Newform orbit 945.2.db.a

• Label: 945.2.db.a
• Level: $945$
• Weight: $2$
• Character orbit: 945.db
• 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.db (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.

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

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
4.1	−2.73450	+	0.482167i	0.102062	+	1.72904i	5.36564	−	1.95293i	1.89805	−	1.18212i	−1.11277	−	4.67886i	1.87683	−	1.86481i	−8.92135	+	5.15074i	−2.97917	+	0.352938i	−4.62024	+	4.14770i
4.2	−2.70434	+	0.476849i	1.37529	−	1.05289i	5.20670	−	1.89508i	−0.00312468	−	2.23607i	−3.21718	+	3.50319i	−2.62206	−	0.353240i	−8.42072	+	4.86171i	0.782835	−	2.89606i	1.07472	+	6.04560i
4.3	−2.68742	+	0.473864i	1.69820	−	0.340737i	5.11828	−	1.86290i	0.277764	+	2.21875i	−4.40232	+	1.72042i	2.01972	+	1.70901i	−8.14564	+	4.70289i	2.76780	−	1.15728i	−1.79785	−	5.83108i
4.4	−2.67522	+	0.471714i	−1.23636	−	1.21302i	5.05491	−	1.83984i	0.205095	+	2.22664i	3.87973	+	2.66188i	1.78149	−	1.95609i	−7.95002	+	4.58995i	0.0571742	+	2.99946i	−1.59901	−	5.86001i
4.5	−2.60005	+	0.458460i	−1.61487	+	0.626250i	4.67071	−	1.70000i	−2.06049	−	0.868553i	3.91164	−	2.36864i	0.330844	−	2.62498i	−6.79182	+	3.92126i	2.21562	−	2.02263i	5.75558	+	1.31363i
4.6	−2.54713	+	0.449127i	0.139169	−	1.72645i	4.40675	−	1.60393i	−1.64194	+	1.51790i	0.420916	+	4.45999i	−2.63808	+	0.201390i	−6.02437	+	3.47817i	−2.96126	−	0.480535i	3.50050	−	4.60373i
4.7	−2.54166	+	0.448163i	−1.33073	−	1.10867i	4.37979	−	1.59411i	−1.56015	−	1.60185i	3.87913	+	2.22148i	0.359162	+	2.62126i	−5.94732	+	3.43369i	0.541701	+	2.95069i	4.68327	+	3.37215i
4.8	−2.52967	+	0.446050i	−0.820794	+	1.52522i	4.32090	−	1.57268i	−1.82936	+	1.28587i	1.39602	−	4.22442i	1.27126	+	2.32032i	−5.77985	+	3.33700i	−1.65260	−	2.50378i	4.05412	−	4.06880i
4.9	−2.49522	+	0.439974i	1.64122	+	0.553517i	4.15315	−	1.51162i	−2.22164	+	0.253581i	−4.33875	−	0.659048i	−0.163849	−	2.64067i	−5.30943	+	3.06540i	2.38724	+	1.81689i	5.43191	−	1.61021i
4.10	−2.47207	+	0.435893i	1.47768	+	0.903580i	4.04174	−	1.47107i	−0.0768193	−	2.23475i	−4.04680	−	1.58960i	1.99253	+	1.74064i	−5.00243	+	2.88816i	1.36709	+	2.67041i	1.16401	+	5.49097i
4.11	−2.44102	+	0.430417i	0.871025	+	1.49710i	3.89391	−	1.41727i	1.89459	+	1.18766i	−2.77056	−	3.27955i	−1.60480	+	2.10348i	−4.60189	+	2.65690i	−1.48263	+	2.60803i	−5.13591	−	2.08362i
4.12	−2.43852	+	0.429977i	0.516405	+	1.65328i	3.88213	−	1.41298i	−0.975673	+	2.01198i	−1.97014	−	3.80951i	−2.49875	−	0.869630i	−4.57030	+	2.63867i	−2.46665	+	1.70752i	1.51409	−	5.32578i
4.13	−2.31322	+	0.407883i	1.37660	−	1.05118i	3.30522	−	1.20300i	2.23169	+	0.139869i	−2.75562	+	2.99309i	0.496619	−	2.59872i	−3.08659	+	1.78204i	0.790061	−	2.89410i	−5.21943	+	0.586720i
4.14	−2.29493	+	0.404658i	−0.220460	−	1.71796i	3.22358	−	1.17329i	0.551797	−	2.16691i	1.20113	+	3.85340i	2.06310	−	1.65639i	−2.88686	+	1.66673i	−2.90279	+	0.757483i	−0.389477	+	5.19621i
4.15	−2.28758	+	0.403362i	−0.995428	−	1.41744i	3.19095	−	1.16141i	2.23220	+	0.131406i	2.84886	+	2.84098i	−2.62695	−	0.314838i	−2.80775	+	1.62106i	−1.01825	+	2.82191i	−5.15935	+	0.599786i
4.16	−2.27690	+	0.401479i	−1.71486	−	0.243413i	3.14372	−	1.14422i	2.05093	+	0.890880i	4.00230	−	0.134254i	2.14647	+	1.54682i	−2.69401	+	1.55539i	2.88150	+	0.834839i	−5.02745	−	1.20504i
4.17	−2.27254	+	0.400710i	−1.36646	+	1.06432i	3.12448	−	1.13722i	1.09030	+	1.95224i	2.67886	−	2.96627i	−1.66237	−	2.05828i	−2.64794	+	1.52879i	0.734442	−	2.90871i	−3.26003	−	3.99965i
4.18	−2.25442	+	0.397514i	1.01661	−	1.40232i	3.04499	−	1.10828i	−2.23484	−	0.0740040i	−1.73442	+	3.56553i	2.58087	−	0.582314i	−2.45911	+	1.41977i	−0.933012	−	2.85123i	5.06768	−	0.721546i
4.19	−2.18712	+	0.385649i	1.69490	+	0.356828i	2.75540	−	1.00288i	2.00570	−	0.988510i	−3.84456	−	0.126792i	−2.34611	+	1.22301i	−1.79299	+	1.03518i	2.74535	+	1.20957i	−4.00550	+	2.93549i
4.20	−2.17890	+	0.384199i	−1.68342	+	0.407550i	2.72061	−	0.990220i	1.39471	−	1.74779i	3.51142	−	1.53478i	2.61173	+	0.422917i	−1.71530	+	0.990331i	2.66781	−	1.37215i	−2.36743	+	4.34411i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
189.u	even	9	1	inner
945.db	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.db.a	yes	840
5.b	even	2	1	inner	945.2.db.a	yes	840
7.c	even	3	1		945.2.cu.a	✓	840
27.e	even	9	1		945.2.cu.a	✓	840
35.j	even	6	1		945.2.cu.a	✓	840
135.p	even	18	1		945.2.cu.a	✓	840
189.u	even	9	1	inner	945.2.db.a	yes	840
945.db	even	18	1	inner	945.2.db.a	yes	840

    

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

Hecke kernels

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