Newform orbit 148.3.p.a

• Label: 148.3.p.a
• Level: $148$
• Weight: $3$
• Character orbit: 148.p
• Analytic conductor: $4.033$
• Analytic rank: $0$
• Dimension: $216$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 148 = 2^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	148.p (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.03270791253\)
Analytic rank:	\(0\)
Dimension:	\(216\)
Relative dimension:	\(36\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 216 q - 9 q^{2} - 15 q^{4} - 18 q^{5} - 12 q^{6} - 18 q^{8} - 12 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
7.1	−1.99367	+	0.159041i	0.926846	−	2.54649i	3.94941	−	0.634149i	1.33378	+	7.56425i	−1.44283	+	5.22426i	−9.59980	+	1.69270i	−7.77295	+	1.89240i	1.26883	+	1.06468i	−3.86214	−	14.8685i
7.2	−1.99107	−	0.188785i	0.113834	−	0.312758i	3.92872	+	0.751769i	−0.228083	−	1.29352i	−0.285696	+	0.601232i	2.80762	−	0.495059i	−7.68043	−	2.23851i	6.80954	+	5.71388i	0.209931	+	2.61856i
7.3	−1.92543	+	0.541040i	−1.49861	+	4.11739i	3.41455	−	2.08347i	−0.220937	−	1.25300i	0.657787	−	8.73854i	−9.68910	+	1.70845i	−5.44723	+	5.85898i	−7.81266	−	6.55560i	1.10332	+	2.29302i
7.4	−1.90189	−	0.618730i	−1.28409	+	3.52800i	3.23435	+	2.35351i	−0.486678	−	2.76009i	4.62507	−	5.91535i	8.74829	−	1.54256i	−4.69517	−	6.47730i	−3.90350	−	3.27543i	−0.782144	+	5.55050i
7.5	−1.86130	−	0.731810i	1.62113	−	4.45401i	2.92891	+	2.72424i	−1.46584	−	8.31319i	−6.27690	+	7.10391i	−8.10164	+	1.42854i	−3.45796	−	7.21405i	−10.3157	−	8.65594i	−3.35530	+	16.5461i
7.6	−1.82274	+	0.823181i	1.49861	−	4.11739i	2.64475	−	3.00088i	−0.220937	−	1.25300i	0.657787	+	8.73854i	9.68910	−	1.70845i	−2.35041	+	7.64693i	−7.81266	−	6.55560i	1.43415	+	2.10201i
7.7	−1.62947	+	1.15967i	−0.926846	+	2.54649i	1.31032	−	3.77929i	1.33378	+	7.56425i	−1.44283	−	5.22426i	9.59980	−	1.69270i	2.24761	+	7.67778i	1.26883	+	1.06468i	−10.9454	−	10.7789i
7.8	−1.55862	−	1.25327i	−1.60515	+	4.41012i	0.858619	+	3.90676i	1.65941	+	9.41098i	8.02890	−	4.86203i	−4.53061	+	0.798869i	3.55797	−	7.16525i	−9.97823	−	8.37273i	9.20812	−	16.7479i
7.9	−1.47381	−	1.35200i	−0.199424	+	0.547914i	0.344210	+	3.98516i	−0.663699	−	3.76402i	1.03469	−	0.537898i	−6.05243	+	1.06721i	4.88063	−	6.33873i	6.63396	+	5.56655i	−4.11078	+	6.44476i
7.10	−1.40390	+	1.42445i	−0.113834	+	0.312758i	−0.0581333	−	3.99958i	−0.228083	−	1.29352i	−0.285696	−	0.601232i	−2.80762	+	0.495059i	5.77882	+	5.53220i	6.80954	+	5.71388i	2.16277	+	1.49108i
7.11	−1.38449	−	1.44333i	0.827071	−	2.27236i	−0.166393	+	3.99654i	0.759818	+	4.30914i	−4.42483	+	1.95232i	5.31451	−	0.937092i	5.99869	−	5.29299i	2.41483	+	2.02628i	5.16755	−	7.06262i
7.12	−1.05922	+	1.69648i	1.28409	−	3.52800i	−1.75612	−	3.59389i	−0.486678	−	2.76009i	4.62507	+	5.91535i	−8.74829	+	1.54256i	7.95709	+	0.827487i	−3.90350	−	3.27543i	5.19794	+	2.09789i
7.13	−0.955444	+	1.75702i	−1.62113	+	4.45401i	−2.17426	−	3.35747i	−1.46584	−	8.31319i	−6.27690	−	7.10391i	8.10164	−	1.42854i	7.97653	−	0.612340i	−10.3157	−	8.65594i	16.0070	+	5.36727i
7.14	−0.781379	−	1.84105i	−1.28859	+	3.54038i	−2.77889	+	2.87711i	−1.12327	−	6.37038i	7.52487	−	0.394020i	−0.783489	+	0.138150i	7.46825	+	2.86796i	−3.97939	−	3.33911i	−10.8505	+	7.04567i
7.15	−0.388388	+	1.96193i	1.60515	−	4.41012i	−3.69831	−	1.52398i	1.65941	+	9.41098i	8.02890	+	4.86203i	4.53061	−	0.798869i	4.42631	−	6.66392i	−9.97823	−	8.37273i	−19.1081	−	0.399471i
7.16	−0.387239	−	1.96215i	1.19017	−	3.26996i	−3.70009	+	1.51965i	−1.40994	−	7.99615i	−6.87705	−	1.06904i	11.4377	−	2.01677i	4.41460	+	6.67168i	−2.38176	−	1.99854i	−15.1437	+	5.86293i
7.17	−0.365617	−	1.96630i	1.85429	−	5.09463i	−3.73265	+	1.43782i	0.575818	+	3.26562i	−10.6955	−	1.78341i	−9.57596	+	1.68850i	4.19190	+	6.81381i	−15.6224	−	13.1088i	6.21066	−	2.32620i
7.18	−0.259954	+	1.98303i	0.199424	−	0.547914i	−3.86485	−	1.03100i	−0.663699	−	3.76402i	1.03469	+	0.537898i	6.05243	−	1.06721i	3.04919	−	7.39611i	6.63396	+	5.56655i	7.63672	−	0.337663i
7.19	−0.188975	−	1.99105i	−0.236031	+	0.648489i	−3.92858	+	0.752520i	0.621226	+	3.52315i	1.33578	+	0.347401i	−6.34854	+	1.11942i	2.24071	+	7.67979i	6.52957	+	5.47896i	6.89737	−	1.90268i
7.20	−0.132825	+	1.99558i	−0.827071	+	2.27236i	−3.96472	−	0.530126i	0.759818	+	4.30914i	−4.42483	−	1.95232i	−5.31451	+	0.937092i	1.58452	−	7.84151i	2.41483	+	2.02628i	−8.70018	+	0.943920i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
37.f	even	9	1	inner
148.p	odd	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	148.3.p.a	✓	216
4.b	odd	2	1	inner	148.3.p.a	✓	216
37.f	even	9	1	inner	148.3.p.a	✓	216
148.p	odd	18	1	inner	148.3.p.a	✓	216

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
148.3.p.a	✓	216	1.a	even	1	1	trivial
148.3.p.a	✓	216	4.b	odd	2	1	inner
148.3.p.a	✓	216	37.f	even	9	1	inner
148.3.p.a	✓	216	148.p	odd	18	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(148, [\chi])\).