Newform orbit 148.3.j.b

• Label: 148.3.j.b
• Level: $148$
• Weight: $3$
• Character orbit: 148.j
• Analytic conductor: $4.033$
• Analytic rank: $0$
• Dimension: $68$
• CM: no
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(4.03270791253\)
Analytic rank:	\(0\)
Dimension:	\(68\)
Relative dimension:	\(34\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 68 q - 6 q^{2} - 6 q^{4} + 18 q^{5} + 112 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
11.1	−1.99919	+	0.0569066i	3.70854	+	2.14112i	3.99352	−	0.227534i	6.75428	+	3.89958i	−7.53591	−	4.06947i	4.85786	+	2.80469i	−7.97086	+	0.682142i	4.66882	+	8.08664i	−13.7250	−	7.41165i
11.2	−1.99145	−	0.184741i	−1.20421	−	0.695251i	3.93174	+	0.735805i	−3.52137	−	2.03306i	2.26968	+	1.60702i	4.13072	+	2.38488i	−7.69393	−	2.19167i	−3.53325	−	6.11977i	6.63704	+	4.69929i
11.3	−1.98053	+	0.278418i	−1.71919	−	0.992575i	3.84497	−	1.10283i	4.77877	+	2.75902i	3.68125	+	1.48717i	−3.08241	−	1.77963i	−7.30801	+	3.25469i	−2.52959	−	4.38138i	−10.2326	−	4.13382i
11.4	−1.93920	−	0.489393i	2.96814	+	1.71366i	3.52099	+	1.89806i	−4.70918	−	2.71885i	−4.91717	−	4.77571i	−10.3175	−	5.95682i	−5.89900	−	5.40387i	1.37324	+	2.37852i	7.80145	+	7.57702i
11.5	−1.85753	−	0.741342i	−5.09320	−	2.94056i	2.90083	+	2.75413i	2.82921	+	1.63344i	7.28080	+	9.23797i	5.88422	+	3.39726i	−3.34662	−	7.26637i	12.7938	+	22.1594i	−4.04440	−	5.13158i
11.6	−1.74866	+	0.970668i	4.42260	+	2.55339i	2.11561	−	3.39473i	−6.40860	−	3.70001i	−10.2121	−	0.172125i	7.11328	+	4.10686i	−0.404310	+	7.98978i	8.53959	+	14.7910i	14.7979	+	0.249419i
11.7	−1.71495	+	1.02905i	−4.42260	−	2.55339i	1.88212	−	3.52953i	−6.40860	−	3.70001i	10.2121	−	0.172125i	−7.11328	−	4.10686i	0.404310	+	7.98978i	8.53959	+	14.7910i	14.7979	−	0.249419i
11.8	−1.56793	−	1.24161i	2.91587	+	1.68348i	0.916820	+	3.89351i	1.81627	+	1.04863i	−2.48167	−	6.25995i	1.39912	+	0.807782i	3.39670	−	7.24309i	1.16820	+	2.02339i	−1.54581	−	3.89927i
11.9	−1.46162	−	1.36516i	−1.40726	−	0.812485i	0.272661	+	3.99070i	4.47400	+	2.58306i	0.947711	+	3.10869i	−8.12634	−	4.69175i	5.04942	−	6.20510i	−3.17974	−	5.50747i	−3.01298	−	9.88319i
11.10	−1.27508	−	1.54084i	0.166299	+	0.0960130i	−0.748360	+	3.92937i	−3.36614	−	1.94344i	−0.0641040	−	0.378664i	10.9389	+	6.31559i	7.00874	−	3.85715i	−4.48156	−	7.76229i	1.29756	+	7.66471i
11.11	−1.23138	+	1.57598i	1.71919	+	0.992575i	−0.967406	−	3.88125i	4.77877	+	2.75902i	−3.68125	+	1.48717i	3.08241	+	1.77963i	7.30801	+	3.25469i	−2.52959	−	4.38138i	−10.2326	+	4.13382i
11.12	−1.04888	+	1.70290i	−3.70854	−	2.14112i	−1.79971	−	3.57226i	6.75428	+	3.89958i	7.53591	−	4.06947i	−4.85786	−	2.80469i	7.97086	+	0.682142i	4.66882	+	8.08664i	−13.7250	+	7.41165i
11.13	−0.835734	+	1.81702i	1.20421	+	0.695251i	−2.60310	−	3.03709i	−3.52137	−	2.03306i	−2.26968	+	1.60702i	−4.13072	−	2.38488i	7.69393	−	2.19167i	−3.53325	−	6.11977i	6.63704	−	4.69929i
