Newform orbit 805.2.l.a

• Label: 805.2.l.a
• Level: $805$
• Weight: $2$
• Character orbit: 805.l
• Analytic conductor: $6.428$
• Analytic rank: $0$
• Dimension: $144$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.42795736271\)
Analytic rank:	\(0\)
Dimension:	\(144\)
Relative dimension:	\(72\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 144 q + 8 q^{3} - 16 q^{6}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
22.1	−1.98362	−	1.98362i	1.42454	−	1.42454i			5.86953i	−1.24587	−	1.85682i	−5.65151			0.707107	−	0.707107i	7.67570	−	7.67570i		−	1.05864i	−1.21190	+	6.15459i
22.2	−1.98362	−	1.98362i	1.42454	−	1.42454i			5.86953i	1.24587	+	1.85682i	−5.65151			−0.707107	+	0.707107i	7.67570	−	7.67570i		−	1.05864i	1.21190	−	6.15459i
22.3	−1.86964	−	1.86964i	−1.61024	+	1.61024i			4.99109i	−1.86179	+	1.23845i	6.02111			−0.707107	+	0.707107i	5.59225	−	5.59225i		−	2.18572i	5.79631	+	1.16541i
22.4	−1.86964	−	1.86964i	−1.61024	+	1.61024i			4.99109i	1.86179	−	1.23845i	6.02111			0.707107	−	0.707107i	5.59225	−	5.59225i		−	2.18572i	−5.79631	−	1.16541i
22.5	−1.83662	−	1.83662i	−0.379823	+	0.379823i			4.74636i	−1.45047	+	1.70180i	1.39518			0.707107	−	0.707107i	5.04402	−	5.04402i			2.71147i	5.78954	−	0.461590i
22.6	−1.83662	−	1.83662i	−0.379823	+	0.379823i			4.74636i	1.45047	−	1.70180i	1.39518			−0.707107	+	0.707107i	5.04402	−	5.04402i			2.71147i	−5.78954	+	0.461590i
22.7	−1.60576	−	1.60576i	0.871410	−	0.871410i			3.15695i	−2.02341	+	0.951750i	−2.79856			0.707107	−	0.707107i	1.85780	−	1.85780i			1.48129i	4.77740	+	1.72083i
22.8	−1.60576	−	1.60576i	0.871410	−	0.871410i			3.15695i	2.02341	−	0.951750i	−2.79856			−0.707107	+	0.707107i	1.85780	−	1.85780i			1.48129i	−4.77740	−	1.72083i
22.9	−1.59754	−	1.59754i	2.27399	−	2.27399i			3.10428i	−2.19447	−	0.429310i	−7.26558			−0.707107	+	0.707107i	1.76414	−	1.76414i		−	7.34202i	2.81992	+	4.19160i
22.10	−1.59754	−	1.59754i	2.27399	−	2.27399i			3.10428i	2.19447	+	0.429310i	−7.26558			0.707107	−	0.707107i	1.76414	−	1.76414i		−	7.34202i	−2.81992	−	4.19160i
22.11	−1.46985	−	1.46985i	1.77687	−	1.77687i			2.32090i	−0.533967	+	2.17138i	−5.22345			0.707107	−	0.707107i	0.471674	−	0.471674i		−	3.31453i	3.97644	−	2.40674i
22.12	−1.46985	−	1.46985i	1.77687	−	1.77687i			2.32090i	0.533967	−	2.17138i	−5.22345			−0.707107	+	0.707107i	0.471674	−	0.471674i		−	3.31453i	−3.97644	+	2.40674i
22.13	−1.46882	−	1.46882i	−2.33093	+	2.33093i			2.31485i	−0.350000	−	2.20851i	6.84742			−0.707107	+	0.707107i	0.462459	−	0.462459i		−	7.86647i	−2.72981	+	3.75798i
22.14	−1.46882	−	1.46882i	−2.33093	+	2.33093i			2.31485i	0.350000	+	2.20851i	6.84742			0.707107	−	0.707107i	0.462459	−	0.462459i		−	7.86647i	2.72981	−	3.75798i
22.15	−1.44201	−	1.44201i	0.110138	−	0.110138i			2.15879i	−0.378849	−	2.20374i	−0.317641			0.707107	−	0.707107i	0.228977	−	0.228977i			2.97574i	−2.63151	+	3.72412i
22.16	−1.44201	−	1.44201i	0.110138	−	0.110138i			2.15879i	0.378849	+	2.20374i	−0.317641			−0.707107	+	0.707107i	0.228977	−	0.228977i			2.97574i	2.63151	−	3.72412i
22.17	−1.13928	−	1.13928i	0.402331	−	0.402331i			0.595896i	−2.20214	−	0.388024i	−0.916732			−0.707107	+	0.707107i	−1.59966	+	1.59966i			2.67626i	2.06678	+	2.95091i
22.18	−1.13928	−	1.13928i	0.402331	−	0.402331i			0.595896i	2.20214	+	0.388024i	−0.916732			0.707107	−	0.707107i	−1.59966	+	1.59966i			2.67626i	−2.06678	−	2.95091i
22.19	−1.12953	−	1.12953i	−1.49782	+	1.49782i			0.551658i	−1.77441	+	1.36069i	3.38366			−0.707107	+	0.707107i	−1.63594	+	1.63594i		−	1.48695i	3.54117	+	0.467305i
22.20	−1.12953	−	1.12953i	−1.49782	+	1.49782i			0.551658i	1.77441	−	1.36069i	3.38366			0.707107	−	0.707107i	−1.63594	+	1.63594i		−	1.48695i	−3.54117	−	0.467305i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
23.b	odd	2	1	inner
115.e	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	805.2.l.a	✓	144
5.c	odd	4	1	inner	805.2.l.a	✓	144
23.b	odd	2	1	inner	805.2.l.a	✓	144
115.e	even	4	1	inner	805.2.l.a	✓	144

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
805.2.l.a	✓	144	1.a	even	1	1	trivial
805.2.l.a	✓	144	5.c	odd	4	1	inner
805.2.l.a	✓	144	23.b	odd	2	1	inner
805.2.l.a	✓	144	115.e	even	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(805, [\chi])\).