Newform orbit 927.2.bm.a

• Label: 927.2.bm.a
• Level: $927$
• Weight: $2$
• Character orbit: 927.bm
• 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.bm (of order \(102\), degree \(32\), minimal)

Newform invariants

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

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 3264 q - 51 q^{2} - 31 q^{3} + 185 q^{4} - 45 q^{5} - 43 q^{6} - 17 q^{7} - 23 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
5.1	−1.86888	−	2.05006i	1.35785	−	1.07529i	−0.525513	+	5.67119i	−2.15147	−	1.33213i	−4.74207	−	0.774083i	1.15207	+	2.72188i	8.18091	−	6.17793i	0.687497	−	2.92016i	1.28988	+	6.90026i
5.2	−1.83052	−	2.00799i	0.253448	+	1.71341i	−0.496666	+	5.35988i	0.179392	+	0.111075i	2.97656	−	3.64535i	−1.43593	−	3.39252i	7.33510	−	5.53921i	−2.87153	+	0.868519i	−0.105344	−	0.563543i
5.3	−1.82531	−	2.00227i	−1.46629	+	0.921947i	−0.492787	+	5.31802i	−0.294806	−	0.182536i	4.52241	+	1.25307i	1.04489	+	2.46864i	7.22330	−	5.45478i	1.30003	−	2.70369i	0.172625	+	0.923463i
5.4	−1.81801	−	1.99426i	1.70268	−	0.317615i	−0.487382	+	5.25969i	3.08923	+	1.91277i	−3.72889	−	2.81816i	−0.149787	−	0.353885i	7.06825	−	5.33770i	2.79824	−	1.08159i	−1.80168	−	9.63816i
5.5	−1.76686	−	1.93815i	−0.102860	−	1.72899i	−0.450104	+	4.85739i	1.34687	+	0.833946i	−3.16931	+	3.25424i	−1.66562	−	3.93517i	6.02381	−	4.54897i	−2.97884	+	0.355690i	−0.763413	−	4.08390i
5.6	−1.74783	−	1.91728i	−1.39292	−	1.02945i	−0.436511	+	4.71070i	2.58074	+	1.59793i	0.460847	+	4.46993i	1.20230	+	2.84054i	5.65394	−	4.26966i	0.880462	+	2.86789i	−1.44703	−	7.74092i
5.7	−1.74189	−	1.91076i	−1.05461	−	1.37397i	−0.432295	+	4.66521i	−2.53889	−	1.57201i	−0.788333	+	4.40841i	0.0759366	+	0.179407i	5.54045	−	4.18396i	−0.775615	+	2.89800i	1.41872	+	7.58949i
5.8	−1.66863	−	1.83040i	1.06012	+	1.36973i	−0.381502	+	4.11707i	2.06580	+	1.27909i	0.738211	−	4.22601i	1.66411	+	3.93161i	4.21936	−	3.18631i	−0.752311	+	2.90414i	−1.10581	−	5.91557i
5.9	−1.58683	−	1.74067i	1.59607	+	0.672727i	−0.327367	+	3.53285i	−0.326024	−	0.201866i	−1.36170	−	3.84574i	−0.573476	−	1.35489i	2.90969	−	2.19730i	2.09488	+	2.14744i	0.165964	+	0.887830i
5.10	−1.58157	−	1.73490i	1.49222	+	0.879360i	−0.323978	+	3.49628i	−2.00176	−	1.23943i	−0.834454	−	3.97963i	0.731543	+	1.72834i	2.83123	−	2.13804i	1.45345	+	2.62440i	1.01562	+	5.43310i
5.11	−1.56651	−	1.71838i	−1.29514	+	1.15005i	−0.314340	+	3.39227i	−3.28907	−	2.03650i	4.00508	+	0.423973i	−0.774230	−	1.82919i	2.61045	−	1.97132i	0.354765	−	2.97895i	1.65287	+	8.84208i
5.12	−1.56163	−	1.71303i	−1.72428	+	0.163844i	−0.311235	+	3.35876i	2.99108	+	1.85200i	2.97336	+	2.69788i	−1.56242	−	3.69136i	2.54006	−	1.91817i	2.94631	−	0.565026i	−1.49844	−	8.01593i
5.13	−1.55750	−	1.70850i	−0.396705	+	1.68601i	−0.308619	+	3.33052i	1.89166	+	1.17127i	3.49842	−	1.94819i	0.0739494	+	0.174712i	2.48104	−	1.87359i	−2.68525	−	1.33770i	−0.945159	−	5.05615i
5.14	−1.55234	−	1.70283i	1.47143	−	0.913727i	−0.305352	+	3.29527i	−2.75838	−	1.70791i	−3.84008	−	1.08718i	−1.84255	−	4.35319i	2.40771	−	1.81822i	1.33020	−	2.68897i	1.37364	+	7.34831i
5.15	−1.51819	−	1.66538i	−0.342537	−	1.69784i	−0.284038	+	3.06526i	1.20782	+	0.747848i	−2.30751	+	3.14810i	0.563616	+	1.33160i	1.93933	−	1.46451i	−2.76534	+	1.16315i	−0.588248	−	3.14685i
5.16	−1.43844	−	1.57790i	0.822755	−	1.52416i	−0.236104	+	2.54796i	−0.539942	−	0.334318i	−3.58846	+	0.894201i	1.43034	+	3.37930i	0.952267	−	0.719118i	−1.64615	−	2.50803i	0.249157	+	1.33287i
5.17	−1.39955	−	1.53523i	1.36793	−	1.06243i	−0.213664	+	2.30581i	0.712815	+	0.441356i	−3.54557	−	0.613172i	−0.0640532	−	0.151332i	0.523347	−	0.395214i	0.742482	−	2.90667i	−0.320035	−	1.71204i
5.18	−1.37094	−	1.50385i	−1.30502	+	1.13883i	−0.197553	+	2.13193i	−1.15803	−	0.717020i	3.50174	+	0.401292i	−1.11324	−	2.63014i	0.229081	−	0.172994i	0.406151	−	2.97238i	0.509297	+	2.72450i
5.19	−1.28497	−	1.40954i	0.00726007	−	1.73204i	−0.151131	+	1.63096i	−1.94499	−	1.20429i	−2.45071	+	2.21538i	−0.517096	−	1.22169i	−0.551074	+	0.416151i	−2.99989	−	0.0251494i	0.801757	+	4.28902i
5.20	−1.26279	−	1.38522i	−1.65299	−	0.517326i	−0.139646	+	1.50702i	0.0313476	+	0.0194096i	1.37078	+	2.94303i	0.491456	+	1.16111i	−0.727749	+	0.549571i	2.46475	+	1.71027i	−0.0126990	−	0.0679335i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
927.bm	even	102	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	927.2.bm.a	yes	3264
9.d	odd	6	1		927.2.bg.a	✓	3264
103.h	odd	102	1		927.2.bg.a	✓	3264
927.bm	even	102	1	inner	927.2.bm.a	yes	3264

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
927.2.bg.a	✓	3264	9.d	odd	6	1
927.2.bg.a	✓	3264	103.h	odd	102	1
927.2.bm.a	yes	3264	1.a	even	1	1	trivial
927.2.bm.a	yes	3264	927.bm	even	102	1	inner

Hecke kernels

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