Newform orbit 192.3.t.a

• Label: 192.3.t.a
• Level: $192$
• Weight: $3$
• Character orbit: 192.t
• Analytic conductor: $5.232$
• Analytic rank: $0$
• Dimension: $256$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	192.t (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.23162107572\)
Analytic rank:	\(0\)
Dimension:	\(256\)
Relative dimension:	\(32\) over \(\Q(\zeta_{16})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 256 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
19.1	−1.99032	−	0.196561i	1.44015	−	0.962276i	3.92273	+	0.782437i	−1.54570	−	7.77077i	−3.05550	+	1.63216i	−11.5402	+	4.78010i	−7.65368	−	2.32835i	1.14805	−	2.77164i	1.54901	+	15.7701i
19.2	−1.97540	−	0.312752i	−1.44015	+	0.962276i	3.80437	+	1.23562i	−0.279220	−	1.40373i	3.14581	−	1.45047i	−3.62990	+	1.50355i	−7.12870	−	3.63066i	1.14805	−	2.77164i	0.112549	+	2.86026i
19.3	−1.92244	+	0.551559i	−1.44015	+	0.962276i	3.39156	−	2.12068i	1.64535	+	8.27175i	2.23785	−	2.64425i	8.64107	−	3.57925i	−5.35040	+	5.94754i	1.14805	−	2.77164i	−7.72546	−	14.9945i
19.4	−1.84535	+	0.771151i	1.44015	−	0.962276i	2.81065	−	2.84609i	−0.118194	−	0.594202i	−1.91552	+	2.88631i	4.91350	−	2.03524i	−2.99188	+	7.41948i	1.14805	−	2.77164i	0.676329	+	1.00537i
19.5	−1.77755	−	0.916684i	1.44015	−	0.962276i	2.31938	+	3.25891i	0.937462	+	4.71294i	−3.44204	+	0.390335i	6.22692	−	2.57928i	−1.13543	−	7.91901i	1.14805	−	2.77164i	2.65389	−	9.23685i
19.6	−1.75449	+	0.960092i	−1.44015	+	0.962276i	2.15645	−	3.36894i	−0.982422	−	4.93897i	1.60285	−	3.07097i	2.14513	−	0.888543i	−0.548972	+	7.98114i	1.14805	−	2.77164i	6.46551	+	7.72214i
19.7	−1.70771	−	1.04102i	−1.44015	+	0.962276i	1.83257	+	3.55552i	1.29633	+	6.51710i	3.46110	−	0.144072i	−5.83647	+	2.41754i	0.571859	−	7.97953i	1.14805	−	2.77164i	4.57065	−	12.4788i
19.8	−1.36103	−	1.46546i	1.44015	−	0.962276i	−0.295169	+	3.98909i	0.242100	+	1.21712i	−3.37027	−	0.800794i	−4.94543	+	2.04846i	6.24761	−	4.99674i	1.14805	−	2.77164i	1.45414	−	2.01133i
19.9	−1.27767	+	1.53868i	−1.44015	+	0.962276i	−0.735101	−	3.93187i	0.251501	+	1.26438i	0.359399	−	3.44541i	−9.71768	+	4.02520i	6.98913	+	3.89256i	1.14805	−	2.77164i	−2.26682	−	1.22849i
19.10	−1.27046	+	1.54465i	1.44015	−	0.962276i	−0.771866	−	3.92482i	0.951985	+	4.78595i	−0.343273	+	3.44705i	−6.47911	+	2.68373i	7.04309	+	3.79407i	1.14805	−	2.77164i	−8.60206	−	4.60988i
19.11	−1.26075	−	1.55258i	−1.44015	+	0.962276i	−0.821030	+	3.91483i	−1.08391	−	5.44919i	3.30968	+	1.02276i	−3.97032	+	1.64456i	7.11321	−	3.66090i	1.14805	−	2.77164i	−7.09379	+	8.55292i
19.12	−1.08433	−	1.68055i	1.44015	−	0.962276i	−1.64847	+	3.64452i	−1.65925	−	8.34160i	−3.17874	−	1.37681i	7.15690	−	2.96448i	7.91227	−	1.18154i	1.14805	−	2.77164i	−12.2193	+	11.8335i
19.13	−0.760241	+	1.84987i	−1.44015	+	0.962276i	−2.84407	−	2.81270i	−0.194779	−	0.979220i	−0.685230	−	3.39565i	6.99962	−	2.89934i	7.36532	−	3.12284i	1.14805	−	2.77164i	1.95951	+	0.384127i
19.14	−0.441777	−	1.95060i	−1.44015	+	0.962276i	−3.60967	+	1.72346i	0.109322	+	0.549600i	2.51324	+	2.38404i	6.48355	−	2.68558i	4.95644	+	6.27962i	1.14805	−	2.77164i	1.02375	−	0.456044i
19.15	−0.399279	−	1.95974i	1.44015	−	0.962276i	−3.68115	+	1.56497i	0.758038	+	3.81092i	−2.46083	−	2.43810i	−10.7874	+	4.46830i	4.53673	+	6.58924i	1.14805	−	2.77164i	7.16573	−	3.00718i
19.16	−0.358174	+	1.96767i	1.44015	−	0.962276i	−3.74342	−	1.40954i	−0.809137	−	4.06781i	1.37761	+	3.17839i	−6.21464	+	2.57419i	4.11429	−	6.86095i	1.14805	−	2.77164i	8.29390	−	0.135127i
19.17	0.143105	+	1.99487i	1.44015	−	0.962276i	−3.95904	+	0.570954i	−0.196739	−	0.989075i	2.12571	+	2.73521i	12.0254	−	4.98107i	−1.70554	−	7.81608i	1.14805	−	2.77164i	1.94492	−	0.534012i
19.18	0.195531	+	1.99042i	−1.44015	+	0.962276i	−3.92354	+	0.778375i	1.68587	+	8.47543i	−2.19693	−	2.67834i	−3.67509	+	1.52227i	−2.31646	−	7.65728i	1.14805	−	2.77164i	−16.5400	+	5.01279i
19.19	0.377294	−	1.96409i	1.44015	−	0.962276i	−3.71530	−	1.48208i	1.80347	+	9.06666i	−1.34664	−	3.19164i	9.72216	−	4.02705i	−4.31270	+	6.73800i	1.14805	−	2.77164i	18.4882	−	0.121382i
19.20	0.679497	−	1.88103i	−1.44015	+	0.962276i	−3.07657	−	2.55631i	0.892221	+	4.48550i	0.831497	+	3.36283i	−2.40197	+	0.994929i	−6.89902	+	4.05012i	1.14805	−	2.77164i	9.04363	+	1.36958i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
64.j	odd	16	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	192.3.t.a	✓	256
64.j	odd	16	1	inner	192.3.t.a	✓	256

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
192.3.t.a	✓	256	1.a	even	1	1	trivial
192.3.t.a	✓	256	64.j	odd	16	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(192, [\chi])\).