Newform orbit 270.3.o.a

• Label: 270.3.o.a
• Level: $270$
• Weight: $3$
• Character orbit: 270.o
• Analytic conductor: $7.357$
• Analytic rank: $0$
• Dimension: $144$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	270.o (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.35696713773\)
Analytic rank:	\(0\)
Dimension:	\(144\)
Relative dimension:	\(24\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 144 q - 12 q^{6} + 12 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
11.1	−0.909039	+	1.08335i	−2.93678	−	0.612626i	−0.347296	−	1.96962i	0.764780	−	2.10122i	3.33334	−	2.62466i	0.0495203	−	0.280843i	2.44949	+	1.41421i	8.24938	+	3.59830i	1.58114	+	2.73861i
11.2	−0.909039	+	1.08335i	−2.83320	+	0.986392i	−0.347296	−	1.96962i	−0.764780	+	2.10122i	1.50688	−	3.96602i	1.48752	−	8.43615i	2.44949	+	1.41421i	7.05406	−	5.58929i	−1.58114	−	2.73861i
11.3	−0.909039	+	1.08335i	−2.68781	−	1.33254i	−0.347296	−	1.96962i	−0.764780	+	2.10122i	3.88693	−	1.70051i	−0.412516	+	2.33949i	2.44949	+	1.41421i	5.44867	+	7.16324i	−1.58114	−	2.73861i
11.4	−0.909039	+	1.08335i	−1.90490	+	2.31762i	−0.347296	−	1.96962i	0.764780	−	2.10122i	−0.779161	−	4.17048i	−0.438855	+	2.48887i	2.44949	+	1.41421i	−1.74270	−	8.82967i	1.58114	+	2.73861i
11.5	−0.909039	+	1.08335i	−1.34040	+	2.68390i	−0.347296	−	1.96962i	−0.764780	+	2.10122i	−1.68914	−	3.89189i	−1.75836	+	9.97218i	2.44949	+	1.41421i	−5.40668	−	7.19498i	−1.58114	−	2.73861i
11.6	−0.909039	+	1.08335i	−0.959500	−	2.84242i	−0.347296	−	1.96962i	0.764780	−	2.10122i	3.95156	+	1.54440i	−1.57222	+	8.91648i	2.44949	+	1.41421i	−7.15872	+	5.45460i	1.58114	+	2.73861i
11.7	−0.909039	+	1.08335i	−0.352338	−	2.97924i	−0.347296	−	1.96962i	−0.764780	+	2.10122i	3.54785	+	2.32654i	−0.871340	+	4.94162i	2.44949	+	1.41421i	−8.75172	+	2.09940i	−1.58114	−	2.73861i
11.8	−0.909039	+	1.08335i	0.568194	+	2.94570i	−0.347296	−	1.96962i	0.764780	−	2.10122i	−3.70774	−	2.06220i	0.715686	−	4.05886i	2.44949	+	1.41421i	−8.35431	+	3.34746i	1.58114	+	2.73861i
11.9	−0.909039	+	1.08335i	1.25636	−	2.72425i	−0.347296	−	1.96962i	0.764780	−	2.10122i	1.80924	+	3.83753i	1.06651	−	6.04848i	2.44949	+	1.41421i	−5.84311	−	6.84529i	1.58114	+	2.73861i
11.10	−0.909039	+	1.08335i	2.46914	−	1.70392i	−0.347296	−	1.96962i	−0.764780	+	2.10122i	−0.398600	+	4.22387i	0.704886	−	3.99761i	2.44949	+	1.41421i	3.19330	−	8.41444i	−1.58114	−	2.73861i
11.11	−0.909039	+	1.08335i	2.62867	+	1.44571i	−0.347296	−	1.96962i	−0.764780	+	2.10122i	−3.95578	+	1.53357i	−0.950184	+	5.38876i	2.44949	+	1.41421i	4.81985	+	7.60060i	−1.58114	−	2.73861i
11.12	−0.909039	+	1.08335i	2.76211	+	1.17079i	−0.347296	−	1.96962i	0.764780	−	2.10122i	−3.77924	+	1.92804i	1.47540	−	8.36743i	2.44949	+	1.41421i	6.25849	+	6.46771i	1.58114	+	2.73861i
11.13	0.909039	−	1.08335i	−2.81378	+	1.04050i	−0.347296	−	1.96962i	−0.764780	+	2.10122i	−1.43061	+	3.99416i	−0.415662	+	2.35733i	−2.44949	−	1.41421i	6.83473	−	5.85547i	1.58114	+	2.73861i
11.14	0.909039	−	1.08335i	−2.77069	−	1.15033i	−0.347296	−	1.96962i	−0.764780	+	2.10122i	−3.76488	+	1.95593i	2.20716	−	12.5174i	−2.44949	−	1.41421i	6.35346	+	6.37444i	1.58114	+	2.73861i
11.15	0.909039	−	1.08335i	−2.56486	+	1.55611i	−0.347296	−	1.96962i	0.764780	−	2.10122i	−0.645745	+	4.19321i	−1.72161	+	9.76375i	−2.44949	−	1.41421i	4.15703	−	7.98242i	−1.58114	−	2.73861i
11.16	0.909039	−	1.08335i	−1.68760	−	2.48032i	−0.347296	−	1.96962i	−0.764780	+	2.10122i	−4.22115	−	0.426446i	−2.08160	+	11.8053i	−2.44949	−	1.41421i	−3.30400	+	8.37159i	1.58114	+	2.73861i
11.17	0.909039	−	1.08335i	−0.780619	−	2.89666i	−0.347296	−	1.96962i	0.764780	−	2.10122i	−3.84771	−	1.78749i	0.876165	−	4.96898i	−2.44949	−	1.41421i	−7.78127	+	4.52237i	−1.58114	−	2.73861i
11.18	0.909039	−	1.08335i	−0.723894	+	2.91135i	−0.347296	−	1.96962i	0.764780	−	2.10122i	2.49597	+	3.43076i	1.23886	−	7.02591i	−2.44949	−	1.41421i	−7.95196	−	4.21502i	−1.58114	−	2.73861i
11.19	0.909039	−	1.08335i	−0.524408	+	2.95381i	−0.347296	−	1.96962i	−0.764780	+	2.10122i	2.72330	+	3.25325i	−0.390677	+	2.21564i	−2.44949	−	1.41421i	−8.44999	−	3.09800i	1.58114	+	2.73861i
11.20	0.909039	−	1.08335i	1.47721	+	2.61110i	−0.347296	−	1.96962i	0.764780	−	2.10122i	4.17158	+	0.773252i	−1.92096	+	10.8943i	−2.44949	−	1.41421i	−4.63568	+	7.71430i	−1.58114	−	2.73861i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
27.f	odd	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	270.3.o.a	✓	144
27.f	odd	18	1	inner	270.3.o.a	✓	144

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
270.3.o.a	✓	144	1.a	even	1	1	trivial
270.3.o.a	✓	144	27.f	odd	18	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(270, [\chi])\).