Newform orbit 855.2.bm.a

• Label: 855.2.bm.a
• Level: $855$
• Weight: $2$
• Character orbit: 855.bm
• Analytic conductor: $6.827$
• Analytic rank: $0$
• Dimension: $232$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.bm (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.82720937282\)
Analytic rank:	\(0\)
Dimension:	\(232\)
Relative dimension:	\(116\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 232 q + 114 q^{4} - 10 q^{6} - 2 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
734.1	−2.37082	−	1.36879i	−1.30626	+	1.13740i	2.74719	+	4.75827i	1.97621	+	1.04623i	4.65377	−	0.908582i	−3.67033	+	2.11907i		−	9.56616i	0.412624	−	2.97149i	−3.25317	−	5.18544i
734.2	−2.36642	−	1.36625i	1.18598	−	1.26232i	2.73329	+	4.73419i	1.40550	+	1.73913i	−4.53117	+	1.36683i	1.95703	−	1.12989i		−	9.47243i	−0.186900	−	2.99417i	−0.949916	−	6.03577i
734.3	−2.34930	−	1.35637i	0.754265	−	1.55919i	2.67947	+	4.64097i	−2.22250	−	0.245972i	−3.88683	+	2.63995i	−3.32996	+	1.92255i		−	9.11190i	−1.86217	−	2.35209i	4.88768	+	3.59239i
734.4	−2.34798	−	1.35561i	1.15121	+	1.29411i	2.67533	+	4.63381i	−0.636412	+	2.14359i	−0.948707	−	4.59913i	1.24030	−	0.716087i		−	9.08437i	−0.349442	+	2.97958i	4.40014	−	4.17038i
734.5	−2.30517	−	1.33089i	−1.45127	−	0.945421i	2.54253	+	4.40379i	0.526521	−	2.17319i	2.08717	+	4.11083i	−0.704988	+	0.407025i		−	8.21172i	1.21236	+	2.74412i	−4.10600	+	4.30883i
734.6	−2.26618	−	1.30838i	−0.120237	+	1.72787i	2.42370	+	4.19798i	−1.84891	−	1.25759i	2.53319	−	3.75835i	0.225642	−	0.130274i		−	7.45096i	−2.97109	−	0.415508i	2.54455	+	5.26900i
734.7	−2.26264	−	1.30634i	1.72550	−	0.150466i	2.41304	+	4.17951i	−0.545397	−	2.16853i	−4.10076	−	1.91364i	3.85492	−	2.22564i		−	7.38362i	2.95472	−	0.519260i	−1.59880	+	5.61909i
734.8	−2.22513	−	1.28468i	1.22922	+	1.22025i	2.30081	+	3.98511i	2.00835	−	0.983127i	−1.16754	−	4.29438i	−1.25137	+	0.722479i		−	6.68448i	0.0219680	+	2.99992i	−5.73184	−	0.392498i
734.9	−2.12945	−	1.22944i	−1.66388	+	0.481162i	2.02303	+	3.50400i	−1.55889	+	1.60308i	4.13470	+	1.02102i	2.97922	−	1.72005i		−	5.03103i	2.53697	−	1.60119i	5.29046	−	1.49711i
734.10	−2.07381	−	1.19732i	−1.72464	−	0.160012i	1.86713	+	3.23397i	2.15457	+	0.598194i	3.38500	+	2.39678i	3.53648	−	2.04179i		−	4.15292i	2.94879	+	0.551928i	−3.75194	−	3.82024i
734.11	−2.03485	−	1.17482i	−0.732811	−	1.56939i	1.76042	+	3.04914i	−2.10258	−	0.761013i	−0.352594	+	4.05440i	3.13722	−	1.81128i		−	3.57344i	−1.92598	+	2.30013i	3.38440	+	4.01871i
734.12	−2.02945	−	1.17170i	−0.502875	−	1.65744i	1.74577	+	3.02376i	2.12158	+	0.706333i	−0.921469	+	3.95291i	−0.512676	+	0.295994i		−	3.49527i	−2.49423	+	1.66697i	−3.47802	−	3.91932i
734.13	−1.98920	−	1.14846i	1.68123	−	0.416501i	1.63794	+	2.83699i	0.947438	−	2.02543i	−3.82263	−	1.10232i	−1.78790	+	1.03224i		−	2.93058i	2.65305	−	1.40047i	−4.21077	+	2.94088i
734.14	−1.97447	−	1.13996i	−0.583787	−	1.63070i	1.59903	+	2.76961i	−0.0797553	+	2.23465i	−0.706268	+	3.88528i	−1.54089	+	0.889632i		−	2.73151i	−2.31838	+	1.90397i	2.70489	−	4.32133i
734.15	−1.94418	−	1.12247i	−1.55931	+	0.754028i	1.51988	+	2.63251i	−0.554100	−	2.16633i	3.87794	+	0.284314i	0.0552195	−	0.0318810i		−	2.33420i	1.86288	−	2.35152i	−1.35437	+	4.83368i
734.16	−1.92950	−	1.11399i	−0.934187	+	1.45852i	1.48197	+	2.56685i	−1.25908	+	1.84790i	3.42730	−	1.77354i	−0.671550	+	0.387720i		−	2.14764i	−1.25459	−	2.72507i	4.48793	−	2.16290i
734.17	−1.87836	−	1.08447i	1.72742	+	0.126504i	1.35215	+	2.34200i	0.764540	+	2.10130i	−3.10753	−	2.11096i	−3.93283	+	2.27062i		−	1.52760i	2.96799	+	0.437053i	0.842723	−	4.77612i
734.18	−1.87412	−	1.08202i	0.566004	+	1.63696i	1.34154	+	2.32361i	2.10026	−	0.767400i	0.710468	−	3.68028i	1.71387	−	0.989501i		−	1.47821i	−2.35928	+	1.85305i	−4.76647	−	0.834331i
734.19	−1.82977	−	1.05642i	1.38563	+	1.03924i	1.23204	+	2.13396i	−2.19806	−	0.410525i	−1.43752	−	3.36538i	−1.48259	+	0.855974i		−	0.980535i	0.839964	+	2.88001i	3.58826	+	3.07324i
734.20	−1.76483	−	1.01892i	0.955746	−	1.44449i	1.07642	+	1.86441i	−1.15033	+	1.91748i	−3.15855	+	1.57545i	2.17641	−	1.25655i		−	0.311446i	−1.17310	−	2.76113i	3.98391	−	2.21193i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
171.k	even	6	1	inner
855.bm	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	855.2.bm.a	yes	232
5.b	even	2	1	inner	855.2.bm.a	yes	232
9.d	odd	6	1		855.2.t.a	✓	232
19.d	odd	6	1		855.2.t.a	✓	232
45.h	odd	6	1		855.2.t.a	✓	232
95.h	odd	6	1		855.2.t.a	✓	232
171.k	even	6	1	inner	855.2.bm.a	yes	232
855.bm	even	6	1	inner	855.2.bm.a	yes	232

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
855.2.t.a	✓	232	9.d	odd	6	1
855.2.t.a	✓	232	19.d	odd	6	1
855.2.t.a	✓	232	45.h	odd	6	1
855.2.t.a	✓	232	95.h	odd	6	1
855.2.bm.a	yes	232	1.a	even	1	1	trivial
855.2.bm.a	yes	232	5.b	even	2	1	inner
855.2.bm.a	yes	232	171.k	even	6	1	inner
855.2.bm.a	yes	232	855.bm	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(855, [\chi])\).