Properties

 Label 201.3.h.b Level 201 Weight 3 Character orbit 201.h Analytic conductor 5.477 Analytic rank 0 Dimension 24 CM no Inner twists 2

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$201 = 3 \cdot 67$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 201.h (of order $$6$$, degree $$2$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$5.47685331364$$ Analytic rank: $$0$$ Dimension: $$24$$ Relative dimension: $$12$$ over $$\Q(\zeta_{6})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

 $$\operatorname{Tr}(f)(q) =$$ $$24q + 34q^{4} + 21q^{7} - 72q^{9} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$24q + 34q^{4} + 21q^{7} - 72q^{9} + 30q^{10} + 12q^{11} + 102q^{12} + 30q^{13} + 6q^{14} - 6q^{15} - 98q^{16} + 4q^{17} + 39q^{19} + 108q^{20} - 21q^{21} - 82q^{22} - 13q^{23} - 36q^{24} - 222q^{25} + 29q^{26} + 189q^{28} - 90q^{30} - 93q^{31} - 33q^{32} - 12q^{33} + 72q^{34} - 93q^{35} - 102q^{36} - 33q^{37} - 210q^{38} + 30q^{39} + 274q^{40} - 15q^{41} - 9q^{44} - 228q^{46} - 131q^{47} + 294q^{48} + 295q^{49} - 423q^{50} - 12q^{51} - 56q^{55} + 349q^{56} - 117q^{57} - 116q^{59} - 108q^{60} + 120q^{61} + 282q^{62} - 63q^{63} - 276q^{64} + 136q^{65} - 25q^{67} + 10q^{68} + 39q^{69} + 169q^{71} + 187q^{73} + 849q^{74} + 386q^{76} - 348q^{77} + 87q^{78} + 51q^{80} + 216q^{81} - 14q^{82} + 104q^{83} + 189q^{84} - 243q^{85} + 641q^{86} - 766q^{88} + 152q^{89} - 90q^{90} + 32q^{91} - 216q^{92} + 93q^{93} + 762q^{95} + 33q^{96} - 84q^{97} - 1086q^{98} - 36q^{99} + O(q^{100})$$

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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
97.1 −3.23066 + 1.86522i 1.73205i 4.95809 8.58766i 1.91835i −3.23066 5.59566i −11.0264 6.36611i 22.0700i −3.00000 3.57814 + 6.19753i
97.2 −3.01185 + 1.73889i 1.73205i 4.04748 7.01044i 4.44467i −3.01185 5.21667i 8.21480 + 4.74282i 14.2414i −3.00000 7.72880 + 13.3867i
97.3 −2.78358 + 1.60710i 1.73205i 3.16555 5.48289i 6.80030i −2.78358 4.82130i 9.81487 + 5.66662i 7.49262i −3.00000 −10.9288 18.9292i
97.4 −1.79024 + 1.03359i 1.73205i 0.136637 0.236663i 0.118573i −1.79024 3.10078i −4.18772 2.41778i 7.70385i −3.00000 −0.122556 0.212274i
97.5 −0.893138 + 0.515653i 1.73205i −1.46820 + 2.54300i 8.85241i −0.893138 1.54696i 7.85559 + 4.53543i 7.15356i −3.00000 4.56478 + 7.90642i
97.6 −0.415796 + 0.240060i 1.73205i −1.88474 + 3.26447i 7.03218i −0.415796 0.720180i 1.25782 + 0.726201i 3.73029i −3.00000 −1.68815 2.92395i
97.7 0.535032 0.308901i 1.73205i −1.80916 + 3.13356i 6.48720i 0.535032 + 0.926703i −10.3489 5.97496i 4.70662i −3.00000 −2.00390 3.47086i
97.8 1.15796 0.668551i 1.73205i −1.10608 + 1.91579i 0.749427i 1.15796 + 2.00565i 2.89468 + 1.67125i 8.30629i −3.00000 0.501030 + 0.867810i
97.9 2.00217 1.15595i 1.73205i 0.672461 1.16474i 1.12578i 2.00217 + 3.46786i 6.42822 + 3.71133i 6.13830i −3.00000 −1.30135 2.25401i
97.10 2.13074 1.23018i 1.73205i 1.02670 1.77830i 7.82361i 2.13074 + 3.69055i −7.43732 4.29394i 4.78934i −3.00000 9.62447 + 16.6701i
97.11 2.98997 1.72626i 1.73205i 3.95993 6.85880i 6.27203i 2.98997 + 5.17877i −1.92187 1.10959i 13.5334i −3.00000 −10.8271 18.7532i
97.12 3.30938 1.91067i 1.73205i 5.30134 9.18219i 8.30841i 3.30938 + 5.73202i 8.95628 + 5.17091i 25.2311i −3.00000 15.8747 + 27.4957i
172.1 −3.23066 1.86522i 1.73205i 4.95809 + 8.58766i 1.91835i −3.23066 + 5.59566i −11.0264 + 6.36611i 22.0700i −3.00000 3.57814 6.19753i
172.2 −3.01185 1.73889i 1.73205i 4.04748 + 7.01044i 4.44467i −3.01185 + 5.21667i 8.21480 4.74282i 14.2414i −3.00000 7.72880 13.3867i
172.3 −2.78358 1.60710i 1.73205i 3.16555 + 5.48289i 6.80030i −2.78358 + 4.82130i 9.81487 5.66662i 7.49262i −3.00000 −10.9288 + 18.9292i
172.4 −1.79024 1.03359i 1.73205i 0.136637 + 0.236663i 0.118573i −1.79024 + 3.10078i −4.18772 + 2.41778i 7.70385i −3.00000 −0.122556 + 0.212274i
172.5 −0.893138 0.515653i 1.73205i −1.46820 2.54300i 8.85241i −0.893138 + 1.54696i 7.85559 4.53543i 7.15356i −3.00000 4.56478 7.90642i
172.6 −0.415796 0.240060i 1.73205i −1.88474 3.26447i 7.03218i −0.415796 + 0.720180i 1.25782 0.726201i 3.73029i −3.00000 −1.68815 + 2.92395i
172.7 0.535032 + 0.308901i 1.73205i −1.80916 3.13356i 6.48720i 0.535032 0.926703i −10.3489 + 5.97496i 4.70662i −3.00000 −2.00390 + 3.47086i
172.8 1.15796 + 0.668551i 1.73205i −1.10608 1.91579i 0.749427i 1.15796 2.00565i 2.89468 1.67125i 8.30629i −3.00000 0.501030 0.867810i
See all 24 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 172.12 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
67.d odd 6 1 inner

Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 201.3.h.b 24
67.d odd 6 1 inner 201.3.h.b 24

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
201.3.h.b 24 1.a even 1 1 trivial
201.3.h.b 24 67.d odd 6 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{2}^{24} - \cdots$$ acting on $$S_{3}^{\mathrm{new}}(201, [\chi])$$.

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database