Newform orbit 464.2.bm.a

• Label: 464.2.bm.a
• Level: $464$
• Weight: $2$
• Character orbit: 464.bm
• 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.bm (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.

\(\operatorname{Tr}(f)(q) = \) \( 696 q - 14 q^{2} - 14 q^{3} - 14 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 22 q^{8} + 108 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3.1	−1.41318	+	0.0541193i	1.22454	−	2.54279i	1.99414	−	0.152960i	1.43087	−	2.27721i	−1.59288	+	3.65968i	0.253494	+	0.122076i	−2.80980	+	0.324082i	−3.09580	−	3.88201i	−1.89883	+	3.29554i
3.2	−1.41085	+	0.0974471i	−0.895624	+	1.85978i	1.98101	−	0.274967i	−0.111597	+	0.177606i	1.08236	−	2.71115i	1.84030	+	0.886243i	−2.76812	+	0.580981i	−0.786179	−	0.985837i	0.140140	−	0.261451i
3.3	−1.38943	+	0.263603i	0.152691	−	0.317066i	1.86103	−	0.732515i	−0.563479	+	0.896772i	−0.128573	+	0.480790i	−0.850897	−	0.409770i	−2.39267	+	1.50835i	1.79325	+	2.24867i	0.546523	−	1.39454i
3.4	−1.37930	−	0.312301i	1.16893	−	2.42731i	1.80494	+	0.861513i	−1.45965	+	2.32303i	−2.37035	+	2.98293i	−1.80353	−	0.868536i	−2.22050	−	1.75197i	−2.65495	−	3.32921i	2.73878	−	2.74830i
3.5	−1.37647	+	0.324540i	−1.27589	+	2.64941i	1.78935	−	0.893440i	−1.12402	+	1.78886i	0.896384	−	4.06091i	−2.55529	−	1.23056i	−2.17303	+	1.81051i	−3.52100	−	4.41520i	0.966620	−	2.82711i
3.6	−1.36728	−	0.361311i	−0.792484	+	1.64561i	1.73891	+	0.988025i	1.98774	−	3.16346i	1.67812	−	1.96368i	−4.28894	−	2.06545i	−2.02059	−	1.97919i	−0.209534	−	0.262748i	−3.86078	+	3.60715i
3.7	−1.33485	−	0.467092i	0.300485	−	0.623963i	1.56365	+	1.24700i	−0.0381483	+	0.0607127i	−0.692550	+	0.692543i	−1.53230	−	0.737914i	−1.50478	−	2.39492i	1.57143	+	1.97051i	0.0792807	−	0.0632236i
3.8	−1.31552	−	0.519049i	−0.303124	+	0.629443i	1.46118	+	1.36564i	−2.21600	+	3.52675i	0.725477	−	0.670707i	3.15763	+	1.52064i	−1.21337	−	2.55494i	1.56615	+	1.96390i	4.74575	−	3.48928i
3.9	−1.28199	+	0.597071i	−0.0203140	+	0.0421825i	1.28701	−	1.53088i	1.67880	−	2.67179i	0.000856487	−	0.0662066i	−0.861266	−	0.414764i	−0.735896	+	2.73102i	1.86910	+	2.34378i	−0.556958	+	4.42758i
3.10	−1.24188	+	0.676554i	0.612248	−	1.27135i	1.08455	−	1.68040i	−0.296746	+	0.472269i	0.0997934	+	1.99308i	4.49243	+	2.16344i	−0.210002	+	2.82062i	0.628997	+	0.788738i	0.0490089	−	0.787268i
3.11	−1.19820	+	0.751218i	1.04066	−	2.16095i	0.871343	−	1.80021i	−2.22654	+	3.54352i	0.376432	+	3.37100i	−1.12908	−	0.543734i	0.308313	+	2.81157i	−1.71626	−	2.15212i	0.00587425	−	5.91845i
3.12	−1.18368	−	0.773890i	0.286642	−	0.595217i	0.802188	+	1.83207i	1.62983	−	2.59386i	−0.799924	+	0.482717i	3.20995	+	1.54583i	0.468291	−	2.78939i	1.59835	+	2.00427i	−3.93655	+	1.80898i
3.13	−1.06996	−	0.924759i	−1.32692	+	2.75538i	0.289641	+	1.97892i	0.832602	−	1.32508i	3.96783	−	1.72107i	1.17003	+	0.563457i	1.52012	−	2.38521i	−3.96095	−	4.96687i	−2.11623	+	0.647828i
3.14	−0.995954	+	1.00403i	−0.838265	+	1.74068i	−0.0161500	−	1.99993i	−0.521990	+	0.830742i	−0.912816	−	2.57528i	−1.63815	−	0.788892i	2.02408	+	1.97563i	−0.456794	−	0.572802i	−0.314211	−	1.35147i
3.15	−0.977696	+	1.02182i	−1.44617	+	3.00300i	−0.0882198	−	1.99805i	1.78095	−	2.83436i	−1.65460	−	4.41374i	2.36377	+	1.13833i	2.12790	+	1.86334i	−5.05613	−	6.34019i	1.15497	+	4.59095i
3.16	−0.947503	−	1.04988i	1.31504	−	2.73071i	−0.204476	+	1.98952i	−0.494184	+	0.786489i	−4.11291	+	1.20673i	4.11364	+	1.98102i	2.28249	−	1.67040i	−3.85699	−	4.83651i	1.29396	−	0.226369i
3.17	−0.911014	−	1.08169i	−0.732332	+	1.52070i	−0.340108	+	1.97087i	−1.90132	+	3.02593i	2.31210	−	0.593225i	−4.63223	−	2.23077i	2.44171	−	1.42760i	0.0942398	+	0.118173i	5.00525	−	0.700027i
3.18	−0.869576	−	1.11527i	−0.671670	+	1.39474i	−0.487677	+	1.93963i	0.00690563	−	0.0109903i	2.13958	−	0.463733i	0.705575	+	0.339787i	2.58729	−	1.14276i	0.376318	+	0.471888i	−0.0182621	+	0.00185517i
3.19	−0.810665	+	1.15880i	−0.517103	+	1.07377i	−0.685643	−	1.87880i	−0.238957	+	0.380297i	−0.825095	−	1.46969i	2.54112	+	1.22374i	2.73299	+	0.728554i	0.984873	+	1.23499i	−0.246975	−	0.585197i
3.20	−0.795304	+	1.16940i	0.316263	−	0.656726i	−0.734982	−	1.86005i	−0.371511	+	0.591256i	0.516449	+	0.892134i	−3.89724	−	1.87681i	2.75968	+	0.619824i	1.53920	+	1.93010i	−0.395949	−	0.904673i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
464.bm	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.bm.a	yes	696
16.f	odd	4	1		464.2.bc.a	✓	696
29.f	odd	28	1		464.2.bc.a	✓	696
464.bm	even	28	1	inner	464.2.bm.a	yes	696

    

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

Hecke kernels

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