Newform orbit 935.2.bj.a

• Label: 935.2.bj.a
• Level: $935$
• Weight: $2$
• Character orbit: 935.bj
• Analytic conductor: $7.466$
• Analytic rank: $0$
• Dimension: $384$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 935 = 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	935.bj (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.46601258899\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 384 q + 96 q^{4} + 2 q^{5} + 8 q^{6} + 92 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
69.1	−1.64440	−	2.26333i	−0.377980	+	0.122813i	−1.80056	+	5.54155i	−0.927521	−	2.03463i	0.899519	+	0.653539i	−0.203358	−	0.0660749i	10.1818	−	3.30826i	−2.29927	+	1.67051i	−3.07981	+	5.44503i
69.2	−1.62170	−	2.23208i	−2.18143	+	0.708789i	−1.73424	+	5.33745i	1.96666	+	1.06407i	5.11971	+	3.71969i	2.34406	+	0.761632i	9.47812	−	3.07963i	1.82920	−	1.32899i	−0.814240	−	6.11536i
69.3	−1.55518	−	2.14052i	2.23201	−	0.725225i	−1.54520	+	4.75565i	2.23001	−	0.164498i	−5.02353	−	3.64981i	−2.51126	−	0.815958i	7.54995	−	2.45313i	2.02888	−	1.47407i	−3.82017	−	4.51755i
69.4	−1.54847	−	2.13129i	−2.98596	+	0.970197i	−1.52659	+	4.69835i	−2.05342	+	0.885132i	6.69144	+	4.86161i	−0.411647	−	0.133752i	7.36645	−	2.39350i	5.54762	−	4.03058i	5.06613	+	3.00583i
69.5	−1.54645	−	2.12851i	2.95417	−	0.959869i	−1.52101	+	4.68118i	−2.04627	−	0.901550i	−6.61158	−	4.80360i	3.39149	+	1.10196i	7.31167	−	2.37571i	5.37873	−	3.90788i	1.24550	+	5.74971i
69.6	−1.53729	−	2.11589i	0.126871	−	0.0412229i	−1.49572	+	4.60336i	−1.32852	+	1.79862i	−0.282260	−	0.205074i	−1.23946	−	0.402726i	7.06482	−	2.29550i	−2.41265	+	1.75290i	5.84801	+	0.0460248i
69.7	−1.48596	−	2.04524i	1.38382	−	0.449632i	−1.35692	+	4.17617i	0.120485	−	2.23282i	−2.97591	−	2.16212i	−1.93815	−	0.629742i	5.74895	−	1.86795i	−0.714250	+	0.518933i	−4.74569	+	3.07145i
69.8	−1.45598	−	2.00399i	−0.997104	+	0.323979i	−1.27804	+	3.93342i	0.876451	+	2.05714i	2.10101	+	1.52648i	−4.31392	−	1.40168i	5.03167	−	1.63489i	−1.53780	+	1.11727i	2.84639	−	4.75156i
69.9	−1.45155	−	1.99789i	−2.54386	+	0.826551i	−1.26652	+	3.89795i	1.36546	−	1.77074i	5.34390	+	3.88257i	−2.20723	−	0.717172i	4.92876	−	1.60145i	3.36099	−	2.44191i	−5.51977	−	0.157727i
69.10	−1.42853	−	1.96620i	0.468695	−	0.152288i	−1.20722	+	3.71546i	1.65012	+	1.50900i	−0.968976	−	0.704002i	3.18503	+	1.03488i	4.40708	−	1.43195i	−2.23057	+	1.62060i	0.609754	−	5.40014i
69.11	−1.39130	−	1.91496i	2.04712	−	0.665149i	−1.11331	+	3.42643i	2.03630	−	0.923833i	−4.12188	−	2.99472i	2.98073	+	0.968496i	3.60807	−	1.17233i	1.32121	−	0.959918i	−4.60220	−	2.61410i
69.12	−1.36370	−	1.87697i	2.08828	−	0.678523i	−1.04531	+	3.21714i	−2.21806	+	0.283233i	−4.12135	−	2.99434i	−4.16847	−	1.35442i	3.05095	−	0.991313i	1.47346	−	1.07053i	3.55639	+	3.77699i
69.13	−1.30214	−	1.79224i	−1.06133	+	0.344847i	−0.898527	+	2.76538i	1.29235	−	1.82479i	2.00005	+	1.45312i	3.87200	+	1.25809i	1.91243	−	0.621386i	−1.41955	+	1.03136i	−4.95327	+	0.0599311i
69.14	−1.27945	−	1.76102i	0.506806	−	0.164671i	−0.846146	+	2.60417i	−2.22646	−	0.207059i	−0.938425	−	0.681805i	2.35956	+	0.766667i	1.52820	−	0.496541i	−2.19732	+	1.59644i	2.48402	+	4.18576i
69.15	−1.26869	−	1.74621i	−1.76406	+	0.573179i	−0.821619	+	2.52868i	−1.33137	−	1.79651i	3.23894	+	2.35323i	0.0821390	+	0.0266886i	1.35240	−	0.439423i	0.356332	−	0.258890i	−1.44797	+	4.60407i
69.16	−1.19681	−	1.64727i	−2.14551	+	0.697118i	−0.663107	+	2.04083i	−0.990614	+	2.00467i	3.71611	+	2.69991i	3.44195	+	1.11836i	0.282457	−	0.0917758i	1.69018	−	1.22799i	4.48781	−	0.767399i
69.17	−1.19522	−	1.64508i	−1.29831	+	0.421847i	−0.659705	+	2.03036i	1.83179	−	1.28240i	2.24574	+	1.63163i	−2.01234	−	0.653850i	0.260790	−	0.0847359i	−0.919395	+	0.667980i	−4.29905	−	1.48068i
69.18	−1.17123	−	1.61206i	−2.70356	+	0.878439i	−0.608930	+	1.87409i	−1.85365	−	1.25059i	4.58260	+	3.32945i	−1.71047	−	0.555766i	−0.0558343	+	0.0181417i	4.11052	−	2.98646i	0.155036	+	4.45294i
69.19	−1.14314	−	1.57340i	3.13893	−	1.01990i	−0.550778	+	1.69512i	1.18463	+	1.89649i	−5.19295	−	3.77290i	1.39777	+	0.454162i	−0.402567	+	0.130802i	6.38563	−	4.63944i	1.62974	−	4.03184i
69.20	−1.12995	−	1.55524i	0.694931	−	0.225797i	−0.523957	+	1.61257i	1.91603	+	1.15274i	−1.13641	−	0.825647i	−2.30622	−	0.749337i	−0.556606	+	0.180852i	−1.99511	+	1.44953i	−0.372225	−	4.28244i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
11.c	even	5	1	inner
55.j	even	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	935.2.bj.a	✓	384
5.b	even	2	1	inner	935.2.bj.a	✓	384
11.c	even	5	1	inner	935.2.bj.a	✓	384
55.j	even	10	1	inner	935.2.bj.a	✓	384

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
935.2.bj.a	✓	384	1.a	even	1	1	trivial
935.2.bj.a	✓	384	5.b	even	2	1	inner
935.2.bj.a	✓	384	11.c	even	5	1	inner
935.2.bj.a	✓	384	55.j	even	10	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(935, [\chi])\).