Newform orbit 927.2.z.a

• Label: 927.2.z.a
• Level: $927$
• Weight: $2$
• Character orbit: 927.z
• 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.z (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.

\(\operatorname{Tr}(f)(q) = \) \( 3264 q - 18 q^{2} - 29 q^{3} + 82 q^{4} - 20 q^{5} - 35 q^{6} - 17 q^{7} - 56 q^{8} - 19 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
7.1	−0.916466	−	2.60074i	4.06018e−5		1.73205i	−4.36579	+	3.51314i	1.35118	+	3.19229i	4.50458	−	1.58747i	−3.66718	+	2.27062i	8.44892	+	5.23135i	−3.00000		0.000140649i	7.06401	−	6.43970i
7.2	−0.899030	−	2.55126i	1.52921	−	0.813340i	−4.14253	+	3.33348i	0.569878	+	1.34639i	−3.44985	−	3.17020i	−1.16011	+	0.718307i	7.62911	+	4.72375i	1.67696	−	2.48753i	2.92266	−	2.66435i
7.3	−0.889781	−	2.52502i	−0.870244	−	1.49756i	−4.02583	+	3.23958i	−0.204354	−	0.482805i	−3.00703	+	3.52988i	2.18238	−	1.35127i	7.20968	+	4.46405i	−1.48535	+	2.60648i	−1.03726	+	0.945588i
7.4	−0.881972	−	2.50285i	1.41779	+	0.994922i	−3.92824	+	3.16105i	−1.12371	−	2.65486i	1.23969	−	4.42602i	−0.815450	+	0.504906i	6.86379	+	4.24988i	1.02026	+	2.82118i	−5.65366	+	5.15399i
7.5	−0.865505	−	2.45612i	−0.0501861	+	1.73132i	−3.72529	+	2.99773i	−0.704395	−	1.66420i	4.29578	−	1.37521i	2.27902	−	1.41111i	6.15885	+	3.81340i	−2.99496	−	0.173777i	−3.47782	+	3.17045i
7.6	−0.841981	−	2.38937i	0.393424	−	1.68678i	−3.44198	+	2.76976i	0.191826	+	0.453206i	−4.36159	+	0.480200i	−1.29395	+	0.801179i	5.20820	+	3.22478i	−2.69044	−	1.32724i	0.921363	−	0.839933i
7.7	−0.829690	−	2.35449i	−1.64173	+	0.552029i	−3.29708	+	2.65315i	−1.51951	−	3.58998i	2.66187	+	3.40741i	−2.03970	+	1.26293i	4.73740	+	2.93327i	2.39053	−	1.81256i	−7.19185	+	6.55624i
7.8	−0.819682	−	2.32609i	0.615712	−	1.61892i	−3.18065	+	2.55946i	−1.59490	−	3.76809i	−4.27044	−	0.105202i	1.59095	−	0.985075i	4.36688	+	2.70386i	−2.24180	−	1.99358i	−7.45761	+	6.79851i
7.9	−0.808187	−	2.29347i	−1.25469	+	1.19405i	−3.04866	+	2.45325i	0.00318757	+	0.00753094i	3.75254	+	1.91256i	−1.34913	+	0.835348i	3.95540	+	2.44908i	0.148472	−	2.99632i	0.0146958	−	0.0133970i
7.10	−0.787186	−	2.23387i	−0.309776	−	1.70412i	−2.81236	+	2.26310i	1.60627	+	3.79495i	−3.56294	+	2.03346i	1.75238	−	1.08503i	3.24182	+	2.00725i	−2.80808	+	1.05579i	7.21301	−	6.57552i
7.11	−0.784992	−	2.22764i	1.61940	−	0.614455i	−2.78803	+	2.24352i	0.0717457	+	0.169506i	−2.64000	−	3.12510i	3.30859	−	2.04859i	3.17007	+	1.96282i	2.24489	−	1.99009i	0.321279	−	0.292885i
7.12	−0.755507	−	2.14397i	−1.71122	+	0.267814i	−2.46767	+	1.98573i	0.484209	+	1.14399i	1.86702	+	3.46648i	−0.644988	+	0.399360i	2.25627	+	1.39702i	2.85655	−	0.916577i	2.08686	−	1.90242i
7.13	−0.746544	−	2.11854i	1.59390	+	0.677847i	−2.37271	+	1.90931i	−0.269477	−	0.636664i	0.246126	−	3.88278i	−2.89875	+	1.79483i	1.99673	+	1.23632i	2.08105	+	2.16084i	−1.14762	+	1.04619i
7.14	−0.741882	−	2.10531i	−1.35196	−	1.08269i	−2.32378	+	1.86994i	0.305647	+	0.722119i	−1.27639	+	3.64952i	−3.30506	+	2.04641i	1.86505	+	1.15479i	0.655586	+	2.92749i	1.29353	−	1.17921i
7.15	−0.722266	−	2.04964i	−1.09115	+	1.34514i	−2.12121	+	1.70693i	1.31907	+	3.11643i	3.54515	+	1.26491i	3.55466	−	2.20095i	1.33532	+	0.826798i	−0.618801	−	2.93549i	5.43485	−	4.95452i
7.16	−0.713110	−	2.02366i	−1.61196	−	0.633707i	−2.02851	+	1.63234i	−0.931871	−	2.20163i	−0.132902	+	3.71396i	3.14882	−	1.94966i	1.10134	+	0.681923i	2.19683	+	2.04302i	−3.79083	+	3.45580i
7.17	−0.686481	−	1.94809i	0.472987	+	1.66622i	−1.76564	+	1.42081i	−0.148027	−	0.349728i	2.92125	−	2.06525i	1.74196	−	1.07858i	0.467690	+	0.289581i	−2.55257	+	1.57620i	−0.579685	+	0.528452i
7.18	−0.669905	−	1.90105i	1.32196	−	1.11912i	−1.60707	+	1.29320i	−1.11573	−	2.63601i	−3.01309	−	1.76340i	−3.94225	+	2.44094i	0.107581	+	0.0666115i	0.495134	−	2.95886i	−4.26376	+	3.88694i
7.19	−0.655421	−	1.85995i	0.655162	+	1.60336i	−1.47168	+	1.18425i	1.06869	+	2.52487i	2.55276	−	2.26944i	−1.26002	+	0.780174i	−0.186128	−	0.115245i	−2.14153	+	2.10092i	3.99570	−	3.64256i
7.20	−0.631112	−	1.79097i	1.72938	−	0.0962020i	−1.25109	+	1.00675i	1.51248	+	3.57338i	−1.26372	−	3.03654i	−1.37261	+	0.849881i	−0.636333	−	0.394001i	2.98149	−	0.332739i	5.44526	−	4.96401i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
927.z	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.z.a	yes	3264
9.c	even	3	1		927.2.y.a	✓	3264
103.g	even	51	1		927.2.y.a	✓	3264
927.z	even	51	1	inner	927.2.z.a	yes	3264

    

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

Hecke kernels

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