Newform orbit 140.3.x.a

• Label: 140.3.x.a
• Level: $140$
• Weight: $3$
• Character orbit: 140.x
• Analytic conductor: $3.815$
• Analytic rank: $0$
• Dimension: $176$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	140.x (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.81472370104\)
Analytic rank:	\(0\)
Dimension:	\(176\)
Relative dimension:	\(44\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3.1	−1.99873	−	0.0712513i	2.52686	−	0.677069i	3.98985	+	0.284824i	3.84965	+	3.19064i	−5.09875	+	1.17324i	4.27788	+	5.54073i	−7.95433	−	0.853568i	−1.86765	+	1.07829i	−7.46708	−	6.65152i
3.2	−1.99385	−	0.156661i	−4.96696	+	1.33089i	3.95091	+	0.624720i	2.22087	−	4.47970i	10.1119	−	1.87547i	5.61575	+	4.17892i	−7.77968	−	1.86456i	15.1051	−	8.72096i	−5.12989	+	8.58395i
3.3	−1.98756	−	0.222695i	−1.91216	+	0.512361i	3.90081	+	0.885242i	−4.98223	+	0.421211i	3.91463	−	0.592521i	3.86304	−	5.83754i	−7.55597	−	2.62817i	−4.40040	+	2.54057i	9.99629	+	0.272335i
3.4	−1.87936	+	0.684101i	0.735242	−	0.197008i	3.06401	−	2.57135i	3.91530	−	3.10973i	−1.24701	+	0.873228i	−0.164843	−	6.99806i	−3.99933	+	6.92859i	−7.29246	+	4.21030i	−5.23091	+	8.52277i
3.5	−1.84496	+	0.772090i	−4.02162	+	1.07759i	2.80775	−	2.84895i	−1.52554	+	4.76159i	6.58773	−	5.09316i	−5.22595	+	4.65720i	−2.98055	+	7.42404i	7.21801	−	4.16732i	−0.861808	−	9.96280i
3.6	−1.83263	−	0.800922i	1.91216	−	0.512361i	2.71705	+	2.93558i	−4.98223	+	0.421211i	−3.91463	−	0.592521i	−3.86304	+	5.83754i	−2.62817	−	7.55597i	−4.40040	+	2.54057i	9.46792	+	3.21845i
3.7	−1.80506	−	0.861255i	4.96696	−	1.33089i	2.51648	+	3.10923i	2.22087	−	4.47970i	−10.1119	−	1.87547i	−5.61575	−	4.17892i	−1.86456	−	7.77968i	15.1051	−	8.72096i	−7.86697	+	6.17339i
3.8	−1.77683	+	0.918085i	0.157982	−	0.0423311i	2.31424	−	3.26256i	−2.13622	−	4.52068i	−0.241843	+	0.220256i	−5.40398	+	4.44939i	−1.11671	+	7.92168i	−7.77106	+	4.48662i	7.94606	+	6.07125i
3.9	−1.76658	−	0.937660i	−2.52686	+	0.677069i	2.24159	+	3.31290i	3.84965	+	3.19064i	5.09875	+	1.17324i	−4.27788	−	5.54073i	−0.853568	−	7.95433i	−1.86765	+	1.07829i	−3.80897	−	9.24617i
3.10	−1.70104	+	1.05188i	5.37782	−	1.44098i	1.78709	−	3.57859i	−4.65358	−	1.82871i	−7.63215	+	8.10800i	6.95853	+	0.760820i	0.724341	+	7.96714i	19.0503	−	10.9987i	9.83952	−	1.78431i
3.11	−1.36531	+	1.46148i	−0.596002	+	0.159698i	−0.271875	−	3.99075i	0.111390	+	4.99876i	0.580329	−	1.08909i	6.75948	−	1.81920i	6.20361	+	5.05126i	−7.46451	+	4.30964i	−7.45769	−	6.66204i
