Newform orbit 805.2.k.a

• Label: 805.2.k.a
• Level: $805$
• Weight: $2$
• Character orbit: 805.k
• Analytic conductor: $6.428$
• Analytic rank: $0$
• Dimension: $176$
• CM: no
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(6.42795736271\)
Analytic rank:	\(0\)
Dimension:	\(176\)
Relative dimension:	\(88\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 176 q - 8 q^{7} + 24 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
622.1	−1.94711	−	1.94711i	−1.74100	−	1.74100i			5.58247i	−0.543285	−	2.16906i			6.77985i	1.94567	−	1.79286i	6.97545	−	6.97545i			3.06218i	−3.16557	+	5.28124i
622.2	−1.94711	−	1.94711i	1.74100	+	1.74100i			5.58247i	0.543285	+	2.16906i		−	6.77985i	−1.79286	+	1.94567i	6.97545	−	6.97545i			3.06218i	3.16557	−	5.28124i
622.3	−1.94696	−	1.94696i	−1.15185	−	1.15185i			5.58133i	2.23568	+	0.0417180i			4.48523i	0.569254	+	2.58379i	6.97273	−	6.97273i		−	0.346466i	−4.27156	−	4.43401i
622.4	−1.94696	−	1.94696i	1.15185	+	1.15185i			5.58133i	−2.23568	−	0.0417180i		−	4.48523i	2.58379	+	0.569254i	6.97273	−	6.97273i		−	0.346466i	4.27156	+	4.43401i
622.5	−1.75686	−	1.75686i	−0.312785	−	0.312785i			4.17309i	2.21261	−	0.323041i			1.09904i	−1.53264	−	2.15662i	3.81781	−	3.81781i		−	2.80433i	−4.45478	−	3.31970i
622.6	−1.75686	−	1.75686i	0.312785	+	0.312785i			4.17309i	−2.21261	+	0.323041i		−	1.09904i	−2.15662	−	1.53264i	3.81781	−	3.81781i		−	2.80433i	4.45478	+	3.31970i
622.7	−1.71539	−	1.71539i	−1.62440	−	1.62440i			3.88514i	−1.74980	+	1.39219i			5.57296i	1.18340	−	2.36634i	3.23375	−	3.23375i			2.27734i	5.38975	+	0.613435i
622.8	−1.71539	−	1.71539i	1.62440	+	1.62440i			3.88514i	1.74980	−	1.39219i		−	5.57296i	−2.36634	+	1.18340i	3.23375	−	3.23375i			2.27734i	−5.38975	−	0.613435i
622.9	−1.67567	−	1.67567i	−0.762267	−	0.762267i			3.61575i	−1.75388	−	1.38705i			2.55462i	−1.86652	+	1.87513i	2.70748	−	2.70748i		−	1.83790i	0.614686	+	5.26317i
622.10	−1.67567	−	1.67567i	0.762267	+	0.762267i			3.61575i	1.75388	+	1.38705i		−	2.55462i	1.87513	−	1.86652i	2.70748	−	2.70748i		−	1.83790i	−0.614686	−	5.26317i
622.11	−1.66627	−	1.66627i	−1.13838	−	1.13838i			3.55292i	−0.424355	+	2.19543i			3.79371i	1.16798	+	2.37399i	2.58759	−	2.58759i		−	0.408167i	4.36528	−	2.95110i
622.12	−1.66627	−	1.66627i	1.13838	+	1.13838i			3.55292i	0.424355	−	2.19543i		−	3.79371i	2.37399	+	1.16798i	2.58759	−	2.58759i		−	0.408167i	−4.36528	+	2.95110i
622.13	−1.63134	−	1.63134i	−2.27963	−	2.27963i			3.32251i	1.03343	+	1.98293i			7.43769i	−2.57959	−	0.587970i	2.15746	−	2.15746i			7.39345i	1.54895	−	4.92070i
622.14	−1.63134	−	1.63134i	2.27963	+	2.27963i			3.32251i	−1.03343	−	1.98293i		−	7.43769i	−0.587970	−	2.57959i	2.15746	−	2.15746i			7.39345i	−1.54895	+	4.92070i
622.15	−1.49985	−	1.49985i	−1.75798	−	1.75798i			2.49908i	−0.277450	−	2.21879i			5.27339i	−2.59761	−	0.502421i	0.748540	−	0.748540i			3.18096i	−2.91171	+	3.74397i
622.16	−1.49985	−	1.49985i	1.75798	+	1.75798i			2.49908i	0.277450	+	2.21879i		−	5.27339i	−0.502421	−	2.59761i	0.748540	−	0.748540i			3.18096i	2.91171	−	3.74397i
622.17	−1.38496	−	1.38496i	−0.480524	−	0.480524i			1.83622i	1.23711	−	1.86267i			1.33101i	2.50331	−	0.856408i	−0.226832	+	0.226832i		−	2.53819i	−4.29307	+	0.866381i
622.18	−1.38496	−	1.38496i	0.480524	+	0.480524i			1.83622i	−1.23711	+	1.86267i		−	1.33101i	−0.856408	+	2.50331i	−0.226832	+	0.226832i		−	2.53819i	4.29307	−	0.866381i
622.19	−1.27667	−	1.27667i	−2.27147	−	2.27147i			1.25980i	1.59940	−	1.56266i			5.79986i	1.29479	+	2.30728i	−0.944998	+	0.944998i			7.31917i	−4.03693	−	0.0469070i
622.20	−1.27667	−	1.27667i	2.27147	+	2.27147i			1.25980i	−1.59940	+	1.56266i		−	5.79986i	2.30728	+	1.29479i	−0.944998	+	0.944998i			7.31917i	4.03693	+	0.0469070i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
7.b	odd	2	1	inner
35.f	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.k.a	✓	176
5.c	odd	4	1	inner	805.2.k.a	✓	176
7.b	odd	2	1	inner	805.2.k.a	✓	176
35.f	even	4	1	inner	805.2.k.a	✓	176

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
805.2.k.a	✓	176	1.a	even	1	1	trivial
805.2.k.a	✓	176	5.c	odd	4	1	inner
805.2.k.a	✓	176	7.b	odd	2	1	inner
805.2.k.a	✓	176	35.f	even	4	1	inner

Hecke kernels

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