Newform orbit 273.2.cd.e

• Label: 273.2.cd.e
• Level: $273$
• Weight: $2$
• Character orbit: 273.cd
• Analytic conductor: $2.180$
• Analytic rank: $0$
• Dimension: $112$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cd (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.17991597518\)
Analytic rank:	\(0\)
Dimension:	\(112\)
Relative dimension:	\(28\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 112q - 12q^{3} - 8q^{6} - 4q^{7} + 8q^{9} + O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
44.1	−2.69539	+	0.722228i	1.57685	+	0.716628i	5.01147	−	2.89338i	1.51996	−	0.407273i	−4.76779	−	0.792751i	−0.780863	+	2.52790i	−7.47188	+	7.47188i	1.97289	+	2.26003i	−3.80275	+	2.19552i
44.2	−2.42391	+	0.649484i	−1.28483	−	1.16155i	3.72144	−	2.14858i	3.58252	−	0.959933i	3.86873	+	1.98102i	1.55291	−	2.14207i	−4.07612	+	4.07612i	0.301593	+	2.98480i	−8.06023	+	4.65358i
44.3	−2.41247	+	0.646418i	0.872737	−	1.49611i	3.67009	−	2.11892i	−1.51647	+	0.406338i	−1.13834	+	4.17346i	−1.79039	−	1.94795i	−3.95215	+	3.95215i	−1.47666	−	2.61141i	3.39578	−	1.96055i
44.4	−2.19229	+	0.587422i	−1.51343	+	0.842335i	2.72902	−	1.57560i	0.959762	−	0.257167i	2.82307	−	2.73567i	−2.15459	+	1.53549i	−1.84753	+	1.84753i	1.58094	−	2.54963i	−1.95301	+	1.12757i
44.5	−2.10280	+	0.563443i	−0.755319	−	1.55868i	2.37223	−	1.36961i	−2.37528	+	0.636456i	2.46651	+	2.85201i	1.72404	+	2.00691i	−1.13792	+	1.13792i	−1.85899	+	2.35461i	4.63613	−	2.67667i
44.6	−2.00566	+	0.537415i	−0.123517	+	1.72764i	2.00181	−	1.15574i	0.878767	−	0.235465i	−0.680727	−	3.53144i	−1.67646	−	2.04682i	−0.457340	+	0.457340i	−2.96949	−	0.426786i	−1.63596	+	0.944525i
44.7	−1.87036	+	0.501163i	1.45895	+	0.933521i	1.51505	−	0.874714i	−1.33892	+	0.358762i	−3.19662	−	1.01485i	1.90555	−	1.83545i	0.343083	−	0.343083i	1.25708	+	2.72392i	2.32447	−	1.34203i
44.8	−1.64181	+	0.439921i	1.02109	−	1.39906i	0.769949	−	0.444530i	3.49677	−	0.936956i	−1.06096	+	2.74619i	0.612738	+	2.57382i	1.33522	−	1.33522i	−0.914735	−	2.85714i	−5.32883	+	3.07660i
44.9	−1.55291	+	0.416100i	−1.66835	+	0.465425i	0.506326	−	0.292327i	0.0914679	−	0.0245087i	2.39712	−	1.41696i	2.58235	+	0.575745i	1.60897	−	1.60897i	2.56676	−	1.55298i	−0.131843	+	0.0761195i
44.10	−1.27346	+	0.341222i	1.73165	−	0.0374536i	−0.226792	+	0.130939i	−3.02659	+	0.810973i	−2.19240	+	0.638570i	−0.631669	+	2.56924i	2.10860	−	2.10860i	2.99719	−	0.129713i	3.57751	−	2.06548i
44.11	−1.25001	+	0.334940i	−1.60871	−	0.641920i	−0.281700	+	0.162639i	−3.70264	+	0.992121i	2.22591	+	0.263589i	−1.90960	−	1.83124i	2.12780	−	2.12780i	2.17588	+	2.06532i	4.29606	−	2.48033i
44.12	−0.623254	+	0.167000i	−1.63214	−	0.579750i	−1.37149	+	0.791833i	2.98988	−	0.801137i	1.11406	+	0.0887629i	−2.60516	+	0.461652i	1.63506	−	1.63506i	2.32778	+	1.89247i	−1.72966	+	0.998622i
44.13	−0.578797	+	0.155088i	0.590016	−	1.62846i	−1.42110	+	0.820471i	−0.609213	+	0.163238i	−0.0889444	+	1.03405i	2.12540	−	1.57565i	1.54270	−	1.54270i	−2.30376	−	1.92163i	0.327294	−	0.188963i
44.14	−0.246180	+	0.0659636i	−0.753906	+	1.55937i	−1.67580	+	0.967522i	−2.71744	+	0.728135i	0.0827348	−	0.433615i	1.41179	−	2.23760i	0.709158	−	0.709158i	−1.86325	−	2.35123i	0.620947	−	0.358504i
44.15	0.246180	−	0.0659636i	1.72740	+	0.126782i	−1.67580	+	0.967522i	2.71744	−	0.728135i	0.433615	−	0.0827348i	1.41179	−	2.23760i	−0.709158	+	0.709158i	2.96785	+	0.438007i	0.620947	−	0.358504i
44.16	0.578797	−	0.155088i	−1.70530	−	0.303261i	−1.42110	+	0.820471i	0.609213	−	0.163238i	−1.03405	+	0.0889444i	2.12540	−	1.57565i	−1.54270	+	1.54270i	2.81607	+	1.03430i	0.327294	−	0.188963i
44.17	0.623254	−	0.167000i	0.313993	−	1.70335i	−1.37149	+	0.791833i	−2.98988	+	0.801137i	−0.0887629	−	1.11406i	−2.60516	+	0.461652i	−1.63506	+	1.63506i	−2.80282	−	1.06968i	−1.72966	+	0.998622i
44.18	1.25001	−	0.334940i	0.248434	−	1.71414i	−0.281700	+	0.162639i	3.70264	−	0.992121i	−0.263589	−	2.22591i	−1.90960	−	1.83124i	−2.12780	+	2.12780i	−2.87656	−	0.851703i	4.29606	−	2.48033i
44.19	1.27346	−	0.341222i	−0.898259	+	1.48092i	−0.226792	+	0.130939i	3.02659	−	0.810973i	−0.638570	+	2.19240i	−0.631669	+	2.56924i	−2.10860	+	2.10860i	−1.38626	−	2.66050i	3.57751	−	2.06548i
44.20	1.55291	−	0.416100i	1.23724	−	1.21212i	0.506326	−	0.292327i	−0.0914679	+	0.0245087i	1.41696	−	2.39712i	2.58235	+	0.575745i	−1.60897	+	1.60897i	0.0615393	−	2.99937i	−0.131843	+	0.0761195i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
7.c	even	3	1	inner
13.d	odd	4	1	inner
21.h	odd	6	1	inner
39.f	even	4	1	inner
91.z	odd	12	1	inner
273.cd	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	273.2.cd.e	✓	112
3.b	odd	2	1	inner	273.2.cd.e	✓	112
7.c	even	3	1	inner	273.2.cd.e	✓	112
13.d	odd	4	1	inner	273.2.cd.e	✓	112
21.h	odd	6	1	inner	273.2.cd.e	✓	112
39.f	even	4	1	inner	273.2.cd.e	✓	112
91.z	odd	12	1	inner	273.2.cd.e	✓	112
273.cd	even	12	1	inner	273.2.cd.e	✓	112

