Newform orbit 520.2.bv.a

• Label: 520.2.bv.a
• Level: $520$
• Weight: $2$
• Character orbit: 520.bv
• Analytic conductor: $4.152$
• Analytic rank: $0$
• Dimension: $160$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.bv (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.15222090511\)
Analytic rank:	\(0\)
Dimension:	\(160\)
Relative dimension:	\(80\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 160 q - 2 q^{4} + 6 q^{6} - 76 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
29.1	−1.41419	−	0.00779867i	−0.619154	−	1.07241i	1.99988	+	0.0220576i	2.20863	+	0.349197i	0.867240	+	1.52142i	−2.37426	−	1.37078i	−2.82804	−	0.0467901i	0.733296	−	1.27011i	−3.12071	−	0.511056i
29.2	−1.41097	−	0.0957501i	0.341699	+	0.591840i	1.98166	+	0.270201i	0.354437	+	2.20780i	−0.425457	−	0.867785i	0.325606	+	0.187989i	−2.77019	−	0.570989i	1.26648	−	2.19361i	−0.288703	−	3.14907i
29.3	−1.40561	+	0.155719i	1.08449	+	1.87840i	1.95150	−	0.437762i	1.99181	−	1.01621i	−1.81688	−	2.47142i	1.32785	+	0.766636i	−2.67489	+	0.919212i	−0.852246	+	1.47613i	−2.64148	+	1.73856i
29.4	−1.39884	+	0.207930i	1.22387	+	2.11980i	1.91353	−	0.581724i	−0.687428	−	2.12778i	−2.15277	−	2.71079i	−2.85620	−	1.64903i	−2.55577	+	1.21162i	−1.49569	+	2.59062i	1.40403	+	2.83349i
29.5	−1.39847	−	0.210408i	1.35483	+	2.34663i	1.91146	+	0.588499i	−2.19456	+	0.428841i	−1.40094	−	3.56677i	3.61286	+	2.08588i	−2.54930	−	1.22519i	−2.17113	+	3.76051i	3.15927	−	0.137970i
29.6	−1.38495	+	0.286198i	−1.00869	−	1.74711i	1.83618	−	0.792740i	−1.46339	+	1.69071i	1.89701	+	2.13098i	−0.178819	−	0.103241i	−2.31614	+	1.62342i	−0.534926	+	0.926519i	1.54285	−	2.76036i
29.7	−1.36115	−	0.383771i	0.0254333	+	0.0440518i	1.70544	+	1.04474i	−1.62775	−	1.53311i	−0.0177127	−	0.0697216i	−2.24529	−	1.29632i	−1.92041	−	2.07654i	1.49871	−	2.59584i	1.62724	+	2.71148i
29.8	−1.35951	+	0.389511i	−1.59635	−	2.76496i	1.69656	−	1.05909i	−0.871813	−	2.05911i	3.24724	+	3.13721i	1.36678	+	0.789112i	−1.89397	+	2.10068i	−3.59666	+	6.22960i	1.98729	+	2.45981i
29.9	−1.31000	−	0.532815i	−1.51575	−	2.62536i	1.43222	+	1.39598i	2.20781	+	0.354340i	0.586808	+	4.24684i	0.410435	+	0.236965i	−1.13241	−	2.59184i	−3.09499	+	5.36069i	−2.70345	−	1.64054i
29.10	−1.28402	−	0.592698i	−0.930166	−	1.61109i	1.29742	+	1.52207i	−1.92793	−	1.13274i	0.239459	+	2.61999i	1.78560	+	1.03092i	−0.763780	−	2.72335i	−0.230418	+	0.399095i	1.80412	+	2.59714i
29.11	−1.27368	−	0.614615i	−0.876447	−	1.51805i	1.24450	+	1.56564i	−0.379793	+	2.20358i	0.183292	+	2.47218i	3.99661	+	2.30744i	−0.622818	−	2.75900i	−0.0363199	+	0.0629079i	1.83809	−	2.57322i
