Newform orbit 660.2.bj.a

• Label: 660.2.bj.a
• Level: $660$
• Weight: $2$
• Character orbit: 660.bj
• Analytic conductor: $5.270$
• Analytic rank: $0$
• Dimension: $384$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	660.bj (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.27012653340\)
Analytic rank:	\(0\)
Dimension:	\(384\)
Relative dimension:	\(96\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 384 q + 8 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
71.1	−1.41130	−	0.0908036i	−1.73204	−	0.00469833i	1.98351	+	0.256302i	0.951057	+	0.309017i	2.44400	+	0.163907i	0.187462	+	0.258020i	−2.77604	−	0.541827i	2.99996	+	0.0162754i	−1.31416	−	0.522474i
71.2	−1.40997	−	0.109415i	1.52937	−	0.813028i	1.97606	+	0.308545i	−0.951057	−	0.309017i	−2.24534	+	0.979012i	−1.91048	−	2.62955i	−2.75243	−	0.651251i	1.67797	−	2.48685i	1.30715	+	0.539766i
71.3	−1.40848	−	0.127236i	1.02229	+	1.39819i	1.96762	+	0.358420i	0.951057	+	0.309017i	−1.26197	−	2.09939i	−2.37843	−	3.27363i	−2.72575	−	0.755179i	−0.909858	+	2.85870i	−1.30022	−	0.556253i
71.4	−1.39698	−	0.220121i	−1.59073	−	0.685246i	1.90309	+	0.615009i	−0.951057	−	0.309017i	2.07138	+	1.30743i	0.581332	+	0.800134i	−2.52320	−	1.27807i	2.06088	+	2.18009i	1.26058	+	0.641038i
71.5	−1.39567	+	0.228243i	−0.784428	−	1.54424i	1.89581	−	0.637105i	0.951057	+	0.309017i	1.44727	+	1.97621i	−3.00265	−	4.13279i	−2.50052	+	1.32190i	−1.76935	+	2.42269i	−1.39790	−	0.214215i
71.6	−1.38865	−	0.267689i	−1.13068	+	1.31209i	1.85669	+	0.743452i	−0.951057	−	0.309017i	1.92134	−	1.51936i	1.77229	+	2.43935i	−2.37927	−	1.52941i	−0.443142	−	2.96709i	1.23796	+	0.683703i
71.7	−1.38681	+	0.277038i	1.32639	+	1.11386i	1.84650	−	0.768400i	−0.951057	−	0.309017i	−2.14803	−	1.17726i	1.08183	+	1.48902i	−2.34787	+	1.57718i	0.518610	+	2.95483i	1.40455	+	0.165070i
71.8	−1.37243	−	0.341209i	−0.144068	+	1.72605i	1.76715	+	0.936575i	0.951057	+	0.309017i	0.786668	−	2.31973i	1.33149	+	1.83264i	−2.10573	−	1.88836i	−2.95849	−	0.497338i	−1.19982	−	0.748615i
71.9	−1.36993	−	0.351120i	0.980365	−	1.42789i	1.75343	+	0.962022i	0.951057	+	0.309017i	−1.84440	+	1.61189i	1.40074	+	1.92795i	−2.06429	−	1.93357i	−1.07777	−	2.79972i	−1.19438	−	0.757267i
71.10	−1.35344	+	0.410137i	1.03524	−	1.38862i	1.66358	−	1.11019i	0.951057	+	0.309017i	−0.831609	+	2.30400i	0.778127	+	1.07100i	−1.79621	+	2.18486i	−0.856545	−	2.87512i	−1.41393	−	0.0281712i
71.11	−1.34941	+	0.423209i	−0.340068	+	1.69834i	1.64179	−	1.14216i	−0.951057	−	0.309017i	−0.259863	−	2.43567i	−1.62402	−	2.23527i	−1.73206	+	2.23606i	−2.76871	−	1.15510i	1.41414	+	0.0144934i