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
273.2.cd.e	✓	112	1.a	even	1	1	trivial
273.2.cd.e	✓	112	3.b	odd	2	1	inner
273.2.cd.e	✓	112	7.c	even	3	1	inner
273.2.cd.e	✓	112	13.d	odd	4	1	inner
273.2.cd.e	✓	112	21.h	odd	6	1	inner
273.2.cd.e	✓	112	39.f	even	4	1	inner
273.2.cd.e	✓	112	91.z	odd	12	1	inner
273.2.cd.e	✓	112	273.cd	even	12	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(273, [\chi])\):

\(19\!\cdots\!38\)\( T_{2}^{84} + \)\(57\!\cdots\!64\)\( T_{2}^{80} - \)\(14\!\cdots\!36\)\( T_{2}^{76} + \)\(28\!\cdots\!48\)\( T_{2}^{72} - \)\(49\!\cdots\!22\)\( T_{2}^{68} + \)\(70\!\cdots\!12\)\( T_{2}^{64} - \)\(82\!\cdots\!18\)\( T_{2}^{60} + \)\(79\!\cdots\!87\)\( T_{2}^{56} - \)\(62\!\cdots\!66\)\( T_{2}^{52} + \)\(39\!\cdots\!39\)\( T_{2}^{48} - \)\(19\!\cdots\!32\)\( T_{2}^{44} + \)\(77\!\cdots\!37\)\( T_{2}^{40} - \)\(22\!\cdots\!38\)\( T_{2}^{36} + \)\(49\!\cdots\!38\)\( T_{2}^{32} - \)\(72\!\cdots\!52\)\( T_{2}^{28} + \)\(68\!\cdots\!30\)\( T_{2}^{24} - \)\(18\!\cdots\!78\)\( T_{2}^{20} + \)\(37\!\cdots\!41\)\( T_{2}^{16} - \)\(36\!\cdots\!68\)\( T_{2}^{12} + \)\(25\!\cdots\!34\)\( T_{2}^{8} - \)\(10\!\cdots\!24\)\( T_{2}^{4} + \)\(42\!\cdots\!41\)\( \)">\(T_{2}^{112} - \cdots\)

