Newform orbit 935.2.bt.a

• Label: 935.2.bt.a
• Level: $935$
• Weight: $2$
• Character orbit: 935.bt
• Analytic conductor: $7.466$
• Analytic rank: $0$
• Dimension: $832$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 935 = 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	935.bt (of order \(20\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.46601258899\)
Analytic rank:	\(0\)
Dimension:	\(832\)
Relative dimension:	\(104\) over \(\Q(\zeta_{20})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 832 q - 224 q^{4} - 2 q^{5} + 4 q^{6}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
4.1	−2.26021	−	1.64214i	−2.43170	+	1.23901i	1.79391	+	5.52108i	−0.639061	−	2.14280i	7.53081	+	1.19276i	3.06595	+	1.56218i	3.28513	−	10.1106i	2.61466	−	3.59878i	−2.07437	+	5.89262i
4.2	−2.21733	−	1.61099i	−0.431677	+	0.219951i	1.70325	+	5.24207i	2.23341	−	0.109094i	1.31151	+	0.207723i	−1.35712	−	0.691487i	2.97434	−	9.15408i	−1.62539	+	2.23716i	−5.12795	−	3.35609i
4.3	−2.16621	−	1.57384i	1.90360	−	0.969934i	1.59745	+	4.91643i	−0.682299	+	2.12943i	−5.65012	−	0.894892i	−1.45048	−	0.739055i	2.62245	−	8.07109i	0.919573	−	1.26568i	4.82939	−	3.53896i
4.4	−2.12511	−	1.54398i	1.56970	−	0.799803i	1.51417	+	4.66014i	2.23517	+	0.0632920i	−4.57066	−	0.723922i	4.08856	+	2.08323i	2.35395	−	7.24472i	0.0609211	−	0.0838507i	−4.65226	−	3.58557i
4.5	−2.12279	−	1.54230i	−2.09777	+	1.06887i	1.50952	+	4.64582i	−0.257482	+	2.22119i	6.10164	+	0.966405i	−0.0914463	−	0.0465942i	2.33918	−	7.19925i	1.49481	−	2.05744i	3.97232	−	4.31801i
4.6	−2.09999	−	1.52573i	−0.387324	+	0.197352i	1.46406	+	4.50590i	−2.17839	+	0.504584i	1.11448	+	0.176516i	2.00764	+	1.02295i	2.19604	−	6.75872i	−1.65228	+	2.27417i	5.34445	+	2.26402i
4.7	−2.09694	−	1.52352i	2.27420	−	1.15876i	1.45802	+	4.48734i	−2.17556	−	0.516659i	−6.53424	−	1.03492i	2.01429	+	1.02633i	2.17722	−	6.70080i	2.06588	−	2.84344i	3.77488	+	4.39791i
4.8	−2.03755	−	1.48037i	0.295766	−	0.150700i	1.34210	+	4.13055i	0.250446	−	2.22200i	−0.825731	−	0.130783i	−0.436737	−	0.222528i	1.82359	−	5.61244i	−1.69859	+	2.33791i	−3.79968	+	4.15669i
4.9	−2.00945	−	1.45995i	0.154420	−	0.0786810i	1.28840	+	3.96529i	−1.16773	−	1.90694i	−0.425170	−	0.0673404i	−4.34357	−	2.21316i	1.66507	−	5.12456i	−1.74570	+	2.40275i	−0.437536	+	5.53673i
4.10	−1.89457	−	1.37649i	1.46703	−	0.747488i	1.07665	+	3.31360i	1.02289	+	1.98839i	−3.80830	−	0.603175i	−1.46975	−	0.748874i	1.07401	−	3.30545i	−0.169925	+	0.233882i	0.799045	−	5.17515i
4.11	−1.84400	−	1.33975i	−2.54549	+	1.29699i	0.987391	+	3.03888i	1.72059	−	1.42814i	6.43154	+	1.01866i	−2.26822	−	1.15572i	0.841879	−	2.59104i	3.03399	−	4.17593i	−5.08611	+	0.328345i
