Newform orbit 148.3.i.a

• Label: 148.3.i.a
• Level: $148$
• Weight: $3$
• Character orbit: 148.i
• Analytic conductor: $4.033$
• Analytic rank: $0$
• Dimension: $72$
• CM: no
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(4.03270791253\)
Analytic rank:	\(0\)
Dimension:	\(72\)
Relative dimension:	\(36\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 72 q + 2 q^{4} - 12 q^{6} - 24 q^{8} + 94 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
47.1	−1.99998	+	0.00997845i	0.488136	−	0.281826i	3.99980	−	0.0399133i	−1.34136	−	2.32331i	−0.973449	+	0.568515i	6.29645	−	3.63525i	−7.99910	+	0.119737i	−4.34115	+	7.51909i	2.70588	+	4.63318i
47.2	−1.97408	−	0.320976i	−3.75921	+	2.17038i	3.79395	+	1.26726i	2.95233	+	5.11358i	8.11760	−	3.07788i	5.68964	−	3.28492i	−7.08278	−	3.71944i	4.92110	−	8.52359i	−4.18678	−	11.0422i
47.3	−1.89226	−	0.647579i	4.73410	−	2.73323i	3.16128	+	2.45077i	−1.53746	−	2.66295i	−10.7281	+	2.10628i	3.38285	−	1.95309i	−4.39489	−	6.68468i	10.4411	−	18.0846i	1.18479	+	6.03462i
47.4	−1.88219	+	0.676276i	2.95477	−	1.70594i	3.08530	−	2.54577i	4.64701	+	8.04885i	−4.40776	+	5.20915i	−0.111563	+	0.0644109i	−4.08549	+	6.87814i	1.32045	−	2.28708i	−14.1898	−	12.0068i
47.5	−1.85208	−	0.754844i	0.653202	−	0.377126i	2.86042	+	2.79607i	1.04917	+	1.81722i	−1.49445	+	0.205403i	−9.30077	+	5.36980i	−3.18714	−	7.33772i	−4.21555	+	7.30155i	−0.571437	−	4.15761i
47.6	−1.83160	−	0.803279i	−3.76396	+	2.17312i	2.70949	+	2.94256i	−4.28569	−	7.42303i	8.63968	−	0.956774i	−3.75306	+	2.16683i	−2.59898	−	7.56606i	4.94494	−	8.56489i	1.88689	+	17.0386i
47.7	−1.79525	+	0.881522i	0.163693	−	0.0945082i	2.44584	−	3.16510i	−3.73381	−	6.46715i	−0.210559	+	0.313965i	−2.12520	+	1.22699i	−1.60078	+	7.83821i	−4.48214	+	7.76329i	12.4041	+	8.31871i
47.8	−1.77881	+	0.914241i	−3.35741	+	1.93840i	2.32833	−	3.25252i	1.39387	+	2.41425i	4.20003	−	6.51754i	−9.52931	+	5.50175i	−1.16806	+	7.91427i	3.01482	−	5.22182i	−4.68664	−	3.02017i
47.9	−1.40179	−	1.42653i	1.28121	−	0.739707i	−0.0699618	+	3.99939i	1.88666	+	3.26779i	−2.85120	−	0.790767i	1.32792	−	0.766673i	5.80331	−	5.50651i	−3.40567	+	5.89879i	2.01689	−	7.27213i
47.10	−1.37881	+	1.44875i	−1.39128	+	0.803255i	−0.197780	−	3.99511i	1.20379	+	2.08503i	0.754586	−	3.12316i	8.97902	−	5.18404i	6.06063	+	5.22195i	−3.20956	+	5.55912i	−4.68050	−	1.13086i
47.11	−1.28186	+	1.53520i	4.00651	−	2.31316i	−0.713685	−	3.93582i	−1.79045	−	3.10115i	−1.58461	+	9.11594i	−0.911331	+	0.526157i	6.95711	+	3.94951i	6.20141	−	10.7412i	7.05598	+	1.22653i
47.12	−1.11438	−	1.66077i	−2.75539	+	1.59082i	−1.51630	+	3.70146i	0.0800161	+	0.138592i	5.71254	+	2.80327i	3.49702	−	2.01900i	7.83701	−	1.60662i	0.561432	−	0.972429i	0.141000	−	0.287333i
47.13	−0.783871	−	1.83999i	2.95775	−	1.70766i	−2.77109	+	2.88462i	−4.10693	−	7.11342i	−5.46057	−	4.10364i	−11.4785	+	6.62713i	7.47984	+	2.83760i	1.33220	−	2.30744i	−9.86928	+	13.1327i
47.14	−0.688595	+	1.87772i	−4.00651	+	2.31316i	−3.05168	−	2.58598i	−1.79045	−	3.10115i	−1.58461	−	9.11594i	0.911331	−	0.526157i	6.95711	−	3.94951i	6.20141	−	10.7412i	7.05598	−	1.22653i
47.15	−0.583250	−	1.91307i	3.77929	−	2.18197i	−3.31964	+	2.23159i	2.33723	+	4.04821i	−6.37853	−	5.95739i	5.65225	−	3.26333i	6.20536	+	5.04911i	5.02202	−	8.69840i	6.38129	−	6.83240i
47.16	−0.565255	+	1.91846i	1.39128	−	0.803255i	−3.36097	−	2.16884i	1.20379	+	2.08503i	0.754586	+	3.12316i	−8.97902	+	5.18404i	6.06063	−	5.22195i	−3.20956	+	5.55912i	−4.68050	+	1.13086i
47.17	−0.204797	−	1.98949i	−1.99441	+	1.15147i	−3.91612	+	0.814883i	−2.02244	−	3.50297i	2.69929	+	3.73203i	1.13404	−	0.654736i	2.42321	+	7.62418i	−1.84822	+	3.20121i	−6.55492	+	4.74101i
47.18	0.0976490	+	1.99761i	3.35741	−	1.93840i	−3.98093	+	0.390130i	1.39387	+	2.41425i	4.20003	+	6.51754i	9.52931	−	5.50175i	−1.16806	−	7.91427i	3.01482	−	5.22182i	−4.68664	+	3.02017i
47.19	0.134204	+	1.99549i	−0.163693	+	0.0945082i	−3.96398	+	0.535605i	−3.73381	−	6.46715i	−0.210559	−	0.313965i	2.12520	−	1.22699i	−1.60078	−	7.83821i	−4.48214	+	7.76329i	12.4041	−	8.31871i
47.20	0.219707	−	1.98790i	−0.694628	+	0.401044i	−3.90346	−	0.873511i	3.68918	+	6.38985i	0.644618	+	1.46896i	−6.35357	+	3.66824i	−2.59407	+	7.56775i	−4.17833	+	7.23708i	13.5129	−	5.92981i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
37.c	even	3	1	inner
148.i	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	148.3.i.a	✓	72
4.b	odd	2	1	inner	148.3.i.a	✓	72
37.c	even	3	1	inner	148.3.i.a	✓	72
148.i	odd	6	1	inner	148.3.i.a	✓	72

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
148.3.i.a	✓	72	1.a	even	1	1	trivial
148.3.i.a	✓	72	4.b	odd	2	1	inner
148.3.i.a	✓	72	37.c	even	3	1	inner
148.3.i.a	✓	72	148.i	odd	6	1	inner

Hecke kernels

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