Newform orbit 189.3.k.a

• Label: 189.3.k.a
• Level: $189$
• Weight: $3$
• Character orbit: 189.k
• Analytic conductor: $5.150$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	189.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.14987699641\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Relative dimension:	\(14\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 63)
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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q - q^{2} - 23 q^{4} + 16 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
10.1	−1.91801	+	3.32210i		0		−5.35756	−	9.27956i			0.216546i		0		6.73498	−	1.90790i	25.7594				0		−0.719386	−	0.415338i
10.2	−1.62718	+	2.81835i		0		−3.29541	−	5.70782i		−	3.39483i		0		−6.91332	−	1.09817i	8.43145				0		9.56782	+	5.52398i
10.3	−1.41697	+	2.45427i		0		−2.01561	−	3.49114i		−	2.39855i		0		0.0107242	+	6.99999i	0.0884848				0		5.88667	+	3.39867i
10.4	−0.902282	+	1.56280i		0		0.371774	+	0.643931i			5.75495i		0		6.44289	+	2.73664i	−8.56004				0		−8.99383	−	5.19259i
10.5	−0.826674	+	1.43184i		0		0.633221	+	1.09677i			7.86923i		0		−5.81886	−	3.89113i	−8.70726				0		−11.2675	−	6.50529i
10.6	−0.662399	+	1.14731i		0		1.12246	+	1.94415i		−	7.23514i		0		−3.90816	−	5.80744i	−8.27324				0		8.30093	+	4.79254i
10.7	−0.198068	+	0.343064i		0		1.92154	+	3.32820i		−	2.97240i		0		2.98301	−	6.33259i	−3.10693				0		1.01972	+	0.588737i
10.8	0.178911	−	0.309883i		0		1.93598	+	3.35322i			4.59004i		0		−6.01934	+	3.57317i	2.81677				0		1.42238	+	0.821210i
10.9	0.227576	−	0.394173i		0		1.89642	+	3.28469i		−	4.37081i		0		5.22047	+	4.66334i	3.54692				0		−1.72285	−	0.994690i
10.10	0.840995	−	1.45665i		0		0.585454	+	1.01404i			2.34462i		0		−3.93446	+	5.78964i	8.69742				0		3.41529	+	1.97182i
10.11	1.12025	−	1.94033i		0		−0.509909	−	0.883189i		−	1.93444i		0		3.87064	−	5.83251i	6.67708				0		−3.75345	−	2.16706i
10.12	1.32841	−	2.30087i		0		−1.52933	−	2.64888i			9.20400i		0		6.96620	+	0.687028i	2.50096				0		21.1772	+	12.2267i
10.13	1.67756	−	2.90562i		0		−3.62842	−	6.28461i		−	0.888628i		0		−3.29335	−	6.17688i	−10.9271				0		−2.58202	−	1.49073i
10.14	1.67789	−	2.90618i		0		−3.63061	−	6.28839i		−	8.51666i		0		−2.34142	+	6.59680i	−10.9439				0		−24.7510	−	14.2900i
19.1	−1.91801	−	3.32210i		0		−5.35756	+	9.27956i		−	0.216546i		0		6.73498	+	1.90790i	25.7594				0		−0.719386	+	0.415338i
19.2	−1.62718	−	2.81835i		0		−3.29541	+	5.70782i			3.39483i		0		−6.91332	+	1.09817i	8.43145				0		9.56782	−	5.52398i
19.3	−1.41697	−	2.45427i		0		−2.01561	+	3.49114i			2.39855i		0		0.0107242	−	6.99999i	0.0884848				0		5.88667	−	3.39867i
19.4	−0.902282	−	1.56280i		0		0.371774	−	0.643931i		−	5.75495i		0		6.44289	−	2.73664i	−8.56004				0		−8.99383	+	5.19259i
19.5	−0.826674	−	1.43184i		0		0.633221	−	1.09677i		−	7.86923i		0		−5.81886	+	3.89113i	−8.70726				0		−11.2675	+	6.50529i
19.6	−0.662399	−	1.14731i		0		1.12246	−	1.94415i			7.23514i		0		−3.90816	+	5.80744i	−8.27324				0		8.30093	−	4.79254i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
63.k	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	189.3.k.a		28
3.b	odd	2	1		63.3.k.a	✓	28
7.d	odd	6	1		189.3.t.a		28
9.c	even	3	1		189.3.t.a		28
9.d	odd	6	1		63.3.t.a	yes	28
21.c	even	2	1		441.3.k.b		28
21.g	even	6	1		63.3.t.a	yes	28
21.g	even	6	1		441.3.l.b		28
21.h	odd	6	1		441.3.l.a		28
21.h	odd	6	1		441.3.t.a		28
63.i	even	6	1		441.3.l.a		28
63.j	odd	6	1		441.3.l.b		28
63.k	odd	6	1	inner	189.3.k.a		28
63.n	odd	6	1		441.3.k.b		28
63.o	even	6	1		441.3.t.a		28
63.s	even	6	1		63.3.k.a	✓	28

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
63.3.k.a	✓	28	3.b	odd	2	1
63.3.k.a	✓	28	63.s	even	6	1
63.3.t.a	yes	28	9.d	odd	6	1
63.3.t.a	yes	28	21.g	even	6	1
189.3.k.a		28	1.a	even	1	1	trivial
189.3.k.a		28	63.k	odd	6	1	inner
189.3.t.a		28	7.d	odd	6	1
189.3.t.a		28	9.c	even	3	1
441.3.k.b		28	21.c	even	2	1
441.3.k.b		28	63.n	odd	6	1
441.3.l.a		28	21.h	odd	6	1
441.3.l.a		28	63.i	even	6	1
441.3.l.b		28	21.g	even	6	1
441.3.l.b		28	63.j	odd	6	1
441.3.t.a		28	21.h	odd	6	1
441.3.t.a		28	63.o	even	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(189, [\chi])\).