Newform orbit 935.2.cs.a

• Label: 935.2.cs.a
• Level: $935$
• Weight: $2$
• Character orbit: 935.cs
• Analytic conductor: $7.466$
• Analytic rank: $0$
• Dimension: $3328$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 935 = 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	935.cs (of order \(80\), degree \(32\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.46601258899\)
Analytic rank:	\(0\)
Dimension:	\(3328\)
Relative dimension:	\(104\) over \(\Q(\zeta_{80})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{80}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 3328 q - 24 q^{2} - 24 q^{3} - 24 q^{5} - 48 q^{6} - 24 q^{7} - 56 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3.1	−0.648474	−	2.70109i	1.12317	−	1.42473i	−5.09335	+	2.59519i	−2.23259	+	0.124649i	−4.57667	−	2.10988i	−2.57546	−	0.304826i	6.70461	+	7.85009i	−0.0680189	−	0.283319i	1.78446	+	5.94959i
3.2	−0.625948	−	2.60726i	0.793558	−	1.00662i	−4.62398	+	2.35604i	2.03671	+	0.922937i	−3.12126	−	1.43892i	−0.351689	−	0.0416252i	5.55438	+	6.50335i	0.316780	+	1.31948i	1.13146	−	5.88794i
3.3	−0.621530	−	2.58886i	−0.770067	+	0.976826i	−4.53388	+	2.31013i	−0.935706	+	2.03088i	3.00748	+	1.38647i	−0.0581479	−	0.00688225i	5.34032	+	6.25271i	0.339151	+	1.41267i	5.83922	+	1.16016i
3.4	−0.606258	−	2.52525i	−1.21155	+	1.53684i	−4.22732	+	2.15393i	2.18221	+	0.487812i	4.61543	+	2.12774i	3.35431	+	0.397008i	4.62881	+	5.41963i	−0.193700	−	0.806817i	−0.0911380	−	5.80636i
3.5	−0.604101	−	2.51626i	−1.26689	+	1.60704i	−4.18463	+	2.13217i	0.0982541	−	2.23391i	4.80905	+	2.21700i	1.13099	+	0.133862i	4.53181	+	5.30607i	−0.277232	−	1.15475i	−5.68046	+	1.10227i
3.6	−0.603261	−	2.51276i	0.332919	−	0.422305i	−4.16804	+	2.12372i	0.0650433	−	2.23512i	−1.26199	−	0.581785i	2.35946	+	0.279260i	4.49426	+	5.26211i	0.632829	+	2.63592i	−5.65557	+	1.18492i
3.7	−0.597700	−	2.48960i	1.79719	−	2.27972i	−4.05884	+	2.06808i	−0.149853	+	2.23104i	−6.74976	−	3.11168i	4.95622	+	0.586608i	4.24904	+	4.97499i	−1.26691	−	5.27705i	5.64396	−	0.960419i
3.8	−0.570846	−	2.37774i	−0.185899	+	0.235811i	−3.54579	+	1.80667i	2.19401	−	0.431634i	0.666818	+	0.307407i	−4.50831	−	0.533593i	3.14369	+	3.68079i	0.679287	+	2.82944i	−2.27876	−	4.97040i
3.9	−0.541785	−	2.25670i	1.96726	−	2.49545i	−3.01713	+	1.53731i	−0.624414	−	2.14712i	−6.69730	−	3.08750i	−3.08881	−	0.365584i	2.08936	+	2.44633i	−1.65685	−	6.90127i	−4.50709	+	2.57239i
3.10	−0.541039	−	2.25359i	0.361482	−	0.458538i	−3.00394	+	1.53058i	−2.14724	−	0.623991i	−1.22893	−	0.566546i	3.03457	+	0.359165i	2.06420	+	2.41686i	0.620748	+	2.58560i	−0.244480	+	5.17660i
