Newform orbit 95.3.o.a

• Label: 95.3.o.a
• Level: $95$
• Weight: $3$
• Character orbit: 95.o
• Analytic conductor: $2.589$
• Analytic rank: $0$
• Dimension: $108$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	95.o (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.58856251142\)
Analytic rank:	\(0\)
Dimension:	\(108\)
Relative dimension:	\(18\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 108 q - 18 q^{4} - 6 q^{5} - 30 q^{6} - 12 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
14.1	−3.29435	+	1.19905i	0.887238	−	5.03178i	6.35087	−	5.32901i	2.36949	−	4.40290i	3.11046	+	17.6403i	−5.32695	+	3.07552i	−7.52071	+	13.0263i	−16.0744	−	5.85059i	−2.52664	+	17.3458i
14.2	−3.22902	+	1.17527i	−0.512590	+	2.90704i	5.98113	−	5.01876i	4.49751	−	2.18459i	−1.76139	−	9.98933i	7.09673	−	4.09730i	−6.54229	+	11.3316i	0.269075	+	0.0979352i	−11.9550	+	12.3399i
14.3	−3.05262	+	1.11106i	0.222471	−	1.26170i	5.01987	−	4.21217i	−4.61553	+	1.92272i	0.722705	+	4.09866i	4.38077	−	2.52924i	−4.14670	+	7.18230i	6.91485	+	2.51680i	11.9532	−	10.9975i
14.4	−2.34252	+	0.852608i	−0.448134	+	2.54150i	1.69629	−	1.42336i	−3.50181	−	3.56894i	−1.11714	−	6.33559i	−6.36608	+	3.67546i	2.22569	−	3.85501i	2.19886	+	0.800319i	11.2460	+	5.37466i
14.5	−1.90531	+	0.693476i	0.594504	−	3.37160i	0.0851163	−	0.0714211i	1.02194	+	4.89445i	1.20541	+	6.83621i	3.58940	−	2.07234i	3.94253	−	6.82866i	−2.55702	−	0.930678i	−5.34130	−	8.61675i
14.6	−1.70632	+	0.621050i	−0.831436	+	4.71531i	−0.538348	+	0.451728i	0.700945	+	4.95062i	−1.50975	−	8.56219i	0.865943	−	0.499952i	4.26971	−	7.39535i	−13.0856	−	4.76277i	−4.27062	−	8.01203i
14.7	−1.23308	+	0.448803i	0.129424	−	0.733999i	−1.74513	+	1.46434i	4.93265	+	0.817881i	0.169831	+	0.963161i	−9.87539	+	5.70156i	4.11910	−	7.13449i	7.93523	+	2.88819i	−6.44940	+	1.20528i
14.8	−0.631497	+	0.229846i	0.127323	−	0.722083i	−2.71822	+	2.28086i	2.04074	−	4.56458i	0.0855640	+	0.485258i	6.70036	−	3.86846i	2.53635	−	4.39309i	7.95204	+	2.89431i	−0.239567	+	3.35157i
14.9	−0.569854	+	0.207410i	0.868566	−	4.92588i	−2.78246	+	2.33476i	−4.78534	−	1.44931i	0.526721	+	2.98718i	−1.58810	+	0.916889i	2.31420	−	4.00830i	−15.0527	−	5.47873i	3.02755	−	0.166629i
14.10	0.569854	−	0.207410i	−0.868566	+	4.92588i	−2.78246	+	2.33476i	−2.25826	−	4.46097i	0.526721	+	2.98718i	1.58810	−	0.916889i	−2.31420	+	4.00830i	−15.0527	−	5.47873i	−2.21213	−	2.07371i
14.11	0.631497	−	0.229846i	−0.127323	+	0.722083i	−2.71822	+	2.28086i	−4.14086	+	2.80236i	0.0855640	+	0.485258i	−6.70036	+	3.86846i	−2.53635	+	4.39309i	7.95204	+	2.89431i	−1.97083	+	2.72144i
14.12	1.23308	−	0.448803i	−0.129424	+	0.733999i	−1.74513	+	1.46434i	1.66200	+	4.71569i	0.169831	+	0.963161i	9.87539	−	5.70156i	−4.11910	+	7.13449i	7.93523	+	2.88819i	4.16579	+	5.06889i
14.13	1.70632	−	0.621050i	0.831436	−	4.71531i	−0.538348	+	0.451728i	4.99713	−	0.169371i	−1.50975	−	8.56219i	−0.865943	+	0.499952i	−4.26971	+	7.39535i	−13.0856	−	4.76277i	8.42152	−	3.39247i
14.14	1.90531	−	0.693476i	−0.594504	+	3.37160i	0.0851163	−	0.0714211i	4.99755	+	0.156505i	1.20541	+	6.83621i	−3.58940	+	2.07234i	−3.94253	+	6.82866i	−2.55702	−	0.930678i	9.63041	−	3.16749i
14.15	2.34252	−	0.852608i	0.448134	−	2.54150i	1.69629	−	1.42336i	−4.12281	−	2.82886i	−1.11714	−	6.33559i	6.36608	−	3.67546i	−2.22569	+	3.85501i	2.19886	+	0.800319i	−12.0697	−	3.11154i
14.16	3.05262	−	1.11106i	−0.222471	+	1.26170i	5.01987	−	4.21217i	1.09203	−	4.87929i	0.722705	+	4.09866i	−4.38077	+	2.52924i	4.14670	−	7.18230i	6.91485	+	2.51680i	−2.08764	−	16.1079i
14.17	3.22902	−	1.17527i	0.512590	−	2.90704i	5.98113	−	5.01876i	−1.37042	+	4.80853i	−1.76139	−	9.98933i	−7.09673	+	4.09730i	6.54229	−	11.3316i	0.269075	+	0.0979352i	1.22619	+	17.1374i
14.18	3.29435	−	1.19905i	−0.887238	+	5.03178i	6.35087	−	5.32901i	−3.92455	+	3.09804i	3.11046	+	17.6403i	5.32695	−	3.07552i	7.52071	−	13.0263i	−16.0744	−	5.85059i	−9.21417	+	14.9118i
29.1	−0.660927	−	3.74831i	−1.17436	+	0.985407i	−9.85420	+	3.58663i	−2.14231	−	4.51780i	4.46977	+	3.75058i	−0.966225	−	0.557850i	12.3445	+	21.3812i	−1.15473	+	6.54882i	−15.5182	+	11.0160i
29.2	−0.635690	−	3.60517i	3.83898	−	3.22129i	−8.83441	+	3.21546i	3.88993	+	3.14141i	−14.0537	−	11.7925i	−8.51411	−	4.91562i	9.88667	+	17.1242i	2.79824	−	15.8696i	8.85255	−	16.0208i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
19.f	odd	18	1	inner
95.o	odd	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	95.3.o.a	✓	108
5.b	even	2	1	inner	95.3.o.a	✓	108
19.f	odd	18	1	inner	95.3.o.a	✓	108
95.o	odd	18	1	inner	95.3.o.a	✓	108

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
95.3.o.a	✓	108	1.a	even	1	1	trivial
95.3.o.a	✓	108	5.b	even	2	1	inner
95.3.o.a	✓	108	19.f	odd	18	1	inner
95.3.o.a	✓	108	95.o	odd	18	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(95, [\chi])\).