71.12	−1.34045	+	0.450777i	0.340068	−	1.69834i	1.59360	−	1.20849i	−0.951057	−	0.309017i	0.309729	+	2.42983i	1.62402	+	2.23527i	−1.59138	+	2.33827i	−2.76871	−	1.15510i	1.41414	−	0.0144934i
71.13	−1.33602	+	0.463722i	−1.03524	+	1.38862i	1.56992	−	1.23909i	0.951057	+	0.309017i	0.739175	−	2.33530i	−0.778127	−	1.07100i	−1.52287	+	2.38346i	−0.856545	−	2.87512i	−1.41393	+	0.0281712i
71.14	−1.28479	+	0.591020i	−1.32639	−	1.11386i	1.30139	−	1.51868i	−0.951057	−	0.309017i	2.36245	+	0.647166i	−1.08183	−	1.48902i	−0.774452	+	2.72034i	0.518610	+	2.95483i	1.40455	−	0.165070i
71.15	−1.27089	−	0.620349i	1.66241	−	0.486202i	1.23033	+	1.57679i	−0.951057	−	0.309017i	−2.41436	−	0.413364i	2.29207	+	3.15477i	−0.585461	−	2.76717i	2.52722	−	1.61653i	1.01699	+	0.982714i
71.16	−1.26328	+	0.635704i	0.784428	+	1.54424i	1.19176	−	1.60615i	0.951057	+	0.309017i	−1.97263	−	1.45214i	3.00265	+	4.13279i	−0.484494	+	2.78662i	−1.76935	+	2.42269i	−1.39790	+	0.214215i
71.17	−1.25725	−	0.647552i	0.531844	+	1.64838i	1.16135	+	1.62827i	−0.951057	−	0.309017i	0.398748	−	2.41682i	−0.883665	−	1.21626i	−0.405720	−	2.79918i	−2.43428	+	1.75336i	0.995611	+	1.00437i
71.18	−1.13077	−	0.849335i	−1.45608	−	0.937994i	0.557261	+	1.92080i	−0.951057	−	0.309017i	0.849814	+	2.29735i	−1.54729	−	2.12967i	1.00127	−	2.64527i	1.24033	+	2.73159i	0.812963	+	1.15719i
71.19	−1.08839	+	0.903000i	1.73204	+	0.00469833i	0.369181	−	1.96563i	0.951057	+	0.309017i	−1.88938	+	1.55892i	−0.187462	−	0.258020i	1.37315	+	2.47274i	2.99996	+	0.0162754i	−1.31416	+	0.522474i
71.20	−1.07638	+	0.917281i	−1.52937	+	0.813028i	0.317191	−	1.97469i	−0.951057	−	0.309017i	0.900414	−	2.27799i	1.91048	+	2.62955i	1.46992	+	2.41647i	1.67797	−	2.48685i	1.30715	−	0.539766i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
4.b	odd	2	1	inner
11.c	even	5	1	inner
12.b	even	2	1	inner
33.h	odd	10	1	inner
44.h	odd	10	1	inner
132.o	even	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	660.2.bj.a	✓	384
3.b	odd	2	1	inner	660.2.bj.a	✓	384
4.b	odd	2	1	inner	660.2.bj.a	✓	384
11.c	even	5	1	inner	660.2.bj.a	✓	384
12.b	even	2	1	inner	660.2.bj.a	✓	384
33.h	odd	10	1	inner	660.2.bj.a	✓	384
44.h	odd	10	1	inner	660.2.bj.a	✓	384
132.o	even	10	1	inner	660.2.bj.a	✓	384

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
660.2.bj.a	✓	384	1.a	even	1	1	trivial
660.2.bj.a	✓	384	3.b	odd	2	1	inner
660.2.bj.a	✓	384	4.b	odd	2	1	inner
660.2.bj.a	✓	384	11.c	even	5	1	inner
660.2.bj.a	✓	384	12.b	even	2	1	inner
660.2.bj.a	✓	384	33.h	odd	10	1	inner
660.2.bj.a	✓	384	44.h	odd	10	1	inner
660.2.bj.a	✓	384	132.o	even	10	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(660, [\chi])\).