Newform orbit 945.2.dr.a

• Label: 945.2.dr.a
• Level: $945$
• Weight: $2$
• Character orbit: 945.dr
• Analytic conductor: $7.546$
• Analytic rank: $0$
• Dimension: $1680$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.dr (of order \(36\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.54586299101\)
Analytic rank:	\(0\)
Dimension:	\(1680\)
Relative dimension:	\(140\) over \(\Q(\zeta_{36})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1680 q - 6 q^{2} - 18 q^{3} - 18 q^{5} + 36 q^{6} - 12 q^{7} - 12 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
52.1	−2.53688	−	1.18297i	0.674143	+	1.59547i	3.75079	+	4.47001i	−1.33432	−	1.79432i	0.177171	−	4.84502i	−2.63135	−	0.275641i	−2.77848	−	10.3694i	−2.09106	+	2.15115i	1.26238	+	6.13044i
52.2	−2.46650	−	1.15015i	1.71955	+	0.207721i	3.47523	+	4.14161i	−1.98133	+	1.03649i	−4.00237	−	2.49009i	1.11307	+	2.40022i	−2.39944	−	8.95483i	2.91370	+	0.714373i	6.07909	−	0.277675i
52.3	−2.46532	−	1.14960i	0.406420	−	1.68369i	3.47064	+	4.13615i	1.97266	+	1.05290i	−2.93752	+	3.68362i	−2.16913	−	1.51488i	−2.39326	−	8.93176i	−2.66965	−	1.36857i	−3.65283	−	4.86349i
52.4	−2.46024	−	1.14723i	−0.864414	−	1.50093i	3.45107	+	4.11283i	−2.01277	+	0.974035i	0.404755	+	4.68433i	2.27134	−	1.35684i	−2.36694	−	8.83356i	−1.50558	+	2.59485i	6.06935	−	0.0872476i
52.5	−2.40717	−	1.12248i	−1.50593	+	0.855666i	3.24891	+	3.87190i	−0.140380	−	2.23166i	4.58550	−	0.369351i	2.54647	−	0.717968i	−2.09968	−	7.83611i	1.53567	−	2.57715i	−2.16707	+	5.52954i
52.6	−2.37464	−	1.10731i	−1.72763	+	0.123618i	3.12721	+	3.72687i	2.11497	+	0.725881i	4.23940	+	1.61949i	−0.671595	−	2.55909i	−1.94292	−	7.25109i	2.96944	−	0.427133i	−4.21852	−	4.06565i
52.7	−2.36530	−	1.10296i	−1.23105	−	1.21840i	3.09256	+	3.68557i	0.933249	−	2.03201i	1.56796	+	4.23969i	−1.14366	+	2.38580i	−1.89887	−	7.08666i	0.0309820	+	2.99984i	−4.44863	+	3.77697i
52.8	−2.32524	−	1.08428i	−0.500729	+	1.65809i	2.94550	+	3.51031i	0.750082	+	2.10651i	2.96214	−	3.31253i	2.58946	+	0.542847i	−1.71478	−	6.39964i	−2.49854	−	1.66051i	0.539918	−	5.71143i
52.9	−2.31815	−	1.08097i	−0.862088	+	1.50227i	2.91974	+	3.47961i	−0.905196	+	2.04466i	3.62235	−	2.55058i	−2.55490	+	0.687361i	−1.68303	−	6.28114i	−1.51361	−	2.59017i	4.30859	−	3.76133i
52.10	−2.29023	−	1.06795i	1.73202	−	0.0102067i	2.81904	+	3.35960i	1.93314	+	1.12382i	−3.97762	−	1.82634i	−1.38664	+	2.25327i	−1.56029	−	5.82308i	2.99979	−	0.0353565i	−3.22713	−	4.63830i
52.11	−2.27202	−	1.05946i	0.722662	+	1.57409i	2.75404	+	3.28214i	2.00900	−	0.981800i	0.0257828	−	4.34199i	2.08889	+	1.62374i	−1.48228	−	5.53193i	−1.95552	+	2.27507i	−5.60466	+	0.102217i
