Newform orbit 275.2.j.a

• Label: 275.2.j.a
• Level: $275$
• Weight: $2$
• Character orbit: 275.j
• Analytic conductor: $2.196$
• Analytic rank: $0$
• Dimension: $112$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.j (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.19588605559\)
Analytic rank:	\(0\)
Dimension:	\(112\)
Relative dimension:	\(28\) over \(\Q(\zeta_{5})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 112 q - q^{2} - 4 q^{3} - 27 q^{4} - 5 q^{5} - 34 q^{6} - 4 q^{7} - 3 q^{8} - 28 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
81.1	−0.822587	+	2.53166i	0.825404	+	2.54033i	−4.11463	−	2.98945i	0.575526	+	2.16073i	−7.11023			−1.05656	−	3.25175i	6.64580	−	4.82846i	−3.34495	+	2.43025i	−5.94367	−	0.320354i
81.2	−0.779320	+	2.39850i	−0.572852	−	1.76306i	−3.52743	−	2.56283i	−1.86375	+	1.23549i	4.67513			0.231342	+	0.711999i	4.81537	−	3.49857i	−0.353163	+	0.256588i	−1.51086	−	5.43305i
81.3	−0.741613	+	2.28245i	−0.0966001	−	0.297304i	−3.04156	−	2.20982i	2.05924	+	0.871503i	0.750223			1.02881	+	3.16635i	3.41633	−	2.48211i	2.34799	−	1.70592i	−3.51632	+	4.05380i
81.4	−0.735718	+	2.26431i	0.0475793	+	0.146434i	−2.96778	−	2.15622i	−1.04869	−	1.97490i	−0.366577			−0.947451	−	2.91595i	3.21352	−	2.33476i	2.40787	−	1.74942i	5.24333	−	0.921593i
81.5	−0.679083	+	2.09000i	0.731594	+	2.25162i	−2.28893	−	1.66300i	−1.92554	−	1.13679i	−5.20270			0.976517	+	3.00541i	1.47433	−	1.07116i	−2.10749	+	1.53118i	3.68349	−	3.25242i
81.6	−0.494398	+	1.52160i	−0.303452	−	0.933929i	−0.452802	−	0.328980i	2.04484	−	0.904783i	1.57109			−1.37601	−	4.23492i	−1.86426	+	1.35446i	1.64691	−	1.19655i	0.365754	+	3.55875i
81.7	−0.477735	+	1.47032i	0.656032	+	2.01906i	−0.315572	−	0.229276i	1.71751	−	1.43183i	−3.28207			0.333270	+	1.02570i	−2.01359	+	1.46296i	−1.21917	+	0.885780i	1.28474	+	3.20933i
81.8	−0.368674	+	1.13466i	−0.865695	−	2.66433i	0.466499	+	0.338931i	1.29233	+	1.82480i	3.34227			0.127874	+	0.393557i	−2.48696	+	1.80688i	−3.92220	+	2.84964i	−2.54697	+	0.793599i
81.9	−0.357274	+	1.09957i	0.509327	+	1.56755i	0.536613	+	0.389872i	0.611486	+	2.15083i	−1.90560			0.125130	+	0.385110i	−2.49112	+	1.80990i	0.229263	−	0.166569i	−2.58347	−	0.0960614i
81.10	−0.344419	+	1.06001i	−0.927929	−	2.85587i	0.613033	+	0.445394i	−2.10814	−	0.745474i	3.34685			−0.574621	−	1.76850i	−2.48666	+	1.80667i	−4.86790	+	3.53673i	1.51630	−	1.97790i
81.11	−0.332992	+	1.02484i	−0.0283312	−	0.0871945i	0.678613	+	0.493041i	−1.95021	+	1.09393i	0.0987949			0.409521	+	1.26038i	−2.47483	+	1.79807i	2.42025	−	1.75842i	−0.471698	−	2.36293i
81.12	−0.179614	+	0.552796i	1.02944	+	3.16829i	1.34471	+	0.976990i	−2.22238	−	0.247058i	−1.93632			−0.835007	−	2.56989i	−1.72208	+	1.25116i	−6.55129	+	4.75979i	0.535744	−	1.18415i
81.13	−0.0431104	+	0.132680i	−0.536656	−	1.65166i	1.60229	+	1.16413i	2.22121	−	0.257379i	0.242278			1.32777	+	4.08644i	−0.449261	+	0.326408i	−0.0129233	+	0.00938935i	−0.0616080	+	0.305806i
81.14	0.00834505	−	0.0256834i	0.447400	+	1.37695i	1.61744	+	1.17514i	0.576193	−	2.16056i	0.0390985			0.128187	+	0.394521i	0.0873745	−	0.0634813i	0.731213	−	0.531258i	−0.0506821	−	0.0328285i
81.15	0.0630336	−	0.193997i	−0.222602	−	0.685100i	1.58437	+	1.15111i	−1.89171	−	1.19223i	−0.146939			−0.769943	−	2.36964i	0.653230	−	0.474599i	2.00724	−	1.45835i	−0.350532	+	0.291837i
81.16	0.0637597	−	0.196232i	0.125063	+	0.384906i	1.58359	+	1.15055i	1.33624	+	1.79289i	0.0835048			−1.43441	−	4.41466i	0.660594	−	0.479949i	2.29454	−	1.66708i	0.437021	−	0.147900i
81.17	0.151599	−	0.466573i	−0.785743	−	2.41827i	1.42333	+	1.03411i	0.758089	−	2.10364i	−1.24742			−0.346240	−	1.06562i	1.49204	−	1.08403i	−2.80358	+	2.03692i	−0.866577	−	0.672613i
81.18	0.239459	−	0.736978i	−0.418837	−	1.28905i	1.13224	+	0.822619i	−1.12586	+	1.93195i	−1.05030			0.923459	+	2.84212i	2.13120	−	1.54841i	0.940828	−	0.683552i	1.15421	+	1.29236i
81.19	0.389858	−	1.19986i	0.532561	+	1.63906i	0.330358	+	0.240019i	−1.75660	−	1.38360i	2.17426			1.37330	+	4.22657i	2.45811	−	1.78592i	0.0241700	−	0.0175606i	−2.34496	+	1.56826i
81.20	0.398379	−	1.22608i	0.976712	+	3.00601i	0.273456	+	0.198678i	2.20854	−	0.349793i	4.07473			−0.577657	−	1.77784i	2.43847	−	1.77166i	−5.65509	+	4.10866i	0.450960	−	2.84721i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
275.j	even	5	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	275.2.j.a	yes	112
11.c	even	5	1		275.2.g.a	✓	112
25.d	even	5	1		275.2.g.a	✓	112
275.j	even	5	1	inner	275.2.j.a	yes	112

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
275.2.g.a	✓	112	11.c	even	5	1
275.2.g.a	✓	112	25.d	even	5	1
275.2.j.a	yes	112	1.a	even	1	1	trivial
275.2.j.a	yes	112	275.j	even	5	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(275, [\chi])\).