Newform orbit 980.2.bd.a

• Label: 980.2.bd.a
• Level: $980$
• Weight: $2$
• Character orbit: 980.bd
• Analytic conductor: $7.825$
• Analytic rank: $0$
• Dimension: $168$
• Inner twists: $4$

Newspace parameters

Level:	$N$	$=$	$980 = 2^{2} \cdot 5 \cdot 7^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	980.bd (of order $14$, degree $6$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$28$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

$q$-expansion

The algebraic $q$-expansion of this newform has not been computed, but we have computed the trace expansion.

$\operatorname{Tr}(f)(q) =$ 168 * q + 2 * q^5 + 18 * q^9 + 6 * q^11 + 16 * q^15 + 20 * q^19 - 6 * q^21 + 6 * q^25 - 14 * q^29 + 20 * q^31 + 2 * q^35 + 40 * q^39 - 14 * q^41 + 96 * q^45 + 32 * q^49 + 4 * q^51 - 30 * q^55 - 28 * q^59 - 16 * q^61 - 20 * q^65 + 12 * q^69 + 34 * q^71 - 24 * q^75 - 24 * q^79 - 62 * q^81 - 42 * q^85 - 74 * q^89 + 60 * q^91 - 10 * q^95 + 136 * q^99

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		0		−3.08880	+	0.704999i		0		2.21123	+	0.332343i		0		−2.59041	−	0.538307i		0		6.34078	−	3.05356i		0
29.2		0		−2.98304	+	0.680860i		0		0.808094	+	2.08494i		0		2.38737	+	1.14038i		0		5.73208	−	2.76042i		0
29.3		0		−2.74305	+	0.626084i		0		−2.22364	+	0.235416i		0		0.0771841	−	2.64463i		0		4.42946	−	2.13311i		0
29.4		0		−2.55828	+	0.583912i		0		−1.96921	−	1.05934i		0		−1.86517	+	1.87647i		0		3.50096	−	1.68597i		0
29.5		0		−2.19846	+	0.501785i		0		−1.31265	+	1.81023i		0		0.228420	+	2.63587i		0		1.87855	−	0.904663i		0
29.6		0		−1.89281	+	0.432022i		0		−0.697623	−	2.12446i		0		−2.41857	+	1.07263i		0		0.693184	−	0.333820i		0
29.7		0		−1.87433	+	0.427803i		0		1.93896	−	1.11375i		0		1.31675	+	2.29481i		0		0.627182	−	0.302035i		0
29.8		0		−1.72524	+	0.393776i		0		1.68714	−	1.46750i		0		1.73556	−	1.99695i		0		0.118499	−	0.0570660i		0
29.9		0		−1.42811	+	0.325956i		0		1.41538	+	1.73110i		0		1.54156	−	2.15025i		0		−0.769660	+	0.370649i		0
29.10		0		−0.984698	+	0.224751i		0		−1.10153	+	1.94593i		0		−2.10132	−	1.60762i		0		−1.78379	+	0.859028i		0
29.11		0		−0.631234	+	0.144075i		0		−2.01504	−	0.969345i		0		1.64972	−	2.06843i		0		−2.32521	+	1.11976i		0
29.12		0		−0.622220	+	0.142018i		0		1.29465	+	1.82315i		0		−2.58484	+	0.564461i		0		−2.33592	+	1.12492i		0
29.13		0		−0.441575	+	0.100787i		0		−0.605716	−	2.15247i		0		1.86214	+	1.87948i		0		−2.51808	+	1.21264i		0
29.14		0		−0.332725	+	0.0759423i		0		−2.22696	+	0.201644i		0		2.62035	+	0.365762i		0		−2.59797	+	1.25112i		0
29.15		0		0.332725	−	0.0759423i		0		2.09391	−	0.784566i		0		−2.62035	−	0.365762i		0		−2.59797	+	1.25112i		0
29.16		0		0.441575	−	0.100787i		0		−0.388188	−	2.20211i		0		−1.86214	−	1.87948i		0		−2.51808	+	1.21264i		0
29.17		0		0.622220	−	0.142018i		0		−0.375399	+	2.20433i		0		2.58484	−	0.564461i		0		−2.33592	+	1.12492i		0
29.18		0		0.631234	−	0.144075i		0		1.39490	−	1.74764i		0		−1.64972	+	2.06843i		0		−2.32521	+	1.11976i		0
29.19		0		0.984698	−	0.224751i		0		1.83675	+	1.27529i		0		2.10132	+	1.60762i		0		−1.78379	+	0.859028i		0
29.20		0		1.42811	−	0.325956i		0		−0.524117	+	2.17378i		0		−1.54156	+	2.15025i		0		−0.769660	+	0.370649i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
49.e	even	7	1	inner
245.p	even	14	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	980.2.bd.a	✓	168
5.b	even	2	1	inner	980.2.bd.a	✓	168
49.e	even	7	1	inner	980.2.bd.a	✓	168
245.p	even	14	1	inner	980.2.bd.a	✓	168

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
980.2.bd.a	✓	168	1.a	even	1	1	trivial
980.2.bd.a	✓	168	5.b	even	2	1	inner
980.2.bd.a	✓	168	49.e	even	7	1	inner
980.2.bd.a	✓	168	245.p	even	14	1	inner

Hecke kernels

This newform subspace is the entire newspace $S_{2}^{\mathrm{new}}(980, [\chi])$.