\(80\!\cdots\!00\)\( T_{5}^{92} + \)\(12\!\cdots\!85\)\( T_{5}^{88} - \)\(15\!\cdots\!84\)\( T_{5}^{84} + \)\(15\!\cdots\!83\)\( T_{5}^{80} - \)\(12\!\cdots\!32\)\( T_{5}^{76} + \)\(75\!\cdots\!61\)\( T_{5}^{72} - \)\(36\!\cdots\!88\)\( T_{5}^{68} + \)\(13\!\cdots\!01\)\( T_{5}^{64} - \)\(35\!\cdots\!38\)\( T_{5}^{60} + \)\(68\!\cdots\!46\)\( T_{5}^{56} - \)\(81\!\cdots\!06\)\( T_{5}^{52} + \)\(69\!\cdots\!06\)\( T_{5}^{48} - \)\(41\!\cdots\!76\)\( T_{5}^{44} + \)\(18\!\cdots\!96\)\( T_{5}^{40} - \)\(54\!\cdots\!48\)\( T_{5}^{36} + \)\(11\!\cdots\!61\)\( T_{5}^{32} - \)\(14\!\cdots\!80\)\( T_{5}^{28} + \)\(13\!\cdots\!24\)\( T_{5}^{24} - \)\(75\!\cdots\!88\)\( T_{5}^{20} + \)\(28\!\cdots\!64\)\( T_{5}^{16} - \)\(40\!\cdots\!96\)\( T_{5}^{12} + \)\(42\!\cdots\!48\)\( T_{5}^{8} - \)\(34\!\cdots\!92\)\( T_{5}^{4} + \)\(27\!\cdots\!76\)\( \)">\(T_{5}^{112} - \cdots\)

\(27\!\cdots\!78\)\( T_{19}^{41} + \)\(46\!\cdots\!45\)\( T_{19}^{40} + \)\(22\!\cdots\!12\)\( T_{19}^{39} - \)\(15\!\cdots\!26\)\( T_{19}^{38} + \)\(10\!\cdots\!32\)\( T_{19}^{37} - \)\(31\!\cdots\!98\)\( T_{19}^{36} - \)\(49\!\cdots\!12\)\( T_{19}^{35} + \)\(47\!\cdots\!50\)\( T_{19}^{34} - \)\(41\!\cdots\!80\)\( T_{19}^{33} + \)\(20\!\cdots\!29\)\( T_{19}^{32} - \)\(43\!\cdots\!24\)\( T_{19}^{31} + \)\(14\!\cdots\!56\)\( T_{19}^{30} - \)\(28\!\cdots\!84\)\( T_{19}^{29} - \)\(10\!\cdots\!53\)\( T_{19}^{28} + \)\(69\!\cdots\!12\)\( T_{19}^{27} + \)\(87\!\cdots\!58\)\( T_{19}^{26} + \)\(29\!\cdots\!90\)\( T_{19}^{25} + \)\(48\!\cdots\!77\)\( T_{19}^{24} - \)\(13\!\cdots\!76\)\( T_{19}^{23} - \)\(31\!\cdots\!34\)\( T_{19}^{22} - \)\(50\!\cdots\!96\)\( T_{19}^{21} - \)\(87\!\cdots\!74\)\( T_{19}^{20} + \)\(10\!\cdots\!24\)\( T_{19}^{19} + \)\(74\!\cdots\!18\)\( T_{19}^{18} + \)\(18\!\cdots\!88\)\( T_{19}^{17} + \)\(40\!\cdots\!09\)\( T_{19}^{16} + \)\(73\!\cdots\!68\)\( T_{19}^{15} + \)\(10\!\cdots\!84\)\( T_{19}^{14} + \)\(14\!\cdots\!08\)\( T_{19}^{13} + \)\(17\!\cdots\!39\)\( T_{19}^{12} + \)\(17\!\cdots\!48\)\( T_{19}^{11} + \)\(16\!\cdots\!46\)\( T_{19}^{10} + \)\(13\!\cdots\!94\)\( T_{19}^{9} + \)\(95\!\cdots\!72\)\( T_{19}^{8} + \)\(56\!\cdots\!12\)\( T_{19}^{7} + \)\(29\!\cdots\!62\)\( T_{19}^{6} + \)\(11\!\cdots\!04\)\( T_{19}^{5} + \)\(16\!\cdots\!49\)\( T_{19}^{4} - \)\(25\!\cdots\!60\)\( T_{19}^{3} + \)\(92\!\cdots\!50\)\( T_{19}^{2} - \)\(12\!\cdots\!50\)\( T_{19} + \)\(88\!\cdots\!25\)\( \)">\(T_{19}^{56} - \cdots\)