Newform orbit 273.2.bw.b

• Label: 273.2.bw.b
• Level: $273$
• Weight: $2$
• Character orbit: 273.bw
• Analytic conductor: $2.180$
• Analytic rank: $0$
• Dimension: $128$
• CM: no
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(2.17991597518\)
Analytic rank:	\(0\)
Dimension:	\(128\)
Relative dimension:	\(32\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 128 q - 4 q^{3} - 12 q^{4} - 4 q^{6} - 16 q^{7} - 16 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
11.1	−0.700434	−	2.61406i	1.08921	+	1.34671i	−4.61063	+	2.66195i	−2.04884	−	0.548984i	2.75745	−	3.79054i	−0.908491	+	2.48488i	6.36068	+	6.36068i	−0.627240	+	2.93370i			5.74030i
11.2	−0.679659	−	2.53652i	−1.73115	−	0.0557742i	−4.23995	+	2.44794i	2.98598	+	0.800092i	1.03512	+	4.42901i	2.50266	+	0.858313i	5.37724	+	5.37724i	2.99378	+	0.193107i		−	8.11779i
11.3	−0.614189	−	2.29218i	−0.572173	−	1.63481i	−3.14483	+	1.81567i	0.203686	+	0.0545776i	−3.39587	+	2.31561i	−2.22424	−	1.43274i	2.73738	+	2.73738i	−2.34524	+	1.87079i		−	0.500408i
11.4	−0.590022	−	2.20199i	1.60162	−	0.659394i	−2.76859	+	1.59845i	−1.90854	−	0.511391i	−2.39697	−	3.13771i	0.185390	−	2.63925i	1.92936	+	1.92936i	2.13040	−	2.11220i			4.50431i
11.5	−0.588963	−	2.19804i	1.52334	−	0.824281i	−2.75245	+	1.58913i	3.96614	+	1.06272i	−2.70899	−	2.86289i	−1.45144	+	2.21209i	1.89590	+	1.89590i	1.64112	−	2.51132i		−	9.34364i
11.6	−0.548543	−	2.04719i	−0.721270	+	1.57473i	−2.15804	+	1.24594i	−0.706275	−	0.189246i	3.61942	+	0.612770i	2.22477	−	1.43193i	0.737165	+	0.737165i	−1.95954	−	2.27161i			1.54969i
11.7	−0.504901	−	1.88432i	−1.22779	−	1.22170i	−1.56368	+	0.902789i	−3.20968	−	0.860032i	−1.68215	+	2.93037i	0.850713	+	2.50525i	−0.268188	−	0.268188i	0.0149148	+	2.99996i			6.48229i
11.8	−0.428681	−	1.59986i	1.25532	+	1.19339i	−0.643729	+	0.371657i	0.428701	+	0.114870i	1.37112	−	2.51992i	2.29163	+	1.32228i	−1.47180	−	1.47180i	0.151659	+	2.99616i		−	0.735103i
11.9	−0.375380	−	1.40094i	−1.57757	+	0.715025i	−0.0896663	+	0.0517688i	0.283932	+	0.0760792i	1.59390	+	1.94168i	−2.00629	+	1.72476i	−1.94493	−	1.94493i	1.97748	−	2.25601i		−	0.426329i
11.10	−0.329383	−	1.22927i	0.639267	−	1.60976i	0.329428	−	0.190195i	1.27845	+	0.342559i	−2.18940	−	0.255606i	2.63584	+	0.228814i	−2.14209	−	2.14209i	−2.18268	−	2.05814i		−	1.68440i
11.11	−0.305471	−	1.14003i	1.47664	+	0.905280i	0.525688	−	0.303506i	1.64653	+	0.441185i	0.580979	−	1.95996i	−1.12852	−	2.39300i	−2.17571	−	2.17571i	1.36093	+	2.67355i		−	2.01186i
11.12	−0.250255	−	0.933963i	0.138617	+	1.72650i	0.922391	−	0.532543i	−4.14513	−	1.11068i	1.57779	−	0.561527i	−2.32521	−	1.26230i	−2.09562	−	2.09562i	−2.96157	+	0.478645i			4.14935i
11.13	−0.248591	−	0.927753i	−1.67503	−	0.440774i	0.933123	−	0.538739i	2.67091	+	0.715669i	0.00746719	+	1.66358i	−1.47717	−	2.19498i	−2.09011	−	2.09011i	2.61144	+	1.47662i		−	2.65586i
11.14	−0.179441	−	0.669682i	0.594756	−	1.62673i	1.31578	−	0.759664i	−1.48044	−	0.396684i	−1.19612	−	0.106395i	−2.58806	+	0.549511i	−1.72532	−	1.72532i	−2.29253	−	1.93502i			1.06261i
11.15	−0.0262469	−	0.0979549i	−0.748033	+	1.56219i	1.72314	−	0.994858i	2.20563	+	0.590996i	0.172658	+	0.0322707i	1.71000	−	2.01889i	−0.286094	−	0.286094i	−1.88089	−	2.33714i		−	0.231564i
11.16	−0.00573734	−	0.0214121i	−1.43178	−	0.974676i	1.73163	−	0.999754i	2.15869	+	0.578419i	−0.0126552	+	0.0362495i	1.44048	+	2.21924i	−0.0626912	−	0.0626912i	1.10001	+	2.79105i		−	0.0495405i
