1.03216i	−2.52301	−	1.62309i	6.94229	−	4.29848i
4.14	−1.34963	−	1.78719i	1.37881	+	1.04828i	−0.825243	+	2.90043i	−0.365376	+	3.94304i	0.0126062	−	3.87898i	−0.314583	+	0.253144i	2.12078	−	0.821593i	0.802217	+	2.89075i	7.54009	−	4.66863i
4.15	−1.31861	−	1.74612i	−1.66230	−	0.486595i	−0.762875	+	2.68123i	0.0554515	−	0.598417i	1.34226	+	3.54419i	−0.426468	+	0.343178i	1.60704	−	0.622570i	2.52645	+	1.61773i	−1.11802	+	0.692251i
4.16	−1.30021	−	1.72175i	−1.01486	−	1.40359i	−0.726570	+	2.55363i	0.0303836	−	0.327891i	−1.09710	+	3.57230i	1.98924	−	1.60073i	1.31772	−	0.510488i	−0.940117	+	2.84889i	−0.604053	+	0.374014i
4.17	−1.29042	−	1.70879i	−0.513362	−	1.65422i	−0.707459	+	2.48646i	−0.268963	+	2.90257i	−2.16427	+	3.01187i	−3.76298	+	3.02806i	1.16836	−	0.452627i	−2.47292	+	1.69843i	5.30696	−	3.28593i
4.18	−1.21925	−	1.61455i	1.47074	+	0.914834i	−0.572877	+	2.01345i	0.0574777	−	0.620283i	−0.316158	−	3.49001i	−0.647471	+	0.521018i	0.176142	−	0.0682378i	1.32616	+	2.69097i	−1.07156	+	0.663482i
4.19	−1.10631	−	1.46499i	−1.72103	+	0.195088i	−0.374946	+	1.31780i	−0.331641	+	3.57898i	2.18979	+	2.30546i	0.0962599	−	0.0774600i	−1.07827	+	0.417725i	2.92388	−	0.671505i	5.61006	−	3.47360i
4.20	−1.10307	−	1.46070i	−0.207426	−	1.71959i	−0.369559	+	1.29887i	−0.148723	+	1.60498i	−2.28300	+	2.19981i	1.85329	−	1.49133i	−1.10872	+	0.429519i	−2.91395	+	0.713375i	2.50844	−	1.55316i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
927.y	even	51	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	927.2.y.a	✓	3264
9.c	even	3	1		927.2.z.a	yes	3264
103.g	even	51	1		927.2.z.a	yes	3264
927.y	even	51	1	inner	927.2.y.a	✓	3264

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
927.2.y.a	✓	3264	1.a	even	1	1	trivial
927.2.y.a	✓	3264	927.y	even	51	1	inner
927.2.z.a	yes	3264	9.c	even	3	1
927.2.z.a	yes	3264	103.g	even	51	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(927, [\chi])\).