Newform orbit 144.3.v.a

• Label: 144.3.v.a
• Level: $144$
• Weight: $3$
• Character orbit: 144.v
• Analytic conductor: $3.924$
• Analytic rank: $0$
• Dimension: $184$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.v (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.92371580679\)
Analytic rank:	\(0\)
Dimension:	\(184\)
Relative dimension:	\(46\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 184 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
43.1	−1.99771	+	0.0956780i	−2.20012	+	2.03947i	3.98169	−	0.382274i	0.981821	−	3.66421i	4.20008	−	4.28478i	−1.53303	+	2.65528i	−7.91769	+	1.14463i	0.681097	−	8.97419i	−1.61081	+	7.41396i
43.2	−1.96237	+	0.386118i	1.43023	−	2.63713i	3.70183	−	1.51541i	−1.66775	+	6.22412i	−1.78840	+	5.72727i	−3.37227	+	5.84094i	−6.67924	+	4.40315i	−4.90890	−	7.54339i	0.869504	−	12.8580i
43.3	−1.95734	−	0.410895i	−2.99626	−	0.149794i	3.66233	+	1.60852i	−1.99641	+	7.45071i	5.80313	+	1.52435i	3.29099	−	5.70016i	−6.50748	−	4.65325i	8.95512	+	0.897641i	6.96911	−	13.7632i
43.4	−1.94172	+	0.479310i	−1.68621	−	2.48127i	3.54052	−	1.86137i	1.25155	−	4.67084i	4.46343	+	4.00971i	1.88587	−	3.26643i	−5.98252	+	5.31125i	−3.31343	+	8.36787i	−0.191372	+	9.66933i
43.5	−1.92787	−	0.532286i	2.18726	+	2.05326i	3.43334	+	2.05235i	−0.931824	+	3.47761i	−3.12383	−	5.12267i	−4.96512	+	8.59983i	−5.52659	−	5.78418i	0.568222	+	8.98204i	3.64752	−	6.20838i
43.6	−1.91763	−	0.568063i	2.62502	−	1.45234i	3.35461	+	2.17867i	2.50565	−	9.35123i	−5.85883	+	1.29387i	−1.43574	+	2.48677i	−5.19527	−	6.08351i	4.78143	−	7.62483i	−10.1170	+	16.5088i
43.7	−1.83642	+	0.792194i	2.99507	+	0.171846i	2.74486	−	2.90960i	−0.222103	+	0.828901i	−5.63634	+	2.05710i	5.23163	−	9.06144i	−2.73574	+	7.51769i	8.94094	+	1.02938i	−0.248776	−	1.69816i
43.8	−1.81345	−	0.843436i	0.915091	+	2.85703i	2.57723	+	3.05906i	0.136028	−	0.507662i	0.750245	−	5.95291i	6.49628	−	11.2519i	−2.09357	−	7.72120i	−7.32522	+	5.22888i	−0.674860	+	0.805891i
43.9	−1.62235	+	1.16960i	−0.520377	+	2.95452i	1.26405	−	3.79502i	−1.70362	+	6.35798i	−2.61139	−	5.40191i	−0.581649	+	1.00744i	2.38794	+	7.63530i	−8.45841	−	3.07493i	−4.67246	−	12.3074i
43.10	−1.59468	−	1.20706i	−2.00451	−	2.23203i	1.08601	+	3.84975i	0.218413	−	0.815129i	0.502363	+	5.97893i	−4.45068	+	7.70881i	2.91503	−	7.45001i	−0.963885	+	8.94824i	−1.33221	+	1.03623i
43.11	−1.48296	−	1.34195i	1.38752	−	2.65985i	0.398351	+	3.98012i	−0.631342	+	2.35620i	−5.62701	+	2.08248i	3.43083	−	5.94237i	4.75037	−	6.43692i	−5.14959	−	7.38117i	4.09816	−	2.64693i
