Newform orbit 333.3.v.a

• Label: 333.3.v.a
• Level: $333$
• Weight: $3$
• Character orbit: 333.v
• Analytic conductor: $9.074$
• Analytic rank: $0$
• Dimension: $148$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	333.v (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(9.07359280320\)
Analytic rank:	\(0\)
Dimension:	\(148\)
Relative dimension:	\(74\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 148 q - 6 q^{2} - 3 q^{3} + 286 q^{4} - 6 q^{5} - 12 q^{6} - 24 q^{8} - 11 q^{9}+O(q^{10}) \)

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	−3.93082			−2.79001	+	1.10265i	11.4514			7.33868			10.9670	−	4.33432i	−5.52154	−	9.56359i	−29.2901			6.56833	−	6.15280i	−28.8471
11.2	−3.80560			−0.375073	−	2.97646i	10.4826			1.17351			1.42738	+	11.3272i	3.84221	+	6.65490i	−24.6702			−8.71864	+	2.23278i	−4.46591
11.3	−3.78569			2.93941	+	0.599909i	10.3315			−3.36267			−11.1277	−	2.27107i	−3.51636	−	6.09051i	−23.9690			8.28022	+	3.52675i	12.7300
11.4	−3.75265			−0.194704	+	2.99368i	10.0823			−6.96101			0.730654	−	11.2342i	2.06158	+	3.57076i	−22.8249			−8.92418	−	1.16576i	26.1222
11.5	−3.66296			1.35215	+	2.67800i	9.41726			7.27635			−4.95287	−	9.80940i	2.85763	+	4.94956i	−19.8432			−5.34338	+	7.24212i	−26.6530
11.6	−3.56370			−2.71779	−	1.27028i	8.69999			−6.46498			9.68540	+	4.52691i	−1.22734	−	2.12582i	−16.7494			5.77276	+	6.90472i	23.0393
11.7	−3.33721			2.81149	−	1.04667i	7.13698			4.64468			−9.38254	+	3.49295i	−0.0405292	−	0.0701987i	−10.4688			6.80898	−	5.88539i	−15.5003
11.8	−3.29477			2.40595	−	1.79204i	6.85554			−6.91674			−7.92707	+	5.90436i	4.03531	+	6.98937i	−9.40835			2.57721	−	8.62311i	22.7891
11.9	−3.13661			−1.23710	−	2.73306i	5.83833			2.51677			3.88029	+	8.57253i	−3.24448	−	5.61960i	−5.76613			−5.93918	+	6.76211i	−7.89412
11.10	−3.12548			−2.52762	+	1.61590i	5.76862			−1.28429			7.90004	−	5.05045i	2.63842	+	4.56988i	−5.52780			3.77776	−	8.16875i	4.01401
11.11	−3.07922			1.70473	−	2.46858i	5.48159			7.56027			−5.24924	+	7.60130i	−2.73228	−	4.73246i	−4.56214			−3.18779	−	8.41653i	−23.2797
11.12	−3.01120			2.26841	+	1.96324i	5.06732			0.455629			−6.83063	−	5.91171i	−3.12094	−	5.40563i	−3.21392			1.29136	+	8.90687i	−1.37199
11.13	−2.99359			−2.91174	−	0.722356i	4.96155			6.77128			8.71653	+	2.16243i	5.97492	+	10.3489i	−2.87849			7.95641	+	4.20662i	−20.2704
11.14	−2.85103			0.772823	−	2.89875i	4.12840			−7.95504			−2.20335	+	8.26443i	−6.43825	−	11.1514i	−0.366063			−7.80549	−	4.48044i	22.6801
11.15	−2.83394			−1.65307	+	2.50347i	4.03122			−1.49101			4.68469	−	7.09469i	−4.49627	−	7.78776i	−0.0884673			−3.53475	−	8.27681i	4.22544
11.16	−2.69827			0.332450	+	2.98152i	3.28067			4.21646			−0.897041	−	8.04496i	−0.914826	−	1.58452i	1.94095			−8.77895	+	1.98242i	−11.3772
11.17	−2.49962			2.50696	+	1.64778i	2.24810			−2.51738			−6.26644	−	4.11882i	6.21285	+	10.7610i	4.37908			3.56966	+	8.26181i	6.29250
11.18	−2.15804			1.68282	−	2.48357i	0.657137			0.638275			−3.63160	+	5.35964i	2.87478	+	4.97926i	7.21403			−3.33622	−	8.35881i	−1.37742
11.19	−2.06003			−2.98553	+	0.294290i	0.243729			−5.70569			6.15029	−	0.606247i	1.14794	+	1.98828i	7.73804			8.82679	−	1.75722i	11.7539
11.20	−1.94015			−2.77446	−	1.14122i	−0.235827			6.62941			5.38286	+	2.21413i	−4.16264	−	7.20991i	8.21813			6.39525	+	6.33252i	−12.8620

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
333.v	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	333.3.v.a	yes	148
9.d	odd	6	1		333.3.o.a	✓	148
37.e	even	6	1		333.3.o.a	✓	148
333.v	odd	6	1	inner	333.3.v.a	yes	148

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
333.3.o.a	✓	148	9.d	odd	6	1
333.3.o.a	✓	148	37.e	even	6	1
333.3.v.a	yes	148	1.a	even	1	1	trivial
333.3.v.a	yes	148	333.v	odd	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(333, [\chi])\).