Newform orbit 464.2.bc.a

• Label: 464.2.bc.a
• Level: $464$
• Weight: $2$
• Character orbit: 464.bc
• Analytic conductor: $3.705$
• Analytic rank: $0$
• Dimension: $696$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	464.bc (of order \(28\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.70505865379\)
Analytic rank:	\(0\)
Dimension:	\(696\)
Relative dimension:	\(58\) over \(\Q(\zeta_{28})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 696 q - 10 q^{2} - 10 q^{3} - 14 q^{4} - 14 q^{5} - 6 q^{6} - 20 q^{7} - 46 q^{8} - 108 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
11.1	−1.40951	+	0.115235i	1.71212	−	2.14693i	1.97344	−	0.324849i	0.373878	−	0.130826i	−2.16585	+	3.22342i	−1.01386	+	1.27134i	−2.74415	+	0.685288i	−1.01040	−	4.42684i	−0.511910	+	0.227484i
11.2	−1.40514	−	0.159960i	−0.250542	+	0.314169i	1.94883	+	0.449532i	3.37757	−	1.18186i	0.402300	−	0.401374i	−1.37929	+	1.72957i	−2.66646	−	0.943389i	0.631632	+	2.76736i	−4.93500	+	1.12040i
11.3	−1.40300	+	0.177760i	−1.56937	+	1.96792i	1.93680	−	0.498795i	−2.87402	+	1.00566i	1.85200	−	3.03996i	2.50366	−	3.13949i	−2.62866	+	1.04409i	−0.742249	−	3.25200i	3.85347	−	1.92183i
11.4	−1.40298	+	0.177871i	0.944209	−	1.18400i	1.93672	−	0.499100i	−3.07778	+	1.07696i	−1.11411	+	1.82908i	0.0489544	−	0.0613869i	−2.62842	+	1.04472i	0.157236	+	0.688898i	4.12651	−	2.05841i
11.5	−1.39307	−	0.243616i	−0.160604	+	0.201391i	1.88130	+	0.678750i	−0.652184	+	0.228209i	0.272795	−	0.241427i	0.0366070	−	0.0459037i	−2.45544	−	1.40386i	0.652798	+	2.86010i	0.964135	−	0.159029i
11.6	−1.35684	−	0.398723i	−2.13093	+	2.67210i	1.68204	+	1.08201i	0.0127458	−	0.00445997i	3.95676	−	2.77596i	−2.94499	+	3.69290i	−1.85084	−	2.13878i	−1.93169	−	8.46330i	−0.0190724		0.000969403i
11.7	−1.28878	−	0.582284i	1.70928	−	2.14337i	1.32189	+	1.50087i	3.38820	−	1.18558i	−3.45093	+	1.76704i	1.66037	−	2.08204i	−0.829691	−	2.70400i	−1.00483	−	4.40245i	−5.05698	−	0.444944i
11.8	−1.28670	+	0.586852i	−1.04188	+	1.30647i	1.31121	−	1.51021i	2.47738	−	0.866874i	0.573882	−	2.29247i	−0.664471	+	0.833220i	−0.800871	+	2.71268i	0.0461988	+	0.202410i	−2.67893	+	2.56927i
11.9	−1.27599	+	0.609791i	0.639413	−	0.801799i	1.25631	−	1.55618i	1.72705	−	0.604320i	−0.326956	+	1.41300i	3.09291	−	3.87839i	−0.654096	+	2.75176i	0.433531	+	1.89942i	−1.83519	+	1.82425i
11.10	−1.25230	+	0.657074i	−1.15710	+	1.45096i	1.13651	−	1.64571i	−1.40674	+	0.492241i	0.495650	−	2.57734i	−1.46427	+	1.83614i	−0.341897	+	2.80769i	−0.0988355	−	0.433027i	1.43823	−	1.54077i
11.11	−1.17056	−	0.793594i	−1.06077	+	1.33016i	0.740418	+	1.85790i	−1.54239	+	0.539704i	2.29731	−	0.715215i	0.429907	−	0.539086i	0.607712	−	2.76237i	0.0234597	+	0.102784i	2.23376	+	0.592272i
11.12	−1.13711	−	0.840826i	1.78572	−	2.23923i	0.586024	+	1.91222i	−3.03925	+	1.06348i	−3.91336	+	1.04476i	−0.182274	+	0.228565i	0.941470	−	2.66714i	−1.15776	−	5.07249i	4.35016	+	1.34619i
11.13	−1.09754	−	0.891853i	−1.41441	+	1.77362i	0.409195	+	1.95769i	3.06424	−	1.07222i	3.13418	−	0.685169i	1.87913	−	2.35635i	1.29687	−	2.51359i	−0.477591	−	2.09246i	−4.31939	−	1.55604i
11.14	−1.08803	−	0.903433i	0.564990	−	0.708475i	0.367618	+	1.96592i	−2.00989	+	0.703292i	−1.25478	+	0.260411i	2.31151	−	2.89854i	1.37610	−	2.47110i	0.484840	+	2.12422i	2.82220	+	1.05060i
11.15	−1.07868	−	0.914581i	0.814854	−	1.02179i	0.327082	+	1.97307i	1.07604	−	0.376523i	−1.81348	+	0.356934i	−2.51038	+	3.14792i	1.45172	−	2.42745i	0.287486	+	1.25956i	−1.50506	−	0.577981i
11.16	−1.03388	+	0.964930i	0.910032	−	1.14114i	0.137820	−	1.99525i	−1.31073	+	0.458645i	0.160259	+	2.05793i	−1.61499	+	2.02513i	1.78278	+	2.19583i	0.193511	+	0.847827i	0.912582	−	1.73895i
11.17	−0.933592	+	1.06226i	−1.00913	+	1.26541i	−0.256812	−	1.98344i	0.481921	−	0.168631i	−0.402083	−	2.25333i	1.13605	−	1.42456i	2.34670	+	1.57892i	0.0846484	+	0.370869i	−0.270786	+	0.669361i
11.18	−0.861243	+	1.12172i	0.391335	−	0.490718i	−0.516520	−	1.93215i	−3.62565	+	1.26867i	0.213415	+	0.861597i	0.961458	−	1.20563i	2.61218	+	1.08466i	0.579901	+	2.54071i	1.69947	−	5.15961i
11.19	−0.834766	+	1.14156i	2.04445	−	2.56366i	−0.606330	−	1.90588i	1.12142	−	0.392400i	1.21994	+	4.47392i	−0.0239934	+	0.0300868i	2.68182	+	0.898798i	−1.72501	−	7.55776i	−0.488171	+	1.60773i
11.20	−0.725055	−	1.21421i	0.109888	−	0.137795i	−0.948589	+	1.76073i	1.07871	−	0.377456i	−0.246986	−	0.0335174i	−1.37144	+	1.71973i	2.82567	−	0.124846i	0.660651	+	2.89450i	−1.24043	−	1.03610i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
464.bc	even	28	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	464.2.bc.a	✓	696
16.f	odd	4	1		464.2.bm.a	yes	696
29.f	odd	28	1		464.2.bm.a	yes	696
464.bc	even	28	1	inner	464.2.bc.a	✓	696

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
464.2.bc.a	✓	696	1.a	even	1	1	trivial
464.2.bc.a	✓	696	464.bc	even	28	1	inner
464.2.bm.a	yes	696	16.f	odd	4	1
464.2.bm.a	yes	696	29.f	odd	28	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(464, [\chi])\).