Newform orbit 855.2.bk.a

• Label: 855.2.bk.a
• Level: $855$
• Weight: $2$
• Character orbit: 855.bk
• 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.bk (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.

\(\operatorname{Tr}(f)(q) = \) \( 232 q + 114 q^{4} - 2 q^{5} - 10 q^{6} - 2 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
619.1	−2.40800	+	1.39026i	−0.445567	+	1.67376i	2.86563	−	4.96341i	−1.09149	−	1.95158i	−1.25403	−	4.64986i	2.44832	+	1.41354i			10.3748i	−2.60294	−	1.49154i	5.34150	+	3.18193i
619.2	−2.37590	+	1.37173i	−0.758902	−	1.55694i	2.76327	−	4.78612i	1.64696	+	1.51246i	3.93878	+	2.65813i	1.46938	+	0.848348i			9.67490i	−1.84813	+	2.36313i	−5.98769	−	1.33426i
619.3	−2.36669	+	1.36641i	0.616907	−	1.61846i	2.73415	−	4.73569i	−2.21687	+	0.292392i	0.751456	+	4.67335i	1.62972	+	0.940918i			9.47823i	−2.23885	−	1.99688i	4.84712	−	3.72115i
619.4	−2.29368	+	1.32426i	1.67612	−	0.436595i	2.50731	−	4.34280i	0.330297	+	2.21154i	−3.26632	+	3.22103i	−3.10566	−	1.79305i			7.98429i	2.61877	−	1.46357i	−3.68624	−	4.63517i
619.5	−2.25938	+	1.30445i	−1.55359	−	0.765732i	2.40318	−	4.16244i	−2.10823	−	0.745240i	4.50901	−	0.296512i	−3.04365	−	1.75725i			7.32154i	1.82731	+	2.37927i	5.73540	−	1.06630i
619.6	−2.25061	+	1.29939i	1.48041	+	0.899108i	2.37683	−	4.11679i	1.38531	−	1.75525i	−4.50011	−	0.0999145i	−0.834324	−	0.481697i			7.15615i	1.38321	+	2.66209i	−0.837030	+	5.75045i
619.7	−2.21273	+	1.27752i	−1.69026	−	0.378178i	2.26411	−	3.92156i	1.20111	−	1.88609i	4.22322	−	1.32253i	1.86729	+	1.07808i			6.45971i	2.71396	+	1.27844i	−0.248214	+	5.70785i
619.8	−2.18587	+	1.26201i	1.36119	+	1.07105i	2.18536	−	3.78515i	1.97941	+	1.04017i	−4.32708	−	0.623335i	2.62968	+	1.51825i			5.98375i	0.705699	+	2.91582i	−5.63944	+	0.224368i
619.9	−2.17333	+	1.25477i	−1.55265	+	0.767638i	2.14890	−	3.72200i	−1.26013	+	1.84718i	2.41121	−	3.61655i	−0.287799	−	0.166161i			5.76640i	1.82146	−	2.38375i	0.420896	−	5.59569i
619.10	−2.17233	+	1.25420i	0.628411	−	1.61403i	2.14602	−	3.71702i	0.790244	−	2.09177i	0.659197	+	4.29437i	−3.62710	−	2.09411i			5.74937i	−2.21020	−	2.02855i	0.906823	+	5.53515i
619.11	−2.06053	+	1.18965i	0.0963643	+	1.72937i	1.83052	−	3.17055i	−0.439596	+	2.19243i	−2.25590	−	3.44877i	−1.36859	−	0.790155i			3.95210i	−2.98143	+	0.333299i	−1.70242	−	5.04053i
619.12	−2.03946	+	1.17748i	1.71521	+	0.240975i	1.77293	−	3.07080i	−2.01107	+	0.977556i	−3.78184	+	1.52817i	3.59061	+	2.07304i			3.64045i	2.88386	+	0.826643i	2.95043	−	4.36168i
619.13	−1.96984	+	1.13729i	0.765960	+	1.55348i	1.58685	−	2.74851i	−2.22170	+	0.253098i	−3.27558	−	2.18900i	0.431864	+	0.249337i			2.66968i	−1.82661	+	2.37981i	4.08855	−	3.02528i
619.14	−1.94963	+	1.12562i	1.68432	−	0.403807i	1.53405	−	2.65705i	−1.59512	−	1.56704i	−2.82928	+	2.68318i	−0.656911	−	0.379268i			2.40453i	2.67388	−	1.36028i	4.87378	+	1.25965i
619.15	−1.92513	+	1.11147i	1.23145	−	1.21801i	1.47075	−	2.54741i	2.21849	−	0.279858i	−1.01691	+	3.71354i	1.30755	+	0.754912i			2.09291i	0.0329232	−	2.99982i	−3.95982	+	3.00455i
619.16	−1.89209	+	1.09240i	−1.42242	+	0.988297i	1.38666	−	2.40177i	1.90234	−	1.17520i	1.61172	−	3.42379i	0.138311	+	0.0798541i			1.68955i	1.04654	−	2.81154i	−2.31560	+	4.30170i
619.17	−1.87749	+	1.08397i	−1.01881	+	1.40072i	1.34998	−	2.33823i	−1.15497	−	1.91469i	0.394463	−	3.73420i	−3.98272	−	2.29943i			1.51747i	−0.924055	−	2.85414i	4.24391	+	2.34286i
619.18	−1.86943	+	1.07932i	−1.60863	−	0.642106i	1.32984	−	2.30336i	−1.05173	+	1.97329i	3.70026	−	0.535850i	4.12771	+	2.38314i			1.42402i	2.17540	+	2.06583i	−0.163660	−	4.82407i
619.19	−1.81202	+	1.04617i	−0.454796	−	1.67128i	1.18894	−	2.05930i	2.20732	+	0.357414i	2.57253	+	2.55259i	−1.42646	−	0.823569i			0.790648i	−2.58632	+	1.52018i	−4.37362	+	1.66159i
619.20	−1.80800	+	1.04385i	−0.551253	+	1.64199i	1.17925	−	2.04252i	2.04984	+	0.893400i	−0.717323	−	3.54414i	4.28952	+	2.47655i			0.748438i	−2.39224	−	1.81030i	−4.63869	+	0.524456i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
171.g	even	3	1	inner
855.bk	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.bk.a	yes	232
5.b	even	2	1	inner	855.2.bk.a	yes	232
9.c	even	3	1		855.2.s.a	✓	232
19.c	even	3	1		855.2.s.a	✓	232
45.j	even	6	1		855.2.s.a	✓	232
95.i	even	6	1		855.2.s.a	✓	232
171.g	even	3	1	inner	855.2.bk.a	yes	232
855.bk	even	6	1	inner	855.2.bk.a	yes	232

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
855.2.s.a	✓	232	9.c	even	3	1
855.2.s.a	✓	232	19.c	even	3	1
855.2.s.a	✓	232	45.j	even	6	1
855.2.s.a	✓	232	95.i	even	6	1
855.2.bk.a	yes	232	1.a	even	1	1	trivial
855.2.bk.a	yes	232	5.b	even	2	1	inner
855.2.bk.a	yes	232	171.g	even	3	1	inner
855.2.bk.a	yes	232	855.bk	even	6	1	inner

Hecke kernels

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