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Properties

Label 2671.2.a.a
Level $2671$
Weight $2$
Character orbit 2671.a
Self dual yes
Analytic conductor $21.328$
Analytic rank $1$
Dimension $100$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2671,2,Mod(1,2671)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2671, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2671.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2671 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2671.a (trivial)

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: yes
Analytic conductor: \(21.3280423799\)
Analytic rank: \(1\)
Dimension: \(100\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9} - 18 q^{10} - 47 q^{11} - 27 q^{12} - 29 q^{13} - 51 q^{14} - 36 q^{15} + 71 q^{16} - 99 q^{17} - 27 q^{18} - 45 q^{19} - 75 q^{20} - 79 q^{21} - 2 q^{22} - 25 q^{23} - 66 q^{24} + 67 q^{25} - 73 q^{26} - 42 q^{27} - 31 q^{28} - 78 q^{29} - 29 q^{30} - 41 q^{31} - 95 q^{32} - 83 q^{33} - 44 q^{34} - 45 q^{35} + 23 q^{36} - 16 q^{37} - 29 q^{38} - 42 q^{39} - 37 q^{40} - 235 q^{41} + 16 q^{42} - 6 q^{43} - 122 q^{44} - 79 q^{45} - 17 q^{46} - 67 q^{47} - 25 q^{48} + 30 q^{49} - 68 q^{50} - 18 q^{51} - 41 q^{52} - 69 q^{53} - 63 q^{54} - 32 q^{55} - 120 q^{56} - 63 q^{57} - 7 q^{58} - 118 q^{59} - 49 q^{60} - 60 q^{61} - 23 q^{62} - 43 q^{63} + 43 q^{64} - 181 q^{65} - 4 q^{66} - 18 q^{67} - 130 q^{68} - 80 q^{69} + 12 q^{70} - 77 q^{71} - 40 q^{72} - 64 q^{73} - 48 q^{74} - 18 q^{75} - 134 q^{76} - 87 q^{77} + 65 q^{78} - 48 q^{79} - 95 q^{80} - 20 q^{81} + 45 q^{82} - 108 q^{83} - 97 q^{84} - 21 q^{85} - 73 q^{86} - 3 q^{87} + 23 q^{88} - 325 q^{89} + 6 q^{90} - 17 q^{91} - 19 q^{92} + 2 q^{93} - 5 q^{94} - 54 q^{95} - 105 q^{96} - 81 q^{97} - 61 q^{98} - 76 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.80496 2.67697 5.86782 −1.54261 −7.50881 −2.92720 −10.8491 4.16618 4.32696
1.2 −2.80384 −1.37761 5.86149 −3.59556 3.86258 1.57324 −10.8270 −1.10220 10.0814
1.3 −2.69051 −1.24665 5.23884 2.30924 3.35414 −0.0663222 −8.71414 −1.44585 −6.21303
1.4 −2.65824 −2.83500 5.06626 1.38285 7.53611 2.52336 −8.15086 5.03721 −3.67595
1.5 −2.65228 1.67415 5.03461 −0.470328 −4.44032 5.05032 −8.04864 −0.197216 1.24744
1.6 −2.63232 0.654225 4.92913 4.21254 −1.72213 2.55546 −7.71041 −2.57199 −11.0888
1.7 −2.55134 2.61383 4.50931 −3.64015 −6.66875 1.17460 −6.40210 3.83208 9.28724
1.8 −2.48925 0.330466 4.19635 −3.29084 −0.822611 −3.86741 −5.46725 −2.89079 8.19171
1.9 −2.48716 0.674976 4.18594 −1.47569 −1.67877 0.0650875 −5.43678 −2.54441 3.67028
1.10 −2.48625 −0.481659 4.18145 −0.210015 1.19752 3.08014 −5.42364 −2.76800 0.522149
1.11 −2.46456 1.92343 4.07405 1.93724 −4.74040 0.00639246 −5.11163 0.699577 −4.77444
1.12 −2.36950 −2.91929 3.61453 −2.45502 6.91725 2.36017 −3.82563 5.52224 5.81717
1.13 −2.34805 −1.17352 3.51335 0.325575 2.75549 −3.11218 −3.55342 −1.62284 −0.764466
1.14 −2.31874 1.73446 3.37653 1.64543 −4.02176 −4.56234 −3.19182 0.00836456 −3.81531
1.15 −2.29881 −1.31088 3.28453 −2.94582 3.01346 3.93138 −2.95288 −1.28160 6.77187
1.16 −2.27914 −1.38876 3.19449 2.94510 3.16518 −0.786669 −2.72241 −1.07135 −6.71230
1.17 −2.25786 3.34765 3.09793 1.77447 −7.55852 −3.19525 −2.47897 8.20674 −4.00650
1.18 −2.05843 −1.01531 2.23713 3.90551 2.08995 −2.16322 −0.488125 −1.96914 −8.03921
1.19 −2.02059 −1.97857 2.08280 −4.01327 3.99789 −3.20759 −0.167301 0.914756 8.10918
1.20 −1.95878 2.24677 1.83681 −3.63031 −4.40093 3.35399 0.319648 2.04798 7.11096
See all 100 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.100
Significant digits:
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Atkin-Lehner signs

\( p \) Sign
\(2671\) \(1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2671.2.a.a ✓ 100
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2671.2.a.a ✓ 100 1.a even 1 1 trivial