Newform orbit 935.2.w.a

• Label: 935.2.w.a
• Level: $935$
• Weight: $2$
• Character orbit: 935.w
• Analytic conductor: $7.466$
• Analytic rank: $0$
• Dimension: $416$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 935 = 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	935.w (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.46601258899\)
Analytic rank:	\(0\)
Dimension:	\(416\)
Relative dimension:	\(104\) over \(\Q(\zeta_{8})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 416 q - 8 q^{3} - 400 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
417.1		−	2.74767i	−0.345746	+	0.143213i	−5.54970			1.96484	−	1.06743i	0.393502	+	0.949997i	0.633777	+	0.262519i			9.75340i	−2.02229	+	2.02229i	−2.93294	−	5.39874i
417.2		−	2.73512i	2.07151	−	0.858046i	−5.48087			−0.846137	+	2.06980i	−2.34686	−	5.66581i	−3.21733	−	1.33266i			9.52057i	1.43357	−	1.43357i	5.66113	+	2.31428i
417.3		−	2.67199i	−1.35153	+	0.559822i	−5.13953			−2.14959	+	0.615828i	1.49584	+	3.61128i	3.97165	+	1.64511i			8.38881i	−0.608088	+	0.608088i	1.64549	+	5.74370i
417.4		−	2.60627i	−0.293076	+	0.121396i	−4.79264			1.51774	+	1.64209i	0.316391	+	0.763835i	−0.161689	−	0.0669739i			7.27837i	−2.05016	+	2.05016i	4.27974	−	3.95564i
417.5		−	2.59527i	2.77646	−	1.15005i	−4.73543			2.21392	+	0.313920i	−2.98468	−	7.20565i	2.06868	+	0.856875i			7.09918i	4.26478	−	4.26478i	0.814706	−	5.74573i
417.6		−	2.58933i	−2.10598	+	0.872326i	−4.70464			−1.20311	+	1.88481i	2.25874	+	5.45309i	−1.70929	−	0.708012i			7.00320i	1.55289	−	1.55289i	4.88041	+	3.11525i
417.7		−	2.48588i	−3.02748	+	1.25402i	−4.17960			−1.00212	−	1.99894i	3.11735	+	7.52595i	0.565002	+	0.234031i			5.41823i	5.47174	−	5.47174i	−4.96912	+	2.49116i
417.8		−	2.45891i	−2.74002	+	1.13495i	−4.04623			2.23188	+	0.136801i	2.79074	+	6.73745i	−4.53807	−	1.87973i			5.03148i	4.09826	−	4.09826i	0.336381	−	5.48799i
417.9		−	2.42277i	1.67900	−	0.695463i	−3.86983			−0.0949524	−	2.23405i	−1.68495	−	4.06782i	3.83034	+	1.58658i			4.53017i	0.214037	−	0.214037i	−5.41260	+	0.230048i
417.10		−	2.36408i	0.799220	−	0.331048i	−3.58890			−2.10373	−	0.757852i	−0.782625	−	1.88942i	0.614237	+	0.254425i			3.75629i	−1.59216	+	1.59216i	−1.79163	+	4.97339i
417.11		−	2.36201i	−1.49286	+	0.618361i	−3.57907			0.130712	−	2.23224i	1.46057	+	3.52613i	1.26648	+	0.524593i			3.72977i	−0.275074	+	0.275074i	−5.27257	−	0.308743i
417.12		−	2.33491i	1.78306	−	0.738569i	−3.45182			1.88616	−	1.20100i	−1.72449	−	4.16330i	−2.56758	−	1.06352i			3.38988i	0.512509	−	0.512509i	−2.80423	−	4.40402i
417.13		−	2.32091i	1.72609	−	0.714970i	−3.38663			−0.669275	+	2.13356i	−1.65938	−	4.00610i	2.84326	+	1.17772i			3.21825i	0.346887	−	0.346887i	4.95180	+	1.55333i
417.14		−	2.30507i	−0.851894	+	0.352866i	−3.31336			−2.08190	−	0.815911i	0.813382	+	1.96368i	−3.57278	−	1.47990i			3.02740i	−1.52011	+	1.52011i	−1.88073	+	4.79892i
417.15		−	2.08439i	0.443711	−	0.183791i	−2.34468			−0.639878	−	2.14256i	−0.383092	−	0.924866i	−0.314576	−	0.130301i			0.718445i	−1.95822	+	1.95822i	−4.46593	+	1.33375i
417.16		−	2.05413i	0.941093	−	0.389813i	−2.21945			−1.23619	+	1.86328i	−0.800727	−	1.93313i	−2.42844	−	1.00589i			0.450776i	−1.38762	+	1.38762i	3.82742	+	2.53930i
417.17		−	2.03129i	−2.50988	+	1.03963i	−2.12616			0.0251829	+	2.23593i	2.11179	+	5.09830i	0.942372	+	0.390343i			0.256264i	3.09735	−	3.09735i	4.54182	−	0.0511540i
417.18		−	2.02897i	3.15251	−	1.30581i	−2.11671			−2.01843	−	0.962248i	−2.64946	−	6.39635i	−3.30878	−	1.37054i			0.236807i	6.11187	−	6.11187i	−1.95237	+	4.09534i
417.19		−	1.98632i	−0.575026	+	0.238184i	−1.94546			1.94736	+	1.09899i	0.473108	+	1.14218i	0.0476715	+	0.0197462i		−	0.108333i	−1.84740	+	1.84740i	2.18295	−	3.86808i
417.20		−	1.96430i	−1.72778	+	0.715668i	−1.85848			1.62349	−	1.53762i	1.40579	+	3.39387i	1.41833	+	0.587491i		−	0.277991i	0.351710	−	0.351710i	−3.02035	−	3.18903i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.b	odd	2	1	inner
85.n	odd	8	1	inner
935.w	even	8	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	935.2.w.a	✓	416
5.c	odd	4	1		935.2.bc.a	yes	416
11.b	odd	2	1	inner	935.2.w.a	✓	416
17.d	even	8	1		935.2.bc.a	yes	416
55.e	even	4	1		935.2.bc.a	yes	416
85.n	odd	8	1	inner	935.2.w.a	✓	416
187.i	odd	8	1		935.2.bc.a	yes	416
935.w	even	8	1	inner	935.2.w.a	✓	416

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
935.2.w.a	✓	416	1.a	even	1	1	trivial
935.2.w.a	✓	416	11.b	odd	2	1	inner
935.2.w.a	✓	416	85.n	odd	8	1	inner
935.2.w.a	✓	416	935.w	even	8	1	inner
935.2.bc.a	yes	416	5.c	odd	4	1
935.2.bc.a	yes	416	17.d	even	8	1
935.2.bc.a	yes	416	55.e	even	4	1
935.2.bc.a	yes	416	187.i	odd	8	1

Hecke kernels

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