11.17	0.00573734	+	0.0214121i	−1.43178	+	0.974676i	1.73163	−	0.999754i	−2.15869	−	0.578419i	−0.0290845	−	0.0250654i	1.44048	+	2.21924i	0.0626912	+	0.0626912i	1.10001	−	2.79105i		−	0.0495405i
11.18	0.0262469	+	0.0979549i	−0.748033	−	1.56219i	1.72314	−	0.994858i	−2.20563	−	0.590996i	0.133391	−	0.114276i	1.71000	−	2.01889i	0.286094	+	0.286094i	−1.88089	+	2.33714i		−	0.231564i
11.19	0.179441	+	0.669682i	0.594756	+	1.62673i	1.31578	−	0.759664i	1.48044	+	0.396684i	−0.982671	+	0.690199i	−2.58806	+	0.549511i	1.72532	+	1.72532i	−2.29253	+	1.93502i			1.06261i
11.20	0.248591	+	0.927753i	−1.67503	+	0.440774i	0.933123	−	0.538739i	−2.67091	−	0.715669i	−0.825325	−	1.44444i	−1.47717	−	2.19498i	2.09011	+	2.09011i	2.61144	−	1.47662i		−	2.65586i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
91.bd	odd	12	1	inner
273.bw	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.bw.b	yes	128
3.b	odd	2	1	inner	273.2.bw.b	yes	128
7.c	even	3	1		273.2.bv.b	✓	128
13.f	odd	12	1		273.2.bv.b	✓	128
21.h	odd	6	1		273.2.bv.b	✓	128
39.k	even	12	1		273.2.bv.b	✓	128
91.bd	odd	12	1	inner	273.2.bw.b	yes	128
273.bw	even	12	1	inner	273.2.bw.b	yes	128

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
273.2.bv.b	✓	128	7.c	even	3	1
273.2.bv.b	✓	128	13.f	odd	12	1
273.2.bv.b	✓	128	21.h	odd	6	1
273.2.bv.b	✓	128	39.k	even	12	1
273.2.bw.b	yes	128	1.a	even	1	1	trivial
273.2.bw.b	yes	128	3.b	odd	2	1	inner
273.2.bw.b	yes	128	91.bd	odd	12	1	inner
273.2.bw.b	yes	128	273.bw	even	12	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^128 + 6*T2^126 - 208*T2^124 - 1320*T2^122 + 25278*T2^120 + 163512*T2^118 - 2083130*T2^116 - 13706802*T2^114 + 129577261*T2^112 + 859384398*T2^110 - 6287627811*T2^108 - 41930992464*T2^106 + 245796787085*T2^104 + 1638500185038*T2^102 - 7829194271110*T2^100 - 51974179643802*T2^98 + 205944273843516*T2^96 + 1352143690207110*T2^94 - 4483577017975169*T2^92 - 28953560080527642*T2^90 + 81109232118761377*T2^88 + 511106220126247296*T2^86 - 1211832215037772833*T2^84 - 7415033970051542298*T2^82 + 14895078345311732332*T2^80 + 87980199518779392696*T2^78 - 148145754805193401685*T2^76 - 845987906307969970836*T2^74 + 1179796725993746051147*T2^72 + 6522934451491047436212*T2^70 - 7299828118375779228698*T2^68 - 39717834408427734331212*T2^66 + 34990891330102598021448*T2^64 + 188209269544382477237448*T2^62 - 125973750648915256018772*T2^60 - 678817036757682251560152*T2^58 + 370725442530700370833603*T2^56 + 1873790788064767489063854*T2^54 - 879028924111586114475598*T2^52 - 3944053228999071261590052*T2^50 + 1780931886617826221516244*T2^48 + 6293309449476603700018044*T2^46 - 2894720254679864241130610*T2^44 - 7525935824817468890134758*T2^42 + 3861841860889780061467551*T2^40 + 6505091309150407445522046*T2^38 - 3819593145572738478876249*T2^36 - 3963576608760541346151156*T2^34 + 2924752542600345609728309*T2^32 + 1453063862971709923899414*T2^30 - 1501888670991868459734698*T2^28 - 233153404397970950199030*T2^26 + 530011104831485184314920*T2^24 - 89774684680643256791214*T2^22 - 69897222377063148275099*T2^20 + 25285805992210591312998*T2^18 + 5625263830337815443069*T2^16 - 5316372462293248103052*T2^14 + 1392222781486690556151*T2^12 - 167664193484103769506*T2^10 + 7096980470343481624*T2^8 + 173497673485311840*T2^6 + 1260370876529673*T2^4 + 990405301344*T2^2 + 269517889