Newform orbit 931.2.bk.a

• Label: 931.2.bk.a
• Level: $931$
• Weight: $2$
• Character orbit: 931.bk
• Analytic conductor: $7.434$
• Analytic rank: $0$
• Dimension: $1104$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.bk (of order \(21\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.43407242818\)
Analytic rank:	\(0\)
Dimension:	\(1104\)
Relative dimension:	\(92\) over \(\Q(\zeta_{21})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1104 q - 5 q^{2} - 10 q^{3} - 189 q^{4} - 7 q^{5} - q^{6} - 26 q^{7} - 10 q^{8} + 82 q^{9}+O(q^{10}) \)

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	−0.615875	−	2.69832i	−0.332007	+	0.845940i	−5.09971	+	2.45589i	−1.15532	−	1.44872i	2.48709	+	0.374869i	2.46158	+	0.969855i	6.31629	+	7.92037i	1.59377	+	1.47880i	−3.19759	+	4.00965i
11.2	−0.609805	−	2.67173i	0.644462	−	1.64206i	−4.96434	+	2.39070i	1.94340	+	2.43695i	−4.78014	−	0.720491i	−2.58384	+	0.569009i	5.99730	+	7.52038i	−0.0818849	−	0.0759781i	5.32577	−	6.67831i
11.3	−0.587425	−	2.57368i	−1.13685	+	2.89665i	−4.47682	+	2.15592i	0.919532	+	1.15306i	8.12286	+	1.22432i	−2.11037	−	1.59573i	4.88659	+	6.12759i	−4.89898	−	4.54559i	2.42744	−	3.04391i
11.4	−0.587289	−	2.57308i	0.140450	−	0.357861i	−4.47390	+	2.15452i	−0.381209	−	0.478022i	−1.00329	−	0.151222i	0.277776	−	2.63113i	4.88012	+	6.11947i	2.09082	+	1.94000i	−1.00611	+	1.26162i
11.5	−0.579392	−	2.53848i	−0.568641	+	1.44887i	−4.30626	+	2.07378i	2.63489	+	3.30404i	4.00741	+	0.604020i	2.30643	−	1.29629i	4.51243	+	5.65841i	0.423271	+	0.392738i	6.86062	−	8.60294i
11.6	−0.552041	−	2.41865i	−1.16445	+	2.96696i	−3.74318	+	1.80262i	−0.393992	−	0.494050i	7.81887	+	1.17850i	1.55186	+	2.14283i	3.33272	+	4.17910i	−5.24778	−	4.86923i	−0.977434	+	1.22566i
11.7	−0.549985	−	2.40964i	0.609760	−	1.55364i	−3.70195	+	1.78277i	−1.40795	−	1.76552i	−4.07908	−	0.614823i	−2.06656	+	1.65206i	3.24980	+	4.07512i	0.157156	+	0.145820i	−3.47991	+	4.36367i
11.8	−0.547285	−	2.39781i	1.04580	−	2.66465i	−3.64804	+	1.75681i	0.578694	+	0.725660i	−6.96169	−	1.04931i	1.14529	−	2.38502i	3.14209	+	3.94006i	−3.80753	−	3.53287i	1.42329	−	1.78474i
11.9	−0.543789	−	2.38249i	−0.265972	+	0.677685i	−3.57863	+	1.72338i	−0.524866	−	0.658161i	1.75921	+	0.265159i	−0.928425	−	2.47750i	3.00463	+	3.76769i	1.81064	+	1.68003i	−1.28265	+	1.60839i
11.10	−0.540332	−	2.36735i	−0.785355	+	2.00105i	−3.51044	+	1.69054i	−2.32503	−	2.91549i	5.16153	+	0.777976i	−2.64118	+	0.155496i	2.87094	+	3.60004i	−1.18827	−	1.10255i	−5.64570	+	7.07948i
11.11	−0.538912	−	2.36113i	0.605126	−	1.54184i	−3.48257	+	1.67712i	1.31442	+	1.64823i	−3.96659	−	0.597867i	1.46589	+	2.20253i	2.81669	+	3.53202i	0.188073	+	0.174506i	3.18334	−	3.99178i
11.12	−0.510055	−	2.23470i	0.0578878	−	0.147496i	−2.93177	+	1.41187i	−0.706743	−	0.886228i	−0.359134	−	0.0541307i	−0.0746171	+	2.64470i	1.79218	+	2.24732i	2.18075	+	2.02344i	−1.61997	+	2.03138i
11.13	−0.482006	−	2.11180i	−0.442854	+	1.12837i	−2.42545	+	1.16804i	1.98377	+	2.48757i	2.59636	+	0.391339i	−0.196080	+	2.63848i	0.934643	+	1.17201i	1.12205	+	1.04111i	4.29708	−	5.38836i
11.14	−0.457382	−	2.00392i	1.05033	−	2.67619i	−2.00456	+	0.965345i	−1.00741	−	1.26325i	−5.84326	−	0.880730i	−2.24653	−	1.39753i	0.288212	+	0.361406i	−3.85964	−	3.58122i	−2.07068	+	2.59655i
11.15	−0.450682	−	1.97457i	−0.818630	+	2.08584i	−1.89387	+	0.912039i	−2.38170	−	2.98656i	4.48757	+	0.676392i	2.02636	−	1.70113i	0.128848	+	0.161571i	−1.48140	−	1.37454i	−4.82377	+	6.04881i
11.16	−0.432719	−	1.89587i	0.00417702	−	0.0106429i	−1.60513	+	0.772990i	1.18614	+	1.48737i	−0.0219850	−	0.00331370i	−1.63071	−	2.08346i	−0.264848	−	0.332109i	2.19906	+	2.04043i	2.30659	−	2.89237i
11.17	−0.426281	−	1.86766i	0.997568	−	2.54176i	−1.50450	+	0.724531i	−1.83257	−	2.29797i	−5.17240	−	0.779613i	2.38424	+	1.14690i	−0.394308	−	0.494446i	−3.26626	−	3.03065i	−3.51064	+	4.40220i
11.18	−0.417108	−	1.82747i	0.442810	−	1.12826i	−1.36373	+	0.656737i	−0.116514	−	0.146105i	−2.24656	−	0.338615i	2.61176	+	0.422728i	−0.568433	−	0.712793i	1.12226	+	1.04131i	−0.218402	+	0.273868i
11.19	−0.412379	−	1.80675i	−0.519618	+	1.32396i	−1.29236	+	0.622368i	0.0580236	+	0.0727593i	2.60636	+	0.392845i	2.64553	+	0.0342878i	−0.653515	−	0.819483i	0.716275	+	0.664606i	0.107530	−	0.134839i
11.20	−0.411670	−	1.80364i	1.07059	−	2.72781i	−1.28172	+	0.617245i	2.19657	+	2.75441i	−5.36072	−	0.807999i	1.06921	+	2.42008i	−0.666011	−	0.835151i	−4.09562	−	3.80018i	4.06371	−	5.09573i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
931.bk	even	21	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	931.2.bk.a	✓	1104
19.c	even	3	1		931.2.bl.a	yes	1104
49.g	even	21	1		931.2.bl.a	yes	1104
931.bk	even	21	1	inner	931.2.bk.a	✓	1104

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
931.2.bk.a	✓	1104	1.a	even	1	1	trivial
931.2.bk.a	✓	1104	931.bk	even	21	1	inner
931.2.bl.a	yes	1104	19.c	even	3	1
931.2.bl.a	yes	1104	49.g	even	21	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(931, [\chi])\).