52.12	−2.22076	−	1.03556i	−1.59217	+	0.681915i	2.57383	+	3.06738i	−2.19108	−	0.446300i	4.24199	+	0.134409i	0.555471	+	2.58678i	−1.27104	−	4.74358i	2.06998	−	2.17144i	4.40369	+	3.26012i
52.13	−2.17247	−	1.01304i	−1.54983	−	0.773325i	2.40782	+	2.86952i	−0.777553	+	2.09652i	2.58355	+	3.25007i	−2.19897	+	1.47123i	−1.08316	−	4.04242i	1.80394	+	2.39704i	3.81308	−	3.76695i
52.14	−2.14517	−	1.00031i	0.794764	−	1.53894i	2.31556	+	2.75958i	−1.39088	−	1.75085i	−3.24433	+	2.50629i	0.572923	+	2.58297i	−0.981630	−	3.66349i	−1.73670	−	2.44619i	1.23228	+	5.14717i
52.15	−2.13922	−	0.997535i	1.08028	−	1.35388i	2.29561	+	2.73580i	−2.21095	+	0.334240i	−3.66150	+	1.81864i	−2.25063	−	1.39092i	−0.959942	−	3.58255i	−0.665993	−	2.92514i	5.06312	+	1.49048i
52.16	−2.12789	−	0.992250i	1.60497	+	0.651197i	2.25777	+	2.69070i	2.00657	−	0.986756i	−2.76905	−	2.97821i	0.462102	−	2.60508i	−0.919080	−	3.43005i	2.15189	+	2.09031i	−5.24886	+	0.108689i
52.17	−2.06603	−	0.963405i	1.45529	−	0.939212i	2.05475	+	2.44875i	0.291264	+	2.21702i	−3.91152	+	0.538403i	2.14407	−	1.55015i	−0.706015	−	2.63488i	1.23576	−	2.73366i	1.53413	−	4.86103i
52.18	−2.04146	−	0.951951i	−0.626812	+	1.61465i	1.97579	+	2.35466i	1.65098	−	1.50807i	2.81668	−	2.69956i	−1.97599	−	1.75940i	−0.626009	−	2.33630i	−2.21421	−	2.02417i	−4.80602	+	1.50702i
52.19	−2.01875	−	0.941358i	−0.554040	−	1.64105i	1.90362	+	2.26864i	−0.690173	−	2.12689i	−0.426346	+	3.83442i	−0.152948	−	2.64133i	−0.554312	−	2.06872i	−2.38608	+	1.81841i	−0.608879	+	4.94336i
52.20	−1.99052	−	0.928195i	−0.281533	−	1.70902i	1.81505	+	2.16309i	1.12926	+	1.92997i	−1.02590	+	3.66315i	1.61063	+	2.09902i	−0.468235	−	1.74748i	−2.84148	+	0.962288i	−0.456436	−	4.88981i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
189.x	odd	18	1	inner
945.dr	even	36	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	945.2.dr.a	yes	1680
5.c	odd	4	1	inner	945.2.dr.a	yes	1680
7.d	odd	6	1		945.2.dk.a	✓	1680
27.e	even	9	1		945.2.dk.a	✓	1680
35.k	even	12	1		945.2.dk.a	✓	1680
135.r	odd	36	1		945.2.dk.a	✓	1680
189.x	odd	18	1	inner	945.2.dr.a	yes	1680
945.dr	even	36	1	inner	945.2.dr.a	yes	1680

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
945.2.dk.a	✓	1680	7.d	odd	6	1
945.2.dk.a	✓	1680	27.e	even	9	1
945.2.dk.a	✓	1680	35.k	even	12	1
945.2.dk.a	✓	1680	135.r	odd	36	1
945.2.dr.a	yes	1680	1.a	even	1	1	trivial
945.2.dr.a	yes	1680	5.c	odd	4	1	inner
945.2.dr.a	yes	1680	189.x	odd	18	1	inner
945.2.dr.a	yes	1680	945.dr	even	36	1	inner

Hecke kernels

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