4.12	−1.80177	−	1.30906i	−0.587078	+	0.299131i	0.914695	+	2.81514i	0.898422	+	2.04764i	1.44936	+	0.229556i	3.25186	+	1.65690i	0.660695	−	2.03341i	−1.50817	+	2.07582i	1.06174	−	4.86547i
4.13	−1.79828	−	1.30653i	−2.31607	+	1.18010i	0.908760	+	2.79688i	1.30063	+	1.81889i	5.70677	+	0.903864i	−0.561998	−	0.286353i	0.646224	−	1.98887i	2.20821	−	3.03934i	0.0375247	−	4.97017i
4.14	−1.78577	−	1.29743i	−0.102527	+	0.0522403i	0.887587	+	2.73171i	−2.23556	+	0.0475962i	0.250868	+	0.0397336i	−0.276381	−	0.140823i	0.594992	−	1.83120i	−1.75557	+	2.41634i	4.05394	+	2.81550i
4.15	−1.76762	−	1.28425i	2.50166	−	1.27466i	0.857152	+	2.63804i	0.565652	−	2.16334i	−6.05898	−	0.959648i	0.537029	+	0.273630i	0.522451	−	1.60794i	2.87019	−	3.95048i	−3.77814	+	3.09753i
4.16	−1.66769	−	1.21165i	−2.04626	+	1.04262i	0.695068	+	2.13920i	−2.09471	+	0.782424i	4.67583	+	0.740579i	0.254615	+	0.129733i	0.158796	−	0.488723i	1.33678	−	1.83992i	4.44135	+	1.23321i
4.17	−1.66639	−	1.21070i	1.85477	−	0.945052i	0.693013	+	2.13287i	2.18189	−	0.489244i	−4.23494	−	0.670748i	−4.20178	−	2.14091i	0.154439	−	0.475313i	0.783690	−	1.07866i	−4.22820	−	1.82634i
4.18	−1.62897	−	1.18351i	−1.34553	+	0.685582i	0.634796	+	1.95370i	1.69785	−	1.45509i	3.00322	+	0.475663i	0.855285	+	0.435790i	0.0337506	−	0.103874i	−0.422928	+	0.582111i	−4.48787	+	0.360865i
4.19	−1.60678	−	1.16739i	2.87842	−	1.46663i	0.600895	+	1.84936i	−2.14882	−	0.618519i	−6.33711	−	1.00370i	−2.71604	−	1.38389i	−0.0340397	+	0.104763i	4.37095	−	6.01609i	2.73062	+	3.50234i
4.20	−1.55767	−	1.13171i	−0.262334	+	0.133666i	0.527520	+	1.62354i	2.12748	−	0.688340i	0.559899	+	0.0886793i	2.16129	+	1.10123i	−0.174273	+	0.536358i	−1.71240	+	2.35692i	−4.09291	−	1.33549i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
11.c	even	5	1	inner
17.c	even	4	1	inner
55.j	even	10	1	inner
85.j	even	4	1	inner
187.p	even	20	1	inner
935.bt	even	20	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	935.2.bt.a	✓	832
5.b	even	2	1	inner	935.2.bt.a	✓	832
11.c	even	5	1	inner	935.2.bt.a	✓	832
17.c	even	4	1	inner	935.2.bt.a	✓	832
55.j	even	10	1	inner	935.2.bt.a	✓	832
85.j	even	4	1	inner	935.2.bt.a	✓	832
187.p	even	20	1	inner	935.2.bt.a	✓	832
935.bt	even	20	1	inner	935.2.bt.a	✓	832

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
935.2.bt.a	✓	832	1.a	even	1	1	trivial
935.2.bt.a	✓	832	5.b	even	2	1	inner
935.2.bt.a	✓	832	11.c	even	5	1	inner
935.2.bt.a	✓	832	17.c	even	4	1	inner
935.2.bt.a	✓	832	55.j	even	10	1	inner
935.2.bt.a	✓	832	85.j	even	4	1	inner
935.2.bt.a	✓	832	187.p	even	20	1	inner
935.2.bt.a	✓	832	935.bt	even	20	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(935, [\chi])\).