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Properties

Label 2645.2.a.y
Level $2645$
Weight $2$
Character orbit 2645.a
Self dual yes
Analytic conductor $21.120$
Analytic rank $0$
Dimension $25$
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] = [2645,2,Mod(1,2645)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2645, 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("2645.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2645 = 5 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2645.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: \(21.1204313346\)
Analytic rank: \(0\)
Dimension: \(25\)
Twist minimal: no (minimal twist has level 115)
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.

\(\operatorname{Tr}(f)(q) = \) \( 25 q + 3 q^{2} + 10 q^{3} + 33 q^{4} + 25 q^{5} + 22 q^{6} + 14 q^{7} + 21 q^{8} + 29 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 25 q + 3 q^{2} + 10 q^{3} + 33 q^{4} + 25 q^{5} + 22 q^{6} + 14 q^{7} + 21 q^{8} + 29 q^{9} + 3 q^{10} - 8 q^{11} + 34 q^{12} + 15 q^{13} - 6 q^{14} + 10 q^{15} + 41 q^{16} + 19 q^{17} + 23 q^{18} - 8 q^{19} + 33 q^{20} - 21 q^{21} + 3 q^{22} + 51 q^{24} + 25 q^{25} + 7 q^{26} + 64 q^{27} + 27 q^{28} + 3 q^{29} + 22 q^{30} + 34 q^{31} + 30 q^{32} - q^{33} - 21 q^{34} + 14 q^{35} + 31 q^{36} - q^{37} - 7 q^{38} + 49 q^{39} + 21 q^{40} - 29 q^{42} + 25 q^{43} - 33 q^{44} + 29 q^{45} - 5 q^{47} + 42 q^{48} + 33 q^{49} + 3 q^{50} + 23 q^{51} + 67 q^{52} + 24 q^{53} + 37 q^{54} - 8 q^{55} - 55 q^{56} - 19 q^{57} + 49 q^{58} + 41 q^{59} + 34 q^{60} - 31 q^{61} - 3 q^{62} + 37 q^{63} + 77 q^{64} + 15 q^{65} - 39 q^{66} - 5 q^{67} + 27 q^{68} - 6 q^{70} + 15 q^{71} + 48 q^{72} + 34 q^{73} - 29 q^{74} + 10 q^{75} - 24 q^{76} - 35 q^{77} - 45 q^{78} - 41 q^{79} + 41 q^{80} + 25 q^{81} + 33 q^{82} + 62 q^{83} - 126 q^{84} + 19 q^{85} - 10 q^{86} + 26 q^{87} - 50 q^{88} - 23 q^{89} + 23 q^{90} + 19 q^{91} + 50 q^{93} + 9 q^{94} - 8 q^{95} + 64 q^{96} + 37 q^{97} - 55 q^{98} - 48 q^{99}+O(q^{100}) \) 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 −2.77886 0.0572572 5.72209 1.00000 −0.159110 1.37543 −10.3432 −2.99672 −2.77886
1.2 −2.47940 −2.25957 4.14745 1.00000 5.60239 4.34106 −5.32439 2.10566 −2.47940
1.3 −2.22274 3.02968 2.94058 1.00000 −6.73420 −1.99392 −2.09066 6.17897 −2.22274
1.4 −1.99415 0.0187055 1.97662 1.00000 −0.0373015 −3.85556 0.0466201 −2.99965 −1.99415
1.5 −1.98212 0.890963 1.92881 1.00000 −1.76600 3.58880 0.141099 −2.20618 −1.98212
1.6 −1.83504 −2.46419 1.36737 1.00000 4.52188 2.88992 1.16091 3.07221 −1.83504
1.7 −1.35155 2.86442 −0.173318 1.00000 −3.87140 4.00873 2.93734 5.20491 −1.35155
1.8 −1.30650 −1.02551 −0.293062 1.00000 1.33983 −1.22710 2.99588 −1.94832 −1.30650
1.9 −0.923959 2.23903 −1.14630 1.00000 −2.06877 3.27601 2.90705 2.01327 −0.923959
1.10 −0.898902 −1.87885 −1.19197 1.00000 1.68890 −2.86688 2.86927 0.530083 −0.898902
1.11 −0.882312 −0.851895 −1.22153 1.00000 0.751637 −1.35320 2.84239 −2.27428 −0.882312
1.12 −0.0882888 −2.89191 −1.99221 1.00000 0.255324 1.36091 0.352467 5.36317 −0.0882888
1.13 −0.00926679 0.278540 −1.99991 1.00000 −0.00258117 −4.18941 0.0370664 −2.92242 −0.00926679
1.14 0.276363 2.30051 −1.92362 1.00000 0.635776 −3.13580 −1.08435 2.29233 0.276363
1.15 0.844928 3.34010 −1.28610 1.00000 2.82214 3.17075 −2.77651 8.15624 0.844928
1.16 1.00674 −0.173368 −0.986478 1.00000 −0.174536 2.34225 −3.00660 −2.96994 1.00674
1.17 1.17302 −1.26837 −0.624029 1.00000 −1.48782 5.03190 −3.07803 −1.39123 1.17302
1.18 1.65528 −2.04439 0.739953 1.00000 −3.38404 1.15113 −2.08573 1.17953 1.65528
1.19 1.80878 −1.07945 1.27169 1.00000 −1.95249 1.74298 −1.31735 −1.83478 1.80878
1.20 2.10124 3.19240 2.41520 1.00000 6.70798 −3.48850 0.872423 7.19141 2.10124
See all 25 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.25
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(23\) \(1\)

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 2645.2.a.y 25
23.b odd 2 1 2645.2.a.x 25
23.c even 11 2 115.2.g.c ✓ 50
115.j even 22 2 575.2.k.d 50
115.k odd 44 4 575.2.p.d 100
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
115.2.g.c ✓ 50 23.c even 11 2
575.2.k.d 50 115.j even 22 2
575.2.p.d 100 115.k odd 44 4
2645.2.a.x 25 23.b odd 2 1
2645.2.a.y 25 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2645))\):

\( T_{2}^{25} - 3 T_{2}^{24} - 37 T_{2}^{23} + 109 T_{2}^{22} + 601 T_{2}^{21} - 1714 T_{2}^{20} + \cdots + 23 \) Copy content Toggle raw display
\( T_{7}^{25} - 14 T_{7}^{24} - 6 T_{7}^{23} + 936 T_{7}^{22} - 3014 T_{7}^{21} - 23152 T_{7}^{20} + \cdots + 455783021 \) Copy content Toggle raw display