Newform orbit 152.3.l.a

• Label: 152.3.l.a
• Level: $152$
• Weight: $3$
• Character orbit: 152.l
• Analytic conductor: $4.142$
• Analytic rank: $0$
• Dimension: $76$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	152.l (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.14170001828\)
Analytic rank:	\(0\)
Dimension:	\(76\)
Relative dimension:	\(38\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 76 q - 3 q^{2} + q^{4} + q^{6} - 8 q^{7} - 104 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
69.1	−1.99956	+	0.0421290i	2.33283	+	4.04058i	3.99645	−	0.168478i	−4.70327	+	2.71544i	−4.83485	−	7.98109i	−10.2250			−7.98403	+	0.505249i	−6.38419	+	11.0577i	9.29006	−	5.62781i
69.2	−1.99673	+	0.114373i	−0.342287	−	0.592859i	3.97384	−	0.456743i	5.46562	−	3.15558i	0.751262	+	1.14463i	−4.20556			−7.88243	+	1.36649i	4.26568	−	7.38837i	−10.5524	+	6.92594i
69.3	−1.97209	−	0.332976i	1.88391	+	3.26303i	3.77825	+	1.31332i	5.24005	−	3.02535i	−2.62872	−	7.06228i	7.51233			−7.01374	−	3.84804i	−2.59824	+	4.50029i	−11.3412	+	4.22143i
69.4	−1.90832	+	0.598597i	−0.624312	−	1.08134i	3.28336	−	2.28463i	−3.10853	+	1.79471i	1.83867	+	1.68983i	−1.42425			−4.89813	+	6.32521i	3.72047	−	6.44404i	4.85776	−	5.28564i
69.5	−1.87961	−	0.683417i	−2.58287	−	4.47366i	3.06588	+	2.56912i	−0.563007	+	0.325052i	1.79742	+	10.1739i	−8.57216			−4.00689	−	6.92422i	−8.84243	+	15.3155i	1.28038	−	0.226203i
69.6	−1.87155	+	0.705191i	−2.32624	−	4.02917i	3.00541	−	2.63960i	1.22746	−	0.708677i	7.19503	+	5.90036i	12.3788			−3.76336	+	7.05954i	−6.32283	+	10.9515i	−1.79751	+	2.19192i
69.7	−1.83029	−	0.806260i	−0.436404	−	0.755874i	2.69989	+	2.95137i	−6.94838	+	4.01165i	0.189313	+	1.73532i	5.96715			−2.56199	−	7.57867i	4.11910	−	7.13450i	15.9520	−	1.74026i
69.8	−1.54649	+	1.26822i	2.32624	+	4.02917i	0.783259	−	3.92256i	−1.22746	+	0.708677i	−8.70737	−	3.28090i	12.3788			3.76336	+	7.05954i	−6.32283	+	10.9515i	0.999506	−	2.65265i
69.9	−1.51263	−	1.30842i	1.59539	+	2.76330i	0.576080	+	3.95830i	−0.355506	+	0.205251i	1.20232	−	6.26729i	1.00665			4.30772	−	6.74118i	−0.590563	+	1.02288i	0.806302	+	0.154682i
69.10	−1.47256	+	1.35335i	0.624312	+	1.08134i	0.336865	−	3.98579i	3.10853	−	1.79471i	−2.38277	−	0.747423i	−1.42425			4.89813	+	6.32521i	3.72047	−	6.44404i	−2.14862	+	6.84976i
69.11	−1.31723	−	1.50496i	−1.69599	−	2.93754i	−0.529832	+	3.96475i	7.32986	−	4.23190i	−2.18689	+	6.42181i	10.9564			6.66472	−	4.42510i	−1.25276	+	2.16985i	−16.0239	−	5.45681i
69.12	−1.12228	−	1.65544i	0.366409	+	0.634639i	−1.48096	+	3.71575i	2.68058	−	1.54763i	0.639391	−	1.31881i	−12.2354			7.81324	−	1.71849i	4.23149	−	7.32915i	−5.57039	−	2.70065i
69.13	−1.09741	+	1.67203i	0.342287	+	0.592859i	−1.59137	−	3.66982i	−5.46562	+	3.15558i	−1.36691	−	0.0782968i	−4.20556			7.88243	+	1.36649i	4.26568	−	7.38837i	0.721825	−	12.6016i
69.14	−1.03626	+	1.71060i	−2.33283	−	4.04058i	−1.85232	−	3.54527i	4.70327	−	2.71544i	9.32925	+	0.196559i	−10.2250			7.98403	+	0.505249i	−6.38419	+	11.0577i	−0.228797	+	10.8593i
69.15	−0.697678	+	1.87437i	−1.88391	−	3.26303i	−3.02649	−	2.61541i	−5.24005	+	3.02535i	7.43047	−	1.25460i	7.51233			7.01374	−	3.84804i	−2.59824	+	4.50029i	−2.01474	−	11.9325i
69.16	−0.696901	−	1.87465i	−1.95071	−	3.37873i	−3.02866	+	2.61290i	−3.59039	+	2.07291i	−4.97449	+	6.01154i	−0.558766			7.00895	+	3.85676i	−3.11052	+	5.38758i	6.38814	+	5.28613i
69.17	−0.378411	−	1.96388i	0.591682	+	1.02482i	−3.71361	+	1.48630i	−1.59909	+	0.923234i	1.78873	−	1.54979i	9.49692			4.32418	+	6.73063i	3.79982	−	6.58149i	2.41823	+	2.79105i
69.18	−0.347949	+	1.96950i	2.58287	+	4.47366i	−3.75786	−	1.37057i	0.563007	−	0.325052i	−9.70959	+	3.53036i	−8.57216			4.00689	−	6.92422i	−8.84243	+	15.3155i	0.444293	+	1.22194i
69.19	−0.216901	+	1.98820i	0.436404	+	0.755874i	−3.90591	−	0.862486i	6.94838	−	4.01165i	−1.59749	+	0.703711i	5.96715			2.56199	−	7.57867i	4.11910	−	7.13450i	6.46887	+	14.6849i
69.20	−0.102518	−	1.99737i	2.78591	+	4.82534i	−3.97898	+	0.409535i	7.91482	−	4.56963i	9.35238	−	6.05918i	−0.829009			1.22591	+	7.90551i	−11.0226	+	19.0917i	−9.93865	−	15.3404i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
8.b	even	2	1	inner
19.d	odd	6	1	inner
152.l	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	152.3.l.a	✓	76
4.b	odd	2	1		608.3.p.a		76
8.b	even	2	1	inner	152.3.l.a	✓	76
8.d	odd	2	1		608.3.p.a		76
19.d	odd	6	1	inner	152.3.l.a	✓	76
76.f	even	6	1		608.3.p.a		76
152.l	odd	6	1	inner	152.3.l.a	✓	76
152.o	even	6	1		608.3.p.a		76

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
152.3.l.a	✓	76	1.a	even	1	1	trivial
152.3.l.a	✓	76	8.b	even	2	1	inner
152.3.l.a	✓	76	19.d	odd	6	1	inner
152.3.l.a	✓	76	152.l	odd	6	1	inner
608.3.p.a		76	4.b	odd	2	1
608.3.p.a		76	8.d	odd	2	1
608.3.p.a		76	76.f	even	6	1
608.3.p.a		76	152.o	even	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(152, [\chi])\).