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Properties

Label 201.3.c.a
Level $201$
Weight $3$
Character orbit 201.c
Analytic conductor $5.477$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [201,3,Mod(68,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.68");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 201.c (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.47685331364\)
Analytic rank: \(0\)
Dimension: \(44\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9} + 12 q^{10} - 20 q^{12} - 32 q^{13} - 30 q^{15} + 204 q^{16} + 22 q^{18} - 32 q^{19} + 36 q^{21} - 8 q^{22} - 24 q^{24} - 164 q^{25} + 42 q^{27} - 48 q^{28} + 58 q^{30} + 20 q^{31} + 6 q^{33} - 48 q^{34} - 78 q^{36} + 100 q^{37} + 4 q^{39} + 160 q^{40} - 204 q^{42} - 108 q^{43} - 132 q^{45} - 244 q^{46} + 34 q^{48} + 332 q^{49} + 114 q^{51} - 8 q^{52} + 432 q^{54} + 128 q^{55} - 26 q^{57} - 12 q^{58} + 250 q^{60} - 164 q^{61} - 290 q^{63} - 432 q^{64} - 78 q^{66} + 76 q^{69} + 612 q^{70} - 464 q^{72} + 156 q^{73} - 118 q^{75} - 180 q^{76} - 392 q^{79} + 348 q^{81} + 524 q^{82} - 202 q^{84} - 188 q^{85} - 68 q^{87} - 348 q^{88} + 94 q^{90} - 44 q^{91} + 322 q^{93} - 304 q^{94} + 224 q^{96} + 68 q^{97} + 104 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
68.1 − 3.85580i 2.40297 + 1.79604i −10.8672 6.40327i 6.92517 − 9.26536i 10.8148 26.4786i 2.54849 + 8.63164i 24.6898
68.2 − 3.83909i −0.0207392 − 2.99993i −10.7386 − 4.79169i −11.5170 + 0.0796199i 5.67115 25.8703i −8.99914 + 0.124433i −18.3957
68.3 − 3.74856i −2.69559 + 1.31674i −10.0517 − 4.74753i 4.93589 + 10.1046i −4.78098 22.6851i 5.53237 − 7.09880i −17.7964
68.4 − 3.48861i 2.56342 + 1.55849i −8.17041 − 4.65961i 5.43698 − 8.94276i −13.4680 14.5490i 4.14220 + 7.99013i −16.2556
68.5 − 3.36787i −2.80521 − 1.06340i −7.34253 7.21139i −3.58138 + 9.44756i −0.105037 11.2572i 6.73838 + 5.96610i 24.2870
68.6 − 3.10162i −1.15101 + 2.77041i −5.62003 1.67791i 8.59275 + 3.57000i 4.25449 5.02473i −6.35035 − 6.37755i 5.20424
68.7 − 2.87376i 2.67705 − 1.35402i −4.25852 2.14706i −3.89115 − 7.69322i 2.18513 0.742934i 5.33323 − 7.24959i 6.17014
68.8 − 2.85257i −0.383029 − 2.97545i −4.13715 2.94424i −8.48767 + 1.09262i −7.08182 0.391240i −8.70658 + 2.27937i 8.39866
68.9 − 2.83332i 2.79666 − 1.08567i −4.02771 − 6.23827i −3.07604 − 7.92385i 3.53484 0.0785029i 6.64266 − 6.07248i −17.6750
68.10 − 2.78110i −0.0951894 + 2.99849i −3.73454 3.67055i 8.33911 + 0.264732i −7.35767 − 0.738266i −8.98188 − 0.570849i 10.2082
68.11 − 2.37672i −2.91725 + 0.699765i −1.64880 − 3.76639i 1.66315 + 6.93348i 9.72750 − 5.58814i 8.02066 − 4.08278i −8.95165
68.12 − 2.26735i −2.13323 − 2.10934i −1.14089 − 6.81017i −4.78262 + 4.83679i −3.54429 − 6.48261i 0.101366 + 8.99943i −15.4411
68.13 − 1.84390i 1.97832 + 2.25527i 0.600017 − 2.65010i 4.15850 − 3.64784i 5.23167 − 8.48199i −1.17249 + 8.92330i −4.88653
68.14 − 1.81184i 0.454991 − 2.96530i 0.717236 6.02732i −5.37264 − 0.824371i 13.4974 − 8.54688i −8.58597 − 2.69837i 10.9205
68.15 − 1.74215i 2.96882 + 0.431379i 0.964903 9.03513i 0.751528 − 5.17214i −5.84306 − 8.64962i 8.62782 + 2.56137i 15.7406
68.16 − 1.16231i −2.84845 + 0.941451i 2.64903 5.51585i 1.09426 + 3.31079i −12.7350 − 7.72825i 7.22734 − 5.36336i 6.41115
68.17 − 1.01079i −0.770133 + 2.89946i 2.97831 − 8.93347i 2.93075 + 0.778442i −6.17840 − 7.05360i −7.81379 − 4.46595i −9.02986
68.18 − 0.898014i 1.52814 − 2.58162i 3.19357 − 1.98358i −2.31833 − 1.37229i −8.12242 − 6.45992i −4.32955 − 7.89018i −1.78129
68.19 − 0.846960i −2.75258 − 1.19301i 3.28266 3.42420i −1.01043 + 2.33133i 3.13578 − 6.16812i 6.15345 + 6.56773i 2.90016
68.20 − 0.777984i −1.77932 + 2.41537i 3.39474 2.01357i 1.87912 + 1.38428i 2.85306 − 5.75299i −2.66805 − 8.59543i 1.56652
See all 44 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 68.44
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 201.3.c.a ✓ 44
3.b odd 2 1 inner 201.3.c.a ✓ 44
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
201.3.c.a ✓ 44 1.a even 1 1 trivial
201.3.c.a ✓ 44 3.b odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(201, [\chi])\).