43.12	−1.35588	+	1.47023i	−2.99965	+	0.0461027i	−0.323163	−	3.98692i	0.803565	−	2.99895i	3.99939	−	4.47268i	−0.723340	+	1.25286i	6.29987	+	4.93068i	8.99575	−	0.276584i	3.31960	+	5.24765i
43.13	−1.23592	−	1.57242i	−1.52445	+	2.58381i	−0.945018	+	3.88676i	0.892831	−	3.33209i	5.94692	−	0.796299i	−1.63564	+	2.83300i	7.27960	−	3.31775i	−4.35212	−	7.87776i	−6.34292	+	2.71428i
43.14	−1.23219	+	1.57534i	0.874159	−	2.86982i	−0.963395	−	3.88225i	0.661418	−	2.46845i	3.44380	+	4.91327i	−2.72334	+	4.71696i	7.30296	+	3.26601i	−7.47169	−	5.01735i	3.07365	+	4.08356i
43.15	−1.17470	+	1.61867i	2.85433	+	0.923476i	−1.24016	−	3.80289i	0.872094	−	3.25470i	−4.84778	+	3.53540i	−5.18069	+	8.97322i	7.61243	+	2.45986i	7.29438	+	5.27181i	4.24382	+	5.23492i
43.16	−0.933784	−	1.76863i	2.99980	+	0.0348191i	−2.25609	+	3.30303i	−1.49557	+	5.58156i	−2.73958	−	5.33804i	−1.11666	+	1.93410i	7.94855	+	0.905871i	8.99758	+	0.208901i	11.2682	−	2.56685i
43.17	−0.915081	+	1.77838i	−1.51894	−	2.58705i	−2.32525	−	3.25472i	−1.91133	+	7.13319i	5.99070	−	0.333879i	5.45754	−	9.45274i	7.91591	−	1.15685i	−4.38567	+	7.85913i	−10.9365	−	9.92651i
43.18	−0.809359	+	1.82892i	−0.155921	+	2.99595i	−2.68988	−	2.96050i	2.03358	−	7.58942i	−5.35314	−	2.70996i	4.60505	−	7.97618i	7.59159	−	2.52345i	−8.95138	−	0.934260i	12.2345	+	9.86181i
43.19	−0.661532	−	1.88743i	2.43372	+	1.75414i	−3.12475	+	2.49718i	1.97813	−	7.38249i	1.70082	−	5.75389i	0.0635994	−	0.110157i	6.78037	+	4.24577i	2.84600	+	8.53817i	−15.2425	+	1.15017i
43.20	−0.536163	−	1.92679i	−2.98561	+	0.293508i	−3.42506	+	2.06615i	−0.686399	+	2.56168i	2.16630	+	5.59528i	1.45323	−	2.51707i	5.81743	+	5.49158i	8.82771	−	1.75260i	5.30384	−	0.0509280i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
9.c	even	3	1	inner
16.f	odd	4	1	inner
144.v	odd	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	144.3.v.a	✓	184
3.b	odd	2	1		432.3.w.a		184
9.c	even	3	1	inner	144.3.v.a	✓	184
9.d	odd	6	1		432.3.w.a		184
16.f	odd	4	1	inner	144.3.v.a	✓	184
48.k	even	4	1		432.3.w.a		184
144.u	even	12	1		432.3.w.a		184
144.v	odd	12	1	inner	144.3.v.a	✓	184

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
144.3.v.a	✓	184	1.a	even	1	1	trivial
144.3.v.a	✓	184	9.c	even	3	1	inner
144.3.v.a	✓	184	16.f	odd	4	1	inner
144.3.v.a	✓	184	144.v	odd	12	1	inner
432.3.w.a		184	3.b	odd	2	1
432.3.w.a		184	9.d	odd	6	1
432.3.w.a		184	48.k	even	4	1
432.3.w.a		184	144.u	even	12	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(144, [\chi])\).