Newform orbit 273.2.bh.a

• Label: 273.2.bh.a
• Level: $273$
• Weight: $2$
• Character orbit: 273.bh
• Analytic conductor: $2.180$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bh (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.17991597518\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(32\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
131.1	−2.34239	−	1.35238i	−1.69032	+	0.377930i	2.65786	+	4.60354i	0.200745	−	0.347701i	4.47048	+	1.40069i	−0.906582	−	2.48558i		−	8.96820i	2.71434	−	1.27764i	−0.940448	+	0.542968i
131.2	−2.16068	−	1.24747i	1.72610	−	0.143491i	2.11235	+	3.65869i	−0.688862	+	1.19314i	−3.90853	−	1.84321i	−2.58242	+	0.575427i		−	5.55045i	2.95882	−	0.495358i	2.97682	−	1.71866i
131.3	−2.13803	−	1.23439i	1.47880	+	0.901745i	2.04745	+	3.54630i	1.98059	−	3.43049i	−2.04862	−	3.75338i	2.62523	−	0.328920i		−	5.17189i	1.37371	+	2.66701i	−8.46914	+	4.88966i
131.4	−2.13534	−	1.23284i	−0.105557	+	1.72883i	2.03979	+	3.53302i	−1.46641	+	2.53990i	2.35677	−	3.56151i	0.805632	+	2.52011i		−	5.12758i	−2.97772	−	0.364982i	6.26259	−	3.61571i
131.5	−1.75475	−	1.01310i	0.351400	−	1.69603i	1.05276	+	1.82344i	0.867268	−	1.50215i	−2.33487	+	2.62010i	−1.44131	−	2.21870i		−	0.213809i	−2.75304	−	1.19197i	−3.04367	+	1.75727i
131.6	−1.71340	−	0.989233i	−1.24374	−	1.20545i	0.957162	+	1.65785i	−0.830302	+	1.43813i	0.938561	+	3.29577i	2.61452	−	0.405294i			0.169506i	0.0937900	+	2.99853i	2.84528	−	1.64272i
131.7	−1.61355	−	0.931585i	−1.54166	−	0.789478i	0.735702	+	1.27427i	0.650945	−	1.12747i	1.75209	+	2.71005i	−0.953821	+	2.46784i			0.984865i	1.75345	+	2.43422i	−2.10067	+	1.21282i
131.8	−1.59036	−	0.918192i	−0.540046	+	1.64571i	0.686154	+	1.18845i	1.90624	−	3.30170i	2.36994	−	2.12139i	−2.46739	+	0.954988i			1.15268i	−2.41670	−	1.77751i	−6.06319	+	3.50058i
131.9	−1.15260	−	0.665454i	−0.732991	+	1.56931i	−0.114341	−	0.198044i	−0.0955042	+	0.165418i	1.88915	−	1.32101i	2.46727	−	0.955290i			2.96617i	−1.92545	−	2.30058i	0.220156	−	0.127107i
131.10	−1.09109	−	0.629943i	−1.60797	+	0.643773i	−0.206343	−	0.357397i	−2.03837	+	3.53057i	2.15998	+	0.310511i	−1.74546	−	1.98831i			3.03971i	2.17111	−	2.07033i	4.44811	−	2.56812i
131.11	−1.00971	−	0.582955i	1.67611	−	0.436646i	−0.320327	−	0.554823i	−0.156706	+	0.271422i	−1.94692	−	0.536211i	2.13875	+	1.55748i			3.07876i	2.61868	−	1.46373i	0.316454	−	0.182705i
131.12	−0.987309	−	0.570023i	1.12414	+	1.31769i	−0.350147	−	0.606472i	−0.578962	+	1.00279i	−0.358764	−	1.94175i	−2.55265	+	0.695677i			3.07846i	−0.472604	+	2.96254i	1.14323	−	0.660043i
131.13	−0.734739	−	0.424202i	0.243844	−	1.71480i	−0.640106	−	1.10870i	−1.44264	+	2.49872i	−0.906583	+	1.15649i	−1.51284	+	2.17056i			2.78294i	−2.88108	−	0.836289i	2.11992	−	1.22394i
131.14	−0.636389	−	0.367419i	1.70069	−	0.328105i	−0.730006	−	1.26441i	1.03100	−	1.78574i	−1.20285	−	0.416064i	−0.617429	−	2.57270i			2.54255i	2.78469	−	1.11601i	−1.31223	+	0.757615i
131.15	−0.326193	−	0.188328i	−0.329203	−	1.70048i	−0.929065	−	1.60919i	2.06368	−	3.57439i	−0.212864	+	0.616683i	2.50486	+	0.851866i			1.45319i	−2.78325	+	1.11960i	−1.34632	+	0.777295i
131.16	−0.0408006	−	0.0235563i	0.539158	+	1.64600i	−0.998890	−	1.73013i	0.697336	−	1.20782i	0.0167755	−	0.0798583i	0.623634	−	2.57120i			0.188345i	−2.41862	+	1.77491i	−0.0569035	+	0.0328532i
131.17	0.0408006	+	0.0235563i	−1.15590	−	1.28992i	−0.998890	−	1.73013i	−0.697336	+	1.20782i	−0.0167755	−	0.0798583i	0.623634	−	2.57120i		−	0.188345i	−0.327806	+	2.98204i	−0.0569035	+	0.0328532i
131.18	0.326193	+	0.188328i	1.30806	+	1.13534i	−0.929065	−	1.60919i	−2.06368	+	3.57439i	0.212864	+	0.616683i	2.50486	+	0.851866i		−	1.45319i	0.422020	+	2.97017i	−1.34632	+	0.777295i
131.19	0.636389	+	0.367419i	1.13449	−	1.30879i	−0.730006	−	1.26441i	−1.03100	+	1.78574i	1.20285	−	0.416064i	−0.617429	−	2.57270i		−	2.54255i	−0.425855	−	2.96962i	−1.31223	+	0.757615i
131.20	0.734739	+	0.424202i	1.60698	+	0.646225i	−0.640106	−	1.10870i	1.44264	−	2.49872i	0.906583	+	1.15649i	−1.51284	+	2.17056i		−	2.78294i	2.16479	+	2.07694i	2.11992	−	1.22394i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
7.d	odd	6	1	inner
21.g	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	273.2.bh.a	✓	64
3.b	odd	2	1	inner	273.2.bh.a	✓	64
7.d	odd	6	1	inner	273.2.bh.a	✓	64
21.g	even	6	1	inner	273.2.bh.a	✓	64

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
273.2.bh.a	✓	64	1.a	even	1	1	trivial
273.2.bh.a	✓	64	3.b	odd	2	1	inner
273.2.bh.a	✓	64	7.d	odd	6	1	inner
273.2.bh.a	✓	64	21.g	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(273, [\chi])\).