Newform orbit 945.2.cu.a

• Label: 945.2.cu.a
• Level: $945$
• Weight: $2$
• Character orbit: 945.cu
• Analytic conductor: $7.546$
• Analytic rank: $0$
• Dimension: $840$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.cu (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.54586299101\)
Analytic rank:	\(0\)
Dimension:	\(840\)
Relative dimension:	\(140\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 840 q - 6 q^{4} - 3 q^{5} - 30 q^{6} - 12 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
184.1	−2.71112	+	0.478044i	−0.201760	−	1.72026i	5.24226	−	1.90803i	0.349151	+	2.20864i	1.36935	+	4.56738i	−2.30650	−	1.29616i	−8.53204	+	4.92598i	−2.91859	+	0.694158i	−2.00242	−	5.82098i
184.2	−2.70699	+	0.477315i	−1.56857	−	0.734565i	5.22056	−	1.90013i	1.75959	−	1.37980i	4.59672	+	1.23976i	2.46388	−	0.963994i	−8.46407	+	4.88673i	1.92083	+	2.30443i	−4.10460	+	4.57497i
184.3	−2.69409	+	0.475040i	1.61345	+	0.629916i	5.15306	−	1.87556i	−1.75366	−	1.38732i	−4.64600	−	0.930597i	−0.532144	+	2.59168i	−8.25356	+	4.76519i	2.20641	+	2.03267i	5.38356	+	2.90451i
184.4	−2.64592	+	0.466547i	1.60085	−	0.661270i	4.90383	−	1.78485i	1.90488	+	1.17108i	−3.92720	+	2.49654i	1.75866	+	1.97664i	−7.48885	+	4.32369i	2.12544	−	2.11719i	−5.58652	−	2.20987i
184.5	−2.64551	+	0.466475i	−1.06734	+	1.36410i	4.90175	−	1.78409i	−1.15556	+	1.91434i	2.18734	−	4.10664i	2.29097	+	1.32343i	−7.48256	+	4.32006i	−0.721563	−	2.91193i	2.16405	−	5.60344i
184.6	−2.62025	+	0.462021i	0.582279	−	1.63124i	4.77286	−	1.73718i	−1.33552	−	1.79343i	−0.772048	+	4.54329i	1.46278	−	2.20460i	−7.09506	+	4.09633i	−2.32190	−	1.89968i	4.32799	+	4.08220i
184.7	−2.50592	+	0.441861i	−0.779054	+	1.54696i	4.20500	−	1.53049i	0.512783	−	2.17648i	1.26871	−	4.22078i	−0.836868	−	2.50991i	−5.45378	+	3.14874i	−1.78615	−	2.41033i	−0.323292	+	5.68065i
184.8	−2.49729	+	0.440340i	1.69666	+	0.348328i	4.16318	−	1.51527i	−1.05146	+	1.97343i	−4.39044	−	0.122767i	0.787260	−	2.52591i	−5.33726	+	3.08147i	2.75734	+	1.18199i	1.75683	−	5.39123i
184.9	−2.49193	+	0.439395i	1.41177	+	1.00345i	4.13728	−	1.50585i	1.74254	−	1.40127i	−3.95895	−	1.88020i	−2.57807	−	0.594612i	−5.26542	+	3.03999i	0.986188	+	2.83327i	−3.72657	+	4.25754i
184.10	−2.45779	+	0.433376i	0.0166227	+	1.73197i	3.97356	−	1.44626i	2.00683	+	0.986228i	−0.791449	−	4.24963i	−1.32492	+	2.29011i	−4.81672	+	2.78093i	−2.99945	+	0.0575802i	−5.35978	−	1.55424i
184.11	−2.43845	+	0.429965i	−1.72287	+	0.178073i	3.88180	−	1.41286i	2.23587	−	0.0295829i	4.12458	−	1.17500i	−1.39126	+	2.25042i	−4.56943	+	2.63816i	2.93658	−	0.613595i	−5.43935	+	1.03348i
