Newform orbit 935.2.q.a

• Label: 935.2.q.a
• Level: $935$
• Weight: $2$
• Character orbit: 935.q
• Analytic conductor: $7.466$
• Analytic rank: $0$
• Dimension: $208$
• CM: no
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(7.46601258899\)
Analytic rank:	\(0\)
Dimension:	\(208\)
Relative dimension:	\(104\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 208 q - 8 q^{3} - 8 q^{5} + 176 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
208.1	−1.95067	+	1.95067i	−1.94974				−	5.61020i	−1.02099	+	1.98937i	3.80328	−	3.80328i			2.39143i	7.04229	+	7.04229i	0.801469			−1.88899	−	5.87220i
208.2	−1.93065	+	1.93065i	2.78549				−	5.45485i	1.49676	+	1.66124i	−5.37781	+	5.37781i		−	3.43341i	6.67011	+	6.67011i	4.75893			−6.09700	−	0.317563i
208.3	−1.88825	+	1.88825i	−0.0115176				−	5.13101i	2.06686	+	0.853278i	0.0217481	−	0.0217481i			3.91069i	5.91215	+	5.91215i	−2.99987			−5.51397	+	2.29156i
208.4	−1.87299	+	1.87299i	2.30080				−	5.01618i	−2.21997	−	0.267811i	−4.30937	+	4.30937i		−	0.212970i	5.64928	+	5.64928i	2.29367			4.65959	−	3.65638i
208.5	−1.84957	+	1.84957i	0.413919				−	4.84181i	−1.61417	−	1.54741i	−0.765571	+	0.765571i			0.498036i	5.25612	+	5.25612i	−2.82867			5.84755	−	0.123476i
208.6	−1.83054	+	1.83054i	−1.82510				−	4.70178i	1.71029	+	1.44046i	3.34093	−	3.34093i		−	4.80254i	4.94573	+	4.94573i	0.330991			−5.76758	+	0.493932i
208.7	−1.80559	+	1.80559i	−2.55965				−	4.52028i	−0.121389	−	2.23277i	4.62167	−	4.62167i			2.31748i	4.55058	+	4.55058i	3.55181			4.25064	+	3.81228i
208.8	−1.79085	+	1.79085i	−0.612853				−	4.41427i	−0.516530	−	2.17559i	1.09753	−	1.09753i		−	2.98254i	4.32358	+	4.32358i	−2.62441			4.82118	+	2.97113i
208.9	−1.77806	+	1.77806i	1.72555				−	4.32297i	1.70442	−	1.44739i	−3.06812	+	3.06812i		−	0.936567i	4.13037	+	4.13037i	−0.0224943			−0.457018	+	5.60410i
208.10	−1.73879	+	1.73879i	−0.730611				−	4.04679i	−1.85275	+	1.25193i	1.27038	−	1.27038i		−	3.70787i	3.55894	+	3.55894i	−2.46621			1.04471	−	5.39838i
208.11	−1.64413	+	1.64413i	−0.525262				−	3.40633i	2.17492	−	0.519340i	0.863599	−	0.863599i			1.12290i	2.31219	+	2.31219i	−2.72410			−2.72199	+	4.42972i
208.12	−1.60206	+	1.60206i	2.77726				−	3.13319i	−1.06634	+	1.96543i	−4.44933	+	4.44933i			4.16310i	1.81544	+	1.81544i	4.71315			−1.44039	−	4.85708i
208.13	−1.57655	+	1.57655i	−3.12574				−	2.97101i	0.547771	+	2.16794i	4.92788	−	4.92788i			1.06056i	1.53084	+	1.53084i	6.77024			−4.28144	−	2.55427i
208.14	−1.52640	+	1.52640i	2.26424				−	2.65978i	0.918795	−	2.03858i	−3.45612	+	3.45612i			1.09760i	1.00709	+	1.00709i	2.12677			1.70924	+	4.51413i
208.15	−1.50648	+	1.50648i	−2.28160				−	2.53897i	−2.21646	+	0.295482i	3.43719	−	3.43719i		−	0.174728i	0.811944	+	0.811944i	2.20570			2.89391	−	3.78419i
208.16	−1.49210	+	1.49210i	0.794618				−	2.45274i	−2.21584	−	0.300111i	−1.18565	+	1.18565i			4.34002i	0.675535	+	0.675535i	−2.36858			3.75405	−	2.85846i
208.17	−1.47446	+	1.47446i	1.45114				−	2.34804i	0.558063	+	2.16531i	−2.13964	+	2.13964i			0.883256i	0.513166	+	0.513166i	−0.894200			−4.01549	−	2.36981i
208.18	−1.44084	+	1.44084i	1.09724				−	2.15207i	0.186733	+	2.22826i	−1.58096	+	1.58096i		−	3.09709i	0.219105	+	0.219105i	−1.79605			−3.47963	−	2.94152i
208.19	−1.43586	+	1.43586i	−3.27687				−	2.12337i	−1.93630	−	1.11837i	4.70512	−	4.70512i		−	3.29593i	0.177142	+	0.177142i	7.73791			4.38606	−	1.17444i
208.20	−1.32072	+	1.32072i	−0.674312				−	1.48860i	0.119902	+	2.23285i	0.890577	−	0.890577i			1.32066i	−0.675422	−	0.675422i	−2.54530			−3.10732	−	2.79061i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.b	odd	2	1	inner
85.i	odd	4	1	inner
935.q	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	935.2.q.a	yes	208
5.c	odd	4	1		935.2.l.a	✓	208
11.b	odd	2	1	inner	935.2.q.a	yes	208
17.c	even	4	1		935.2.l.a	✓	208
55.e	even	4	1		935.2.l.a	✓	208
85.i	odd	4	1	inner	935.2.q.a	yes	208
187.f	odd	4	1		935.2.l.a	✓	208
935.q	even	4	1	inner	935.2.q.a	yes	208

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
935.2.l.a	✓	208	5.c	odd	4	1
935.2.l.a	✓	208	17.c	even	4	1
935.2.l.a	✓	208	55.e	even	4	1
935.2.l.a	✓	208	187.f	odd	4	1
935.2.q.a	yes	208	1.a	even	1	1	trivial
935.2.q.a	yes	208	11.b	odd	2	1	inner
935.2.q.a	yes	208	85.i	odd	4	1	inner
935.2.q.a	yes	208	935.q	even	4	1	inner

Hecke kernels

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