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Properties

Label 2491.2.a.a
Level $2491$
Weight $2$
Character orbit 2491.a
Self dual yes
Analytic conductor $19.891$
Analytic rank $1$
Dimension $43$
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] = [2491,2,Mod(1,2491)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2491, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2491.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2491 = 47 \cdot 53 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2491.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: \(19.8907351435\)
Analytic rank: \(1\)
Dimension: \(43\)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 43 q - 12 q^{2} - 9 q^{3} + 36 q^{4} - 19 q^{5} - 4 q^{6} - 11 q^{7} - 30 q^{8} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 43 q - 12 q^{2} - 9 q^{3} + 36 q^{4} - 19 q^{5} - 4 q^{6} - 11 q^{7} - 30 q^{8} + 24 q^{9} + 11 q^{10} - 19 q^{11} - 6 q^{12} - 8 q^{13} - 9 q^{14} - 2 q^{15} + 30 q^{16} - 19 q^{17} - 25 q^{18} - 15 q^{19} - 61 q^{20} - 47 q^{21} - 7 q^{22} - 11 q^{23} + 5 q^{24} + 26 q^{25} - 26 q^{26} - 33 q^{27} - 41 q^{28} - 70 q^{29} - 16 q^{30} - 2 q^{31} - 77 q^{32} - 28 q^{33} - 20 q^{34} - 4 q^{35} + 40 q^{36} - 23 q^{37} + 20 q^{38} - 36 q^{39} + 51 q^{40} - 51 q^{41} + 19 q^{42} - 3 q^{43} - 31 q^{44} - 13 q^{45} - 32 q^{46} + 43 q^{47} - 26 q^{48} + 26 q^{49} - 70 q^{50} - 15 q^{51} - q^{52} + 43 q^{53} + 17 q^{54} - 19 q^{55} - 33 q^{56} - 33 q^{57} + 28 q^{58} - 74 q^{59} - 39 q^{60} - 50 q^{61} - 31 q^{62} + 15 q^{63} + 52 q^{64} - 78 q^{65} - 34 q^{66} - 22 q^{67} - 12 q^{68} - 35 q^{69} + 32 q^{70} - 50 q^{71} - 41 q^{72} - 45 q^{73} - 98 q^{74} - 42 q^{75} - 25 q^{76} - 58 q^{77} - 17 q^{78} - 48 q^{79} - 114 q^{80} - 93 q^{81} + 82 q^{82} - 46 q^{83} - 69 q^{84} - 53 q^{85} - 82 q^{86} + 18 q^{87} + 33 q^{88} - 48 q^{89} - 13 q^{90} + 47 q^{91} + 8 q^{92} - 10 q^{93} - 12 q^{94} - 39 q^{95} - 51 q^{96} - 19 q^{97} - 32 q^{98} - 26 q^{99}+O(q^{100}) \) 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 −2.74958 −2.65952 5.56016 −3.44621 7.31256 2.57451 −9.78894 4.07307 9.47561
1.2 −2.74853 2.23094 5.55443 −0.944632 −6.13182 2.38679 −9.76948 1.97710 2.59635
1.3 −2.73094 1.52977 5.45801 −4.38555 −4.17771 −4.54429 −9.44360 −0.659796 11.9767
1.4 −2.60617 −1.91390 4.79213 1.85476 4.98794 −2.01164 −7.27678 0.663001 −4.83381
1.5 −2.48790 −1.19714 4.18965 −1.86445 2.97837 2.08143 −5.44764 −1.56685 4.63857
1.6 −2.32996 1.34758 3.42869 0.399433 −3.13979 −1.01938 −3.32879 −1.18404 −0.930660
1.7 −2.30384 −0.966098 3.30768 1.99092 2.22573 −3.12179 −3.01268 −2.06665 −4.58677
1.8 −2.06328 2.19440 2.25714 3.46425 −4.52766 −2.29146 −0.530548 1.81537 −7.14773
1.9 −2.06133 −3.27208 2.24906 −0.510376 6.74483 2.96615 −0.513404 7.70653 1.05205
1.10 −2.03655 2.29213 2.14754 −2.31753 −4.66804 −0.675957 −0.300471 2.25387 4.71977
1.11 −1.67856 −0.734344 0.817574 −3.43305 1.23264 4.41702 1.98478 −2.46074 5.76259
1.12 −1.51953 2.63993 0.308972 −2.18022 −4.01145 2.81611 2.56957 3.96921 3.31290
1.13 −1.50460 −1.17593 0.263824 −4.13535 1.76930 −4.10871 2.61225 −1.61720 6.22206
1.14 −1.46884 1.28847 0.157495 −0.376841 −1.89256 −4.25758 2.70635 −1.33985 0.553520
1.15 −1.40146 −1.82757 −0.0359114 −1.32872 2.56127 −2.07922 2.85325 0.340012 1.86214
1.16 −1.36608 −2.94197 −0.133833 2.85803 4.01896 1.43611 2.91498 5.65520 −3.90429
1.17 −1.11837 −0.525242 −0.749259 0.845707 0.587413 0.0664612 3.07468 −2.72412 −0.945809
1.18 −0.873373 1.40038 −1.23722 3.86489 −1.22306 0.518755 2.82730 −1.03893 −3.37549
1.19 −0.862697 −2.27067 −1.25575 2.07274 1.95890 2.33620 2.80873 2.15593 −1.78815
1.20 −0.574779 1.73433 −1.66963 −3.23570 −0.996858 0.886948 2.10922 0.00791413 1.85981
See all 43 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.43
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(47\) \( -1 \)
\(53\) \( -1 \)

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 2491.2.a.a ✓ 43
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2491.2.a.a ✓ 43 1.a even 1 1 trivial