3.11	−0.534832	−	2.22773i	−0.665727	+	0.844470i	−2.89474	+	1.47494i	−0.554244	+	2.16629i	2.23731	+	1.03141i	−3.04174	−	0.360014i	1.85817	+	2.17563i	0.430398	+	1.79274i	5.12235	+	0.0761081i
3.12	−0.530074	−	2.20792i	1.38093	−	1.75170i	−2.81190	+	1.43274i	−1.22725	+	1.86918i	−4.59960	−	2.12044i	−2.20154	−	0.260570i	1.70454	+	1.99576i	−0.461149	−	1.92082i	4.77754	+	1.71887i
3.13	−0.529624	−	2.20604i	−1.42521	+	1.80787i	−2.80411	+	1.42877i	−2.12080	−	0.708663i	4.74307	+	2.18659i	−0.439467	−	0.0520143i	1.69020	+	1.97897i	−0.536839	−	2.23610i	−0.440114	+	5.05390i
3.14	−0.521277	−	2.17127i	0.239099	−	0.303296i	−2.66069	+	1.35569i	−1.99498	−	1.00998i	−0.783175	−	0.361049i	0.767026	+	0.0907835i	1.43013	+	1.67447i	0.665516	+	2.77207i	−1.15301	+	4.85813i
3.15	−0.514528	−	2.14317i	−0.665304	+	0.843934i	−2.54640	+	1.29746i	1.69160	−	1.46236i	2.15101	+	0.991628i	−2.43897	−	0.288672i	1.22802	+	1.43782i	0.430741	+	1.79417i	−4.00445	−	2.87295i
3.16	−0.509725	−	2.12316i	1.58288	−	2.00788i	−2.46596	+	1.25647i	2.23014	+	0.162687i	−5.06987	−	2.33724i	−0.844233	−	0.0999215i	1.08852	+	1.27449i	−0.825716	−	3.43936i	−0.791348	−	4.81787i
3.17	−0.490175	−	2.04172i	−1.53714	+	1.94985i	−2.14635	+	1.09362i	1.26041	+	1.84699i	4.73452	+	2.18264i	2.44943	+	0.289909i	0.557617	+	0.652886i	−0.738785	−	3.07726i	3.15322	−	3.47875i
3.18	−0.479116	−	1.99566i	−2.01796	+	2.55977i	−1.97111	+	1.00433i	1.06765	−	1.96472i	6.07527	+	2.80074i	−1.65307	−	0.195654i	0.282876	+	0.331206i	−1.77992	−	7.41390i	−4.43245	−	1.18935i
3.19	−0.454876	−	1.89469i	0.389493	−	0.494070i	−1.60094	+	0.815720i	0.541947	+	2.16940i	−1.11328	−	0.513230i	2.19871	+	0.260235i	−0.257171	−	0.301109i	0.607936	+	2.53224i	3.86383	−	2.01363i
3.20	−0.444676	−	1.85221i	1.67943	−	2.13035i	−1.45093	+	0.739286i	1.69978	−	1.45284i	−4.69266	−	2.16334i	2.41065	+	0.285319i	−0.459684	−	0.538221i	−1.01756	−	4.23845i	−3.44682	−	2.50230i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.c	even	5	1	inner
85.o	even	16	1	inner
935.cs	even	80	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	935.2.cs.a	yes	3328
5.c	odd	4	1		935.2.cn.a	✓	3328
11.c	even	5	1	inner	935.2.cs.a	yes	3328
17.e	odd	16	1		935.2.cn.a	✓	3328
55.k	odd	20	1		935.2.cn.a	✓	3328
85.o	even	16	1	inner	935.2.cs.a	yes	3328
187.s	odd	80	1		935.2.cn.a	✓	3328
935.cs	even	80	1	inner	935.2.cs.a	yes	3328

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
935.2.cn.a	✓	3328	5.c	odd	4	1
935.2.cn.a	✓	3328	17.e	odd	16	1
935.2.cn.a	✓	3328	55.k	odd	20	1
935.2.cn.a	✓	3328	187.s	odd	80	1
935.2.cs.a	yes	3328	1.a	even	1	1	trivial
935.2.cs.a	yes	3328	11.c	even	5	1	inner
935.2.cs.a	yes	3328	85.o	even	16	1	inner
935.2.cs.a	yes	3328	935.cs	even	80	1	inner

Hecke kernels

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