29.12	−1.25808	−	0.645931i	1.65229	+	2.86185i	1.16555	+	1.62527i	1.69975	+	1.45287i	−0.230160	−	4.66770i	−3.60170	−	2.07944i	−0.416541	−	2.79759i	−3.96011	+	6.85910i	−1.19998	−	2.92576i
29.13	−1.25338	+	0.655014i	0.720886	+	1.24861i	1.14191	−	1.64196i	−1.14970	+	1.91786i	−1.72140	−	1.09279i	−1.94705	−	1.12413i	−0.355744	+	2.80597i	0.460646	−	0.797862i	0.184790	−	3.15687i
29.14	−1.23690	+	0.685627i	0.277143	+	0.480026i	1.05983	−	1.69610i	−2.07733	−	0.827462i	−0.671917	−	0.403726i	3.57479	+	2.06391i	−0.148007	+	2.82455i	1.34638	−	2.33200i	3.13678	−	0.400789i
29.15	−1.21222	+	0.728371i	−0.277143	−	0.480026i	0.938952	−	1.76589i	2.07733	+	0.827462i	0.685596	+	0.380034i	3.57479	+	2.06391i	0.148007	+	2.82455i	1.34638	−	2.33200i	−3.12088	+	0.510002i
29.16	−1.20004	−	0.748273i	0.350249	+	0.606649i	0.880174	+	1.79591i	1.33505	−	1.79378i	0.0336278	−	0.990084i	−0.552611	−	0.319050i	0.287590	−	2.81377i	1.25465	−	2.17312i	−2.94434	+	1.15362i
29.17	−1.19395	+	0.757951i	−0.720886	−	1.24861i	0.851022	−	1.80991i	1.14970	−	1.91786i	1.80709	+	0.944381i	−1.94705	−	1.12413i	0.355744	+	2.80597i	0.460646	−	0.797862i	0.0809558	+	3.16124i
29.18	−1.07705	−	0.916493i	0.667651	+	1.15641i	0.320080	+	1.97422i	2.18146	+	0.491136i	0.340743	−	1.85741i	2.77315	+	1.60108i	1.46462	−	2.41969i	0.608484	−	1.05393i	−1.89943	−	2.52828i
29.19	−1.02161	−	0.977910i	0.217700	+	0.377067i	0.0873840	+	1.99809i	−2.01103	+	0.977626i	0.146333	−	0.598107i	−0.932274	−	0.538249i	1.86468	−	2.12673i	1.40521	−	2.43390i	3.01053	+	0.967853i
29.20	−1.01708	+	0.982619i	1.59635	+	2.76496i	0.0689208	−	1.99881i	0.871813	+	2.05911i	−4.34052	−	1.24359i	1.36678	+	0.789112i	1.89397	+	2.10068i	−3.59666	+	6.22960i	−2.91003	−	1.23763i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
8.b	even	2	1	inner
13.c	even	3	1	inner
40.f	even	2	1	inner
65.n	even	6	1	inner
104.r	even	6	1	inner
520.bv	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	520.2.bv.a	✓	160
5.b	even	2	1	inner	520.2.bv.a	✓	160
8.b	even	2	1	inner	520.2.bv.a	✓	160
13.c	even	3	1	inner	520.2.bv.a	✓	160
40.f	even	2	1	inner	520.2.bv.a	✓	160
65.n	even	6	1	inner	520.2.bv.a	✓	160
104.r	even	6	1	inner	520.2.bv.a	✓	160
520.bv	even	6	1	inner	520.2.bv.a	✓	160

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
520.2.bv.a	✓	160	1.a	even	1	1	trivial
520.2.bv.a	✓	160	5.b	even	2	1	inner
520.2.bv.a	✓	160	8.b	even	2	1	inner
520.2.bv.a	✓	160	13.c	even	3	1	inner
520.2.bv.a	✓	160	40.f	even	2	1	inner
520.2.bv.a	✓	160	65.n	even	6	1	inner
520.2.bv.a	✓	160	104.r	even	6	1	inner
520.2.bv.a	✓	160	520.bv	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(520, [\chi])\).