Newform orbit 141.3.f.a

• Label: 141.3.f.a
• Level: $141$
• Weight: $3$
• Character orbit: 141.f
• Analytic conductor: $3.842$
• Analytic rank: $0$
• Dimension: $352$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 141 = 3 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	141.f (of order \(46\), degree \(22\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.84197172748\)
Analytic rank:	\(0\)
Dimension:	\(352\)
Relative dimension:	\(16\) over \(\Q(\zeta_{46})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{46}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 352 q - 28 q^{4} + 12 q^{6} - 12 q^{7} + 12 q^{8} - 48 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
10.1	−0.752430	−	3.62089i	−1.18222	−	1.26585i	−8.87588	+	3.85534i	2.02259	+	7.21870i	−3.69395	+	5.23314i	−0.0248678	−	0.0202315i	12.1074	+	17.1523i	−0.204727	+	2.99301i	24.6163	−	12.7551i
10.2	−0.661839	−	3.18495i	1.18222	+	1.26585i	−6.03701	+	2.62224i	0.110015	+	0.392648i	3.24921	−	4.60308i	−9.33592	−	7.59534i	4.84350	+	6.86167i	−0.204727	+	2.99301i	1.17775	−	0.610261i
10.3	−0.636257	−	3.06183i	1.18222	+	1.26585i	−5.30117	+	2.30262i	1.41509	+	5.05054i	3.12362	−	4.42515i	7.31140	+	5.94827i	3.20947	+	4.54678i	−0.204727	+	2.99301i	14.5635	−	7.54622i
10.4	−0.542489	−	2.61060i	−1.18222	−	1.26585i	−2.85209	+	1.23884i	−1.35747	−	4.84488i	−2.66328	+	3.77300i	−0.207666	−	0.168949i	−1.36923	−	1.93975i	−0.204727	+	2.99301i	−11.9116	+	6.17210i
10.5	−0.366735	−	1.76483i	1.18222	+	1.26585i	0.688722	−	0.299154i	−2.35471	−	8.40408i	1.80044	−	2.55064i	8.13446	+	6.61788i	−4.93847	−	6.99622i	−0.204727	+	2.99301i	−13.9682	+	7.23774i
10.6	−0.204460	−	0.983917i	1.18222	+	1.26585i	2.74256	−	1.19126i	−1.13694	−	4.05778i	1.00377	−	1.42202i	−8.26696	−	6.72567i	−4.05095	−	5.73889i	−0.204727	+	2.99301i	−3.76006	+	1.94831i
10.7	−0.188447	−	0.906857i	−1.18222	−	1.26585i	2.88197	−	1.25181i	1.28347	+	4.58076i	−0.925156	+	1.31065i	9.65719	+	7.85671i	−3.81487	−	5.40444i	−0.204727	+	2.99301i	3.91223	−	2.02716i
10.8	−0.0867278	−	0.417357i	1.18222	+	1.26585i	3.50218	−	1.52121i	2.19906	+	7.84854i	0.425778	−	0.603190i	−1.07604	−	0.875424i	−1.92192	−	2.72274i	−0.204727	+	2.99301i	3.08492	−	1.59848i
10.9	0.0165264	+	0.0795296i	−1.18222	−	1.26585i	3.66279	−	1.59098i	−0.828554	−	2.95715i	0.0811343	−	0.114941i	−5.94681	−	4.83809i	0.374434	+	0.530452i	−0.204727	+	2.99301i	0.221488	−	0.114766i
10.10	0.169259	+	0.814519i	1.18222	+	1.26585i	3.03405	−	1.31787i	−0.0397673	−	0.141931i	−0.830954	+	1.17719i	1.92087	+	1.56275i	3.50598	+	4.96685i	−0.204727	+	2.99301i	0.108875	−	0.0564144i
10.11	0.328506	+	1.58086i	−1.18222	−	1.26585i	1.27766	−	0.554964i	1.43507	+	5.12184i	1.61275	−	2.28475i	−2.76083	−	2.24610i	5.02153	+	7.11389i	−0.204727	+	2.99301i	−7.62546	+	3.95120i
10.12	0.443469	+	2.13409i	1.18222	+	1.26585i	−0.688831	+	0.299202i	−0.785592	−	2.80381i	−2.17715	+	3.08432i	5.83508	+	4.74719i	4.08392	+	5.78559i	−0.204727	+	2.99301i	5.63521	−	2.91993i
10.13	0.514396	+	2.47541i	−1.18222	−	1.26585i	−2.19421	+	0.953079i	−2.46376	−	8.79327i	2.52536	−	3.57762i	4.16546	+	3.38886i	2.34411	+	3.32085i	−0.204727	+	2.99301i	20.4996	−	10.6220i
10.14	0.547543	+	2.63492i	−1.18222	−	1.26585i	−2.97416	+	1.29186i	0.952931	+	3.40105i	2.68809	−	3.80815i	5.26350	+	4.28218i	1.17544	+	1.66522i	−0.204727	+	2.99301i	−8.43974	+	4.37312i
10.15	0.664635	+	3.19840i	1.18222	+	1.26585i	−6.11917	+	2.65793i	1.13118	+	4.03722i	−3.26293	+	4.62252i	−2.96428	−	2.41162i	−5.03271	−	7.12972i	−0.204727	+	2.99301i	−12.1608	+	6.30123i
10.16	0.755052	+	3.63351i	−1.18222	−	1.26585i	−8.96344	+	3.89337i	−0.505939	−	1.80572i	3.70682	−	5.25137i	−8.58737	−	6.98634i	−12.3539	−	17.5015i	−0.204727	+	2.99301i	6.17909	−	3.20174i
13.1	−2.15029	−	3.04626i	1.34357	−	1.09308i	−3.31647	+	9.33165i	−4.66192	−	4.35393i	−6.21887	−	1.74244i	−3.26583	+	6.30276i	21.1962	−	5.93890i	0.610368	−	2.93725i	−3.23875	+	23.5637i
13.2	−2.11067	−	2.99014i	−1.34357	+	1.09308i	−3.14648	+	8.85335i	1.16323	+	1.08638i	6.10429	+	1.71034i	−0.365108	+	0.704627i	19.0167	−	5.32823i	0.610368	−	2.93725i	0.793233	−	5.77120i
13.3	−1.85184	−	2.62346i	1.34357	−	1.09308i	−2.11372	+	5.94745i	4.17264	+	3.89698i	−5.35573	−	1.50061i	4.52956	−	8.74166i	7.14866	−	2.00296i	0.610368	−	2.93725i	2.49650	−	18.1634i
13.4	−1.53548	−	2.17528i	−1.34357	+	1.09308i	−1.03463	+	2.91118i	−3.19919	−	2.98783i	4.44078	+	1.24425i	4.09689	−	7.90664i	−2.33425	+	0.654025i	0.610368	−	2.93725i	−1.58709	+	11.5469i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
47.d	odd	46	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	141.3.f.a	✓	352
3.b	odd	2	1		423.3.j.b		352
47.d	odd	46	1	inner	141.3.f.a	✓	352
141.g	even	46	1		423.3.j.b		352

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
141.3.f.a	✓	352	1.a	even	1	1	trivial
141.3.f.a	✓	352	47.d	odd	46	1	inner
423.3.j.b		352	3.b	odd	2	1
423.3.j.b		352	141.g	even	46	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(141, [\chi])\).