3.12	−1.28553	−	1.53213i	−0.735242	+	0.197008i	−0.694847	+	3.93919i	3.91530	−	3.10973i	1.24701	+	0.873228i	0.164843	+	6.99806i	6.92859	−	3.99933i	−7.29246	+	4.21030i	−9.79773	−	2.00112i
3.13	−1.21174	−	1.59113i	4.02162	−	1.07759i	−1.06339	+	3.85606i	−1.52554	+	4.76159i	−6.58773	−	5.09316i	5.22595	−	4.65720i	7.42404	−	2.98055i	7.21801	−	4.16732i	9.42486	−	3.34246i
3.14	−1.12215	+	1.65553i	4.25894	−	1.14118i	−1.48154	−	3.71551i	4.19412	+	2.72202i	−2.88993	+	8.33136i	−6.40643	+	2.82094i	7.81365	+	1.71664i	9.04202	−	5.22041i	−9.21282	+	3.88895i
3.15	−1.07974	−	1.68350i	−0.157982	+	0.0423311i	−1.66834	+	3.63547i	−2.13622	−	4.52068i	0.241843	+	0.220256i	5.40398	−	4.44939i	7.92168	−	1.11671i	−7.77106	+	4.48662i	−5.30401	+	8.47747i
3.16	−0.988980	+	1.73837i	−4.55859	+	1.22147i	−2.04384	−	3.43842i	4.78668	−	1.44488i	2.38499	−	9.13251i	−4.82257	−	5.07374i	7.99855	−	0.152412i	11.4945	−	6.63636i	−2.22220	+	9.74997i
3.17	−0.947205	−	1.76148i	−5.37782	+	1.44098i	−2.20561	+	3.33696i	−4.65358	−	1.82871i	7.63215	+	8.10800i	−6.95853	−	0.760820i	7.96714	+	0.724341i	19.0503	−	10.9987i	1.18667	+	9.92934i
3.18	−0.740287	+	1.85795i	−3.25950	+	0.873381i	−2.90395	−	2.75083i	−3.53116	−	3.53990i	0.790269	−	6.70255i	5.75046	+	3.99152i	7.26066	−	3.35899i	2.06734	−	1.19358i	9.19102	−	3.94019i
3.19	−0.666564	+	1.88565i	1.45477	−	0.389805i	−3.11138	−	2.51382i	−4.74483	+	1.57690i	−0.234662	+	3.00303i	−4.86954	−	5.02867i	6.81413	−	4.19137i	−5.82981	+	3.36584i	0.189237	−	9.99821i
3.20	−0.451648	−	1.94834i	0.596002	−	0.159698i	−3.59203	+	1.75992i	0.111390	+	4.99876i	−0.580329	−	1.08909i	−6.75948	+	1.81920i	5.05126	+	6.20361i	−7.46451	+	4.30964i	9.68895	−	2.47471i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
5.c	odd	4	1	inner
7.d	odd	6	1	inner
20.e	even	4	1	inner
28.f	even	6	1	inner
35.k	even	12	1	inner
140.x	odd	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	140.3.x.a	✓	176
4.b	odd	2	1	inner	140.3.x.a	✓	176
5.c	odd	4	1	inner	140.3.x.a	✓	176
7.d	odd	6	1	inner	140.3.x.a	✓	176
20.e	even	4	1	inner	140.3.x.a	✓	176
28.f	even	6	1	inner	140.3.x.a	✓	176
35.k	even	12	1	inner	140.3.x.a	✓	176
140.x	odd	12	1	inner	140.3.x.a	✓	176

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
140.3.x.a	✓	176	1.a	even	1	1	trivial
140.3.x.a	✓	176	4.b	odd	2	1	inner
140.3.x.a	✓	176	5.c	odd	4	1	inner
140.3.x.a	✓	176	7.d	odd	6	1	inner
140.3.x.a	✓	176	20.e	even	4	1	inner
140.3.x.a	✓	176	28.f	even	6	1	inner
140.3.x.a	✓	176	35.k	even	12	1	inner
140.3.x.a	✓	176	140.x	odd	12	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(140, [\chi])\).