Newform orbit 150.3.i.a

• Label: 150.3.i.a
• Level: $150$
• Weight: $3$
• Character orbit: 150.i
• Analytic conductor: $4.087$
• Analytic rank: $0$
• Dimension: $80$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	150.i (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.08720396540\)
Analytic rank:	\(0\)
Dimension:	\(80\)
Relative dimension:	\(20\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 80 q - 40 q^{4} + 20 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
29.1	−0.437016	+	1.34500i	−2.95317	+	0.527988i	−1.61803	−	1.17557i	4.87810	+	1.09731i	0.580441	−	4.20275i			10.6357i	2.28825	−	1.66251i	8.44246	−	3.11848i	−3.60769	+	6.08149i
29.2	−0.437016	+	1.34500i	−2.88702	−	0.815530i	−1.61803	−	1.17557i	−1.13734	+	4.86893i	2.35856	−	3.52664i		−	10.7444i	2.28825	−	1.66251i	7.66982	+	4.70891i	−6.05166	−	3.65752i
29.3	−0.437016	+	1.34500i	−2.70555	−	1.29615i	−1.61803	−	1.17557i	−2.68239	−	4.21957i	2.92568	−	3.07252i			8.88015i	2.28825	−	1.66251i	5.64000	+	7.01359i	6.84756	−	1.76378i
29.4	−0.437016	+	1.34500i	−1.99435	+	2.24110i	−1.61803	−	1.17557i	2.92277	−	4.05678i	−2.14271	−	3.66180i		−	10.3258i	2.28825	−	1.66251i	−1.04510	−	8.93911i	4.17905	+	5.70399i
29.5	−0.437016	+	1.34500i	−0.0352727	−	2.99979i	−1.61803	−	1.17557i	−4.11716	+	2.83707i	4.05013	+	1.26352i			2.70868i	2.28825	−	1.66251i	−8.99751	+	0.211621i	−2.01659	−	6.77742i
29.6	−0.437016	+	1.34500i	−0.0189915	+	2.99994i	−1.61803	−	1.17557i	−4.54494	−	2.08411i	−4.02661	−	1.33657i			1.94466i	2.28825	−	1.66251i	−8.99928	−	0.113946i	4.78934	−	5.20214i
29.7	−0.437016	+	1.34500i	1.95554	−	2.27505i	−1.61803	−	1.17557i	4.48538	+	2.20939i	2.20534	+	3.62443i			0.464101i	2.28825	−	1.66251i	−1.35173	−	8.89791i	−4.93180	+	5.06728i
29.8	−0.437016	+	1.34500i	2.11142	+	2.13118i	−1.61803	−	1.17557i	−0.399233	+	4.98404i	−3.78915	+	1.90849i		−	0.905152i	2.28825	−	1.66251i	−0.0838289	+	8.99961i	−6.52904	−	2.71507i
29.9	−0.437016	+	1.34500i	2.48265	+	1.68417i	−1.61803	−	1.17557i	3.26810	−	3.78412i	−3.35017	+	2.60315i			7.29758i	2.28825	−	1.66251i	3.32712	+	8.36243i	3.66142	+	6.04930i
29.10	−0.437016	+	1.34500i	2.92672	−	0.659017i	−1.61803	−	1.17557i	−4.08750	−	2.87964i	−0.392649	+	4.22443i		−	12.3067i	2.28825	−	1.66251i	8.13139	−	3.85752i	5.65941	−	4.23923i
29.11	0.437016	−	1.34500i	−2.84724	+	0.945094i	−1.61803	−	1.17557i	4.54494	+	2.08411i	0.0268580	+	4.24256i			1.94466i	−2.28825	+	1.66251i	7.21359	−	5.38183i	4.78934	−	5.20214i
29.12	0.437016	−	1.34500i	−2.67933	−	1.34951i	−1.61803	−	1.17557i	0.399233	−	4.98404i	−2.98600	+	3.01394i		−	0.905152i	−2.28825	+	1.66251i	5.35766	+	7.23156i	−6.52904	−	2.71507i
29.13	0.437016	−	1.34500i	−2.36893	−	1.84070i	−1.61803	−	1.17557i	−3.26810	+	3.78412i	−3.51100	+	2.38178i			7.29758i	−2.28825	+	1.66251i	2.22361	+	8.72098i	3.66142	+	6.04930i
29.14	0.437016	−	1.34500i	−1.51513	+	2.58928i	−1.61803	−	1.17557i	−2.92277	+	4.05678i	2.82044	+	3.16940i		−	10.3258i	−2.28825	+	1.66251i	−4.40877	−	7.84619i	4.17905	+	5.70399i
29.15	0.437016	−	1.34500i	−0.277644	−	2.98712i	−1.61803	−	1.17557i	4.08750	+	2.87964i	−4.13901	−	0.931990i		−	12.3067i	−2.28825	+	1.66251i	−8.84583	+	1.65872i	5.65941	−	4.23923i
29.16	0.437016	−	1.34500i	0.410434	+	2.97179i	−1.61803	−	1.17557i	−4.87810	−	1.09731i	4.17642	+	0.746688i			10.6357i	−2.28825	+	1.66251i	−8.66309	+	2.43945i	−3.60769	+	6.08149i
29.17	0.437016	−	1.34500i	1.55941	−	2.56286i	−1.61803	−	1.17557i	−4.48538	−	2.20939i	−2.76555	−	3.21741i			0.464101i	−2.28825	+	1.66251i	−4.13649	−	7.99309i	−4.93180	+	5.06728i
29.18	0.437016	−	1.34500i	1.66776	+	2.49371i	−1.61803	−	1.17557i	1.13734	−	4.86893i	4.08287	−	1.15333i		−	10.7444i	−2.28825	+	1.66251i	−3.43719	+	8.31780i	−6.05166	−	3.65752i
29.19	0.437016	−	1.34500i	2.06877	+	2.17260i	−1.61803	−	1.17557i	2.68239	+	4.21957i	3.82622	−	1.83303i			8.88015i	−2.28825	+	1.66251i	−0.440370	+	8.98922i	6.84756	−	1.76378i
29.20	0.437016	−	1.34500i	2.86387	−	0.893441i	−1.61803	−	1.17557i	4.11716	−	2.83707i	0.0498831	−	4.24235i			2.70868i	−2.28825	+	1.66251i	7.40353	−	5.11740i	−2.01659	−	6.77742i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
25.e	even	10	1	inner
75.h	odd	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	150.3.i.a	✓	80
3.b	odd	2	1	inner	150.3.i.a	✓	80
25.e	even	10	1	inner	150.3.i.a	✓	80
75.h	odd	10	1	inner	150.3.i.a	✓	80

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
150.3.i.a	✓	80	1.a	even	1	1	trivial
150.3.i.a	✓	80	3.b	odd	2	1	inner
150.3.i.a	✓	80	25.e	even	10	1	inner
150.3.i.a	✓	80	75.h	odd	10	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(150, [\chi])\).