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Properties

Label 9295.2.a.bn
Level $9295$
Weight $2$
Character orbit 9295.a
Self dual yes
Analytic conductor $74.221$
Analytic rank $0$
Dimension $33$
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] = [9295,2,Mod(1,9295)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9295, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("9295.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9295 = 5 \cdot 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9295.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: \(74.2209486788\)
Analytic rank: \(0\)
Dimension: \(33\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 33 q + 8 q^{2} + 12 q^{3} + 38 q^{4} + 33 q^{5} + 18 q^{6} + 4 q^{7} + 21 q^{8} + 35 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 33 q + 8 q^{2} + 12 q^{3} + 38 q^{4} + 33 q^{5} + 18 q^{6} + 4 q^{7} + 21 q^{8} + 35 q^{9} + 8 q^{10} + 33 q^{11} + 24 q^{12} - 5 q^{14} + 12 q^{15} + 44 q^{16} + 9 q^{17} + 18 q^{18} + 8 q^{19} + 38 q^{20} + 9 q^{21} + 8 q^{22} + 7 q^{23} + 54 q^{24} + 33 q^{25} + 42 q^{27} + 15 q^{28} - 11 q^{29} + 18 q^{30} + 13 q^{31} + 85 q^{32} + 12 q^{33} + 31 q^{34} + 4 q^{35} + 26 q^{36} + 22 q^{37} - 2 q^{38} + 21 q^{40} + 36 q^{41} + 11 q^{42} + 26 q^{43} + 38 q^{44} + 35 q^{45} - q^{46} + 46 q^{47} + 36 q^{48} + 29 q^{49} + 8 q^{50} - 41 q^{51} + 9 q^{53} + 70 q^{54} + 33 q^{55} - 10 q^{56} + 70 q^{57} - 23 q^{58} + 18 q^{59} + 24 q^{60} - 42 q^{61} - 24 q^{62} + 68 q^{63} + 39 q^{64} + 18 q^{66} + 26 q^{67} + 8 q^{68} + 12 q^{69} - 5 q^{70} + 43 q^{71} + 46 q^{72} + 21 q^{73} - 22 q^{74} + 12 q^{75} + 2 q^{76} + 4 q^{77} - 22 q^{79} + 44 q^{80} + 41 q^{81} + 156 q^{82} + 26 q^{83} + 11 q^{84} + 9 q^{85} + 17 q^{86} - 30 q^{87} + 21 q^{88} + 95 q^{89} + 18 q^{90} + 37 q^{92} + 62 q^{93} - 14 q^{94} + 8 q^{95} + 53 q^{96} + 40 q^{97} + 132 q^{98} + 35 q^{99}+O(q^{100}) \) 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 −2.58885 −0.164798 4.70213 1.00000 0.426637 1.29450 −6.99539 −2.97284 −2.58885
1.2 −2.46512 −1.46150 4.07683 1.00000 3.60278 −0.651176 −5.11963 −0.864017 −2.46512
1.3 −2.30664 −2.51350 3.32060 1.00000 5.79775 2.51268 −3.04616 3.31769 −2.30664
1.4 −2.12317 1.90615 2.50787 1.00000 −4.04710 −1.10038 −1.07830 0.633418 −2.12317
1.5 −2.09764 2.93662 2.40008 1.00000 −6.15996 3.60886 −0.839226 5.62373 −2.09764
1.6 −2.09229 0.442485 2.37768 1.00000 −0.925807 −3.56147 −0.790226 −2.80421 −2.09229
1.7 −1.89039 2.16689 1.57359 1.00000 −4.09627 0.877387 0.806091 1.69539 −1.89039
1.8 −1.59687 −2.94097 0.550005 1.00000 4.69636 0.406690 2.31546 5.64930 −1.59687
1.9 −1.30927 −1.82341 −0.285811 1.00000 2.38734 1.57243 2.99274 0.324824 −1.30927
1.10 −1.19648 −0.120072 −0.568430 1.00000 0.143664 −2.54576 3.07308 −2.98558 −1.19648
1.11 −0.865026 2.91225 −1.25173 1.00000 −2.51918 2.38769 2.81283 5.48122 −0.865026
1.12 −0.726588 −0.747717 −1.47207 1.00000 0.543283 −1.84423 2.52277 −2.44092 −0.726588
1.13 −0.504644 1.66887 −1.74533 1.00000 −0.842186 1.09425 1.89006 −0.214866 −0.504644
1.14 −0.195188 2.50755 −1.96190 1.00000 −0.489443 −4.23215 0.773314 3.28782 −0.195188
1.15 0.0773181 0.560241 −1.99402 1.00000 0.0433168 0.179955 −0.308810 −2.68613 0.0773181
1.16 0.188836 −0.179741 −1.96434 1.00000 −0.0339416 4.50025 −0.748612 −2.96769 0.188836
1.17 0.676070 1.15350 −1.54293 1.00000 0.779848 −4.22950 −2.39527 −1.66943 0.676070
1.18 0.702071 −2.55552 −1.50710 1.00000 −1.79415 4.02216 −2.46223 3.53066 0.702071
1.19 0.717895 −2.94870 −1.48463 1.00000 −2.11685 −0.587136 −2.50160 5.69480 0.717895
1.20 0.799159 3.45090 −1.36134 1.00000 2.75782 3.69864 −2.68625 8.90870 0.799159
See all 33 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.33
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(11\) \(-1\)
\(13\) \(-1\)

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 9295.2.a.bn yes 33
13.b even 2 1 9295.2.a.bm ✓ 33
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
9295.2.a.bm ✓ 33 13.b even 2 1
9295.2.a.bn yes 33 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(9295))\):

\( T_{2}^{33} - 8 T_{2}^{32} - 20 T_{2}^{31} + 313 T_{2}^{30} - 134 T_{2}^{29} - 5309 T_{2}^{28} + \cdots - 1051 \) Copy content Toggle raw display
\( T_{3}^{33} - 12 T_{3}^{32} + 5 T_{3}^{31} + 478 T_{3}^{30} - 1497 T_{3}^{29} - 7274 T_{3}^{28} + \cdots - 12277 \) Copy content Toggle raw display