Newform orbit 28.5.g.a

• Label: 28.5.g.a
• Level: $28$
• Weight: $5$
• Character orbit: 28.g
• Analytic conductor: $2.894$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	28.g (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.89435896635\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Relative dimension:	\(14\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q + 2 q^{2} - 4 q^{4} - 2 q^{5} - 36 q^{6} - 184 q^{8} + 268 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
11.1	−3.98249	+	0.373846i	−10.4527	−	6.03487i	15.7205	−	2.97768i	13.8853	+	24.0501i	43.8839	+	20.1261i	34.1259	+	35.1628i	−61.4935	+	17.7356i	32.3394	+	56.0135i	−64.2891	−	90.5882i
11.2	−3.86347	−	1.03614i	1.18377	+	0.683453i	13.8528	+	8.00618i	−16.2684	−	28.1777i	−3.86533	−	3.86706i	−47.8742	−	10.4432i	−45.2245	−	45.2851i	−39.5658	−	68.5299i	33.6565	+	125.720i
11.3	−3.31594	+	2.23708i	12.8404	+	7.41339i	5.99095	−	14.8361i	0.212899	+	0.368751i	−59.1623	+	4.14255i	13.4191	+	47.1267i	13.3238	+	62.5977i	69.4168	+	120.233i	−1.53089	−	0.746487i
11.4	−2.68081	−	2.96871i	8.26641	+	4.77262i	−1.62652	+	15.9171i	8.72165	+	15.1063i	−7.99215	−	37.3351i	48.2343	−	8.62858i	51.6137	−	37.8421i	5.05573	+	8.75678i	21.4653	−	66.3893i
11.5	−2.34212	+	3.24261i	−3.98530	−	2.30092i	−5.02899	−	15.1891i	−5.96978	−	10.3400i	16.7950	−	7.53376i	8.20764	−	48.3077i	61.0308	+	19.2677i	−29.9116	−	51.8084i	47.5103	+	4.85975i
11.6	−1.23058	−	3.80601i	−8.26641	−	4.77262i	−12.9714	+	9.36716i	8.72165	+	15.1063i	−7.99215	+	37.3351i	−48.2343	+	8.62858i	51.6137	+	37.8421i	5.05573	+	8.75678i	46.7622	−	51.7842i
11.7	0.123509	+	3.99809i	2.78459	+	1.60768i	−15.9695	+	0.987599i	16.3700	+	28.3536i	−6.08374	+	11.3316i	−41.5540	+	25.9667i	−5.92089	−	63.7255i	−35.3307	−	61.1946i	−111.339	+	68.9506i
11.8	1.03441	−	3.86393i	−1.18377	−	0.683453i	−13.8600	−	7.99382i	−16.2684	−	28.1777i	−3.86533	+	3.86706i	47.8742	+	10.4432i	−45.2245	+	45.2851i	−39.5658	−	68.5299i	−125.705	+	33.7126i
11.9	1.54095	+	3.69127i	−12.5795	−	7.26279i	−11.2510	+	11.3761i	−17.4517	−	30.2272i	7.42457	−	57.6260i	1.32995	+	48.9819i	−59.3294	−	24.0005i	64.9961	+	112.577i	84.6846	−	110.997i
11.10	2.31501	−	3.26202i	10.4527	+	6.03487i	−5.28149	−	15.1032i	13.8853	+	24.0501i	43.8839	−	20.1261i	−34.1259	−	35.1628i	−61.4935	−	17.7356i	32.3394	+	56.0135i	110.596	+	10.3819i
11.11	2.42626	+	3.18013i	12.5795	+	7.26279i	−4.22650	+	15.4317i	−17.4517	−	30.2272i	7.42457	+	57.6260i	−1.32995	−	48.9819i	−59.3294	+	24.0005i	64.9961	+	112.577i	53.7841	−	128.838i
11.12	3.40070	+	2.10601i	−2.78459	−	1.60768i	7.12946	+	14.3238i	16.3700	+	28.3536i	−6.08374	−	11.3316i	41.5540	−	25.9667i	−5.92089	+	63.7255i	−35.3307	−	61.1946i	−4.04367	+	130.897i
11.13	3.59534	−	1.75315i	−12.8404	−	7.41339i	9.85292	−	12.6063i	0.212899	+	0.368751i	−59.1623	−	4.14255i	−13.4191	−	47.1267i	13.3238	−	62.5977i	69.4168	+	120.233i	1.41192	+	0.952543i
11.14	3.97924	−	0.407029i	3.98530	+	2.30092i	15.6687	−	3.23933i	−5.96978	−	10.3400i	16.7950	+	7.53376i	−8.20764	+	48.3077i	61.0308	−	19.2677i	−29.9116	−	51.8084i	−27.9638	−	38.7153i
23.1	−3.98249	−	0.373846i	−10.4527	+	6.03487i	15.7205	+	2.97768i	13.8853	−	24.0501i	43.8839	−	20.1261i	34.1259	−	35.1628i	−61.4935	−	17.7356i	32.3394	−	56.0135i	−64.2891	+	90.5882i
23.2	−3.86347	+	1.03614i	1.18377	−	0.683453i	13.8528	−	8.00618i	−16.2684	+	28.1777i	−3.86533	+	3.86706i	−47.8742	+	10.4432i	−45.2245	+	45.2851i	−39.5658	+	68.5299i	33.6565	−	125.720i
23.3	−3.31594	−	2.23708i	12.8404	−	7.41339i	5.99095	+	14.8361i	0.212899	−	0.368751i	−59.1623	−	4.14255i	13.4191	−	47.1267i	13.3238	−	62.5977i	69.4168	−	120.233i	−1.53089	+	0.746487i
23.4	−2.68081	+	2.96871i	8.26641	−	4.77262i	−1.62652	−	15.9171i	8.72165	−	15.1063i	−7.99215	+	37.3351i	48.2343	+	8.62858i	51.6137	+	37.8421i	5.05573	−	8.75678i	21.4653	+	66.3893i
23.5	−2.34212	−	3.24261i	−3.98530	+	2.30092i	−5.02899	+	15.1891i	−5.96978	+	10.3400i	16.7950	+	7.53376i	8.20764	+	48.3077i	61.0308	−	19.2677i	−29.9116	+	51.8084i	47.5103	−	4.85975i
23.6	−1.23058	+	3.80601i	−8.26641	+	4.77262i	−12.9714	−	9.36716i	8.72165	−	15.1063i	−7.99215	−	37.3351i	−48.2343	−	8.62858i	51.6137	−	37.8421i	5.05573	−	8.75678i	46.7622	+	51.7842i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
7.c	even	3	1	inner
28.g	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	28.5.g.a	✓	28
4.b	odd	2	1	inner	28.5.g.a	✓	28
7.c	even	3	1	inner	28.5.g.a	✓	28
7.c	even	3	1		196.5.c.h		14
7.d	odd	6	1		196.5.c.g		14
28.f	even	6	1		196.5.c.g		14
28.g	odd	6	1	inner	28.5.g.a	✓	28
28.g	odd	6	1		196.5.c.h		14

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
28.5.g.a	✓	28	1.a	even	1	1	trivial
28.5.g.a	✓	28	4.b	odd	2	1	inner
28.5.g.a	✓	28	7.c	even	3	1	inner
28.5.g.a	✓	28	28.g	odd	6	1	inner
196.5.c.g		14	7.d	odd	6	1
196.5.c.g		14	28.f	even	6	1
196.5.c.h		14	7.c	even	3	1
196.5.c.h		14	28.g	odd	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(28, [\chi])\).