11.14	−0.610841	−	1.90444i	−3.41470	−	1.97148i	−3.25375	+	2.32661i	−2.50237	−	1.44474i	−1.66871	+	7.70734i	−2.35741	−	1.36105i	6.41841	+	4.77536i	3.27346	+	5.66981i	−1.22287	+	5.64811i
11.15	−0.545773	+	1.92409i	−2.96814	−	1.71366i	−3.40426	−	2.10024i	−4.70918	−	2.71885i	4.91717	−	4.77571i	10.3175	+	5.95682i	5.89900	−	5.40387i	1.37324	+	2.37852i	7.80145	−	7.57702i
11.16	−0.403426	−	1.95889i	2.42875	+	1.40224i	−3.67450	+	1.58053i	−7.79671	−	4.50143i	1.76701	−	5.32335i	−2.81633	−	1.62601i	4.57847	+	6.56030i	−0.567452	−	0.982855i	−5.67241	+	17.0889i
11.17	−0.286744	+	1.97934i	5.09320	+	2.94056i	−3.83556	−	1.13512i	2.82921	+	1.63344i	−7.28080	+	9.23797i	−5.88422	−	3.39726i	3.34662	−	7.26637i	12.7938	+	22.1594i	−4.04440	+	5.13158i
11.18	−0.264007	−	1.98250i	4.15376	+	2.39818i	−3.86060	+	1.04679i	3.62237	+	2.09138i	3.65776	−	8.86797i	−2.23442	−	1.29004i	3.09448	+	7.37727i	7.00251	+	12.1287i	3.18982	−	7.73349i
11.19	−0.0802398	−	1.99839i	−1.48033	−	0.854667i	−3.98712	+	0.320701i	8.01108	+	4.62520i	−1.58918	+	3.02685i	9.59076	+	5.53723i	0.960812	+	7.94209i	−3.03909	−	5.26385i	8.60014	−	16.3804i
11.20	0.291298	+	1.97867i	−2.91587	−	1.68348i	−3.83029	+	1.15277i	1.81627	+	1.04863i	2.48167	−	6.25995i	−1.39912	−	0.807782i	−3.39670	−	7.24309i	1.16820	+	2.02339i	−1.54581	+	3.89927i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
37.e	even	6	1	inner
148.j	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.j.b	✓	68
4.b	odd	2	1	inner	148.3.j.b	✓	68
37.e	even	6	1	inner	148.3.j.b	✓	68
148.j	odd	6	1	inner	148.3.j.b	✓	68

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
148.3.j.b	✓	68	1.a	even	1	1	trivial
148.3.j.b	✓	68	4.b	odd	2	1	inner
148.3.j.b	✓	68	37.e	even	6	1	inner
148.3.j.b	✓	68	148.j	odd	6	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T3^68 - 209*T3^66 + 23974*T3^64 - 1898445*T3^62 + 114644458*T3^60 - 5551574041*T3^58 + 222470496685*T3^56 - 7528491242936*T3^54 + 218208178241012*T3^52 - 5470313719456624*T3^50 + 119445192766544384*T3^48 - 2282427892175928960*T3^46 + 38287193542157108672*T3^44 - 564765049766968790016*T3^42 + 7329637578015023869184*T3^40 - 83648471217632256964608*T3^38 + 838213862224570998335488*T3^36 - 7356896023657785609506816*T3^34 + 56366939310155980884480000*T3^32 - 375349339390203421258907648*T3^30 + 2160959578521155398871662592*T3^28 - 10686928162814672839772209152*T3^26 + 45069384001782951552843841536*T3^24 - 160632389390848871234383904768*T3^22 + 478998291903770455407835217920*T3^20 - 1178414713739070648115233030144*T3^18 + 2351206249331090818734756986880*T3^16 - 3697013564348170189738673700864*T3^14 + 4406317840290134160864285032448*T3^12 - 3652938122851666545822746542080*T3^10 + 1831521059787775395415405363200*T3^8 - 221966460421789765562271793152*T3^6 + 19901567789504009450884694016*T3^4 - 648767028463989720531075072*T3^2 + 16169151948408323032743936