184.12	−2.41271	+	0.425426i	−0.145298	−	1.72595i	3.76080	−	1.36882i	1.38689	−	1.75400i	1.08482	+	4.10239i	−1.69036	+	2.03536i	−4.24799	+	2.45258i	−2.95778	+	0.501553i	−2.59998	+	4.82192i
184.13	−2.37646	+	0.419034i	0.523015	+	1.65120i	3.59258	−	1.30759i	−1.76383	−	1.37438i	−1.93483	−	3.70484i	2.45782	−	0.979353i	−3.81005	+	2.19973i	−2.45291	+	1.72720i	4.76757	+	2.52705i
184.14	−2.37632	+	0.419009i	0.500519	+	1.65816i	3.59194	−	1.30736i	−1.30052	+	1.81897i	−1.88418	−	3.73058i	−2.62469	−	0.333171i	−3.80839	+	2.19878i	−2.49896	+	1.65988i	2.32828	−	4.86738i
184.15	−2.37335	+	0.418486i	−0.975219	−	1.43141i	3.57830	−	1.30239i	−2.23596	+	0.0223456i	2.91357	+	2.98914i	1.42846	+	2.22700i	−3.77334	+	2.17854i	−1.09790	+	2.79188i	5.29737	−	0.988751i
184.16	−2.24609	+	0.396046i	−1.43438	−	0.970850i	3.00869	−	1.09507i	0.726792	+	2.11466i	3.60625	+	1.61254i	2.21095	−	1.45317i	−2.37372	+	1.37047i	1.11490	+	2.78514i	−2.46994	−	4.46187i
184.17	−2.23721	+	0.394480i	1.31534	−	1.12689i	2.97010	−	1.08103i	−2.09927	−	0.770112i	−2.49816	+	3.03995i	−2.47152	−	0.944249i	−2.28355	+	1.31841i	0.460258	−	2.96448i	5.00029	+	0.894781i
184.18	−2.21032	+	0.389738i	−1.66360	+	0.482108i	2.85421	−	1.03885i	−2.12967	+	0.681541i	3.48919	−	1.71398i	0.437619	−	2.60931i	−2.01639	+	1.16417i	2.53514	−	1.60407i	4.44162	−	2.33644i
184.19	−2.18389	+	0.385079i	1.41453	−	0.999550i	2.74172	−	0.997906i	2.21881	+	0.277302i	−2.70428	+	2.72762i	−1.08591	−	2.41263i	−1.76239	+	1.01752i	1.00180	−	2.82779i	−4.95242	+	0.248818i
184.20	−2.12166	+	0.374106i	1.16633	−	1.28050i	2.48210	−	0.903409i	0.603468	−	2.15310i	−1.99552	+	3.15311i	1.33031	+	2.28698i	−1.19668	+	0.690903i	−0.279337	−	2.98697i	−0.474868	+	4.79390i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
189.w	even	9	1	inner
945.cu	even	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	945.2.cu.a	✓	840
5.b	even	2	1	inner	945.2.cu.a	✓	840
7.c	even	3	1		945.2.db.a	yes	840
27.e	even	9	1		945.2.db.a	yes	840
35.j	even	6	1		945.2.db.a	yes	840
135.p	even	18	1		945.2.db.a	yes	840
189.w	even	9	1	inner	945.2.cu.a	✓	840
945.cu	even	18	1	inner	945.2.cu.a	✓	840

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
945.2.cu.a	✓	840	1.a	even	1	1	trivial
945.2.cu.a	✓	840	5.b	even	2	1	inner
945.2.cu.a	✓	840	189.w	even	9	1	inner
945.2.cu.a	✓	840	945.cu	even	18	1	inner
945.2.db.a	yes	840	7.c	even	3	1
945.2.db.a	yes	840	27.e	even	9	1
945.2.db.a	yes	840	35.j	even	6	1
945.2.db.a	yes	840	135.p	even	18	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(945, [\chi])\).