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Properties

Label 9295.2.a.bh
Level $9295$
Weight $2$
Character orbit 9295.a
Self dual yes
Analytic conductor $74.221$
Analytic rank $0$
Dimension $27$
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: \(27\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 27 q + 8 q^{2} + 20 q^{4} + 27 q^{5} - 8 q^{6} + 6 q^{7} + 21 q^{8} + 23 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 27 q + 8 q^{2} + 20 q^{4} + 27 q^{5} - 8 q^{6} + 6 q^{7} + 21 q^{8} + 23 q^{9} + 8 q^{10} - 27 q^{11} + 2 q^{12} - 11 q^{14} + 2 q^{16} + 13 q^{17} + 28 q^{18} + 8 q^{19} + 20 q^{20} + 23 q^{21} - 8 q^{22} - 9 q^{23} + 16 q^{24} + 27 q^{25} + 6 q^{27} - 7 q^{28} - 5 q^{29} - 8 q^{30} + 23 q^{31} + 5 q^{32} + 49 q^{34} + 6 q^{35} + 18 q^{36} + 16 q^{37} + 28 q^{38} + 21 q^{40} + 54 q^{41} - 7 q^{42} + 8 q^{43} - 20 q^{44} + 23 q^{45} + 31 q^{46} - 4 q^{47} + 58 q^{48} + 5 q^{49} + 8 q^{50} - 13 q^{51} + 11 q^{53} - 26 q^{54} - 27 q^{55} - 12 q^{56} + 30 q^{57} + 15 q^{58} + 42 q^{59} + 2 q^{60} + 12 q^{61} + 46 q^{62} - 14 q^{63} - 15 q^{64} + 8 q^{66} + 24 q^{67} + 34 q^{68} - 36 q^{69} - 11 q^{70} + 49 q^{71} + 74 q^{72} + 45 q^{73} + 26 q^{74} - 18 q^{76} - 6 q^{77} - 2 q^{79} + 2 q^{80} - 33 q^{81} - 32 q^{82} + 60 q^{83} + 57 q^{84} + 13 q^{85} + 53 q^{86} + 64 q^{87} - 21 q^{88} + 59 q^{89} + 28 q^{90} + 29 q^{92} + 2 q^{93} - 32 q^{94} + 8 q^{95} + 77 q^{96} + 18 q^{97} + 16 q^{98} - 23 q^{99}+O(q^{100}) \) 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 −2.36286 0.648070 3.58312 1.00000 −1.53130 0.905399 −3.74068 −2.58000 −2.36286
1.2 −2.29853 1.71528 3.28323 1.00000 −3.94262 3.59768 −2.94955 −0.0578166 −2.29853
1.3 −2.12151 −2.09175 2.50081 1.00000 4.43768 −1.53530 −1.06248 1.37542 −2.12151
1.4 −1.93716 0.685089 1.75260 1.00000 −1.32713 −2.19732 0.479255 −2.53065 −1.93716
1.5 −1.35629 3.15254 −0.160465 1.00000 −4.27577 0.920298 2.93023 6.93848 −1.35629
1.6 −1.17745 −1.02518 −0.613615 1.00000 1.20710 −3.20681 3.07740 −1.94901 −1.17745
1.7 −1.16252 −1.12323 −0.648545 1.00000 1.30578 2.17350 3.07899 −1.73835 −1.16252
1.8 −1.07303 −2.04914 −0.848605 1.00000 2.19879 4.44032 3.05664 1.19897 −1.07303
1.9 −0.840537 1.23975 −1.29350 1.00000 −1.04205 3.16755 2.76831 −1.46303 −0.840537
1.10 −0.717665 −2.54599 −1.48496 1.00000 1.82716 −3.51072 2.50103 3.48204 −0.717665
1.11 −0.636377 2.95097 −1.59502 1.00000 −1.87793 0.612371 2.28779 5.70821 −0.636377
1.12 −0.0960831 1.30916 −1.99077 1.00000 −0.125788 −1.40279 0.383445 −1.28611 −0.0960831
1.13 0.140494 1.29629 −1.98026 1.00000 0.182121 4.03393 −0.559204 −1.31963 0.140494
1.14 0.325483 −2.44484 −1.89406 1.00000 −0.795754 −1.20157 −1.26745 2.97726 0.325483
1.15 0.435051 2.52777 −1.81073 1.00000 1.09971 −2.19046 −1.65786 3.38960 0.435051
1.16 1.05173 −0.440251 −0.893855 1.00000 −0.463027 3.30536 −3.04357 −2.80618 1.05173
1.17 1.12827 −0.441613 −0.727016 1.00000 −0.498257 1.25714 −3.07680 −2.80498 1.12827
1.18 1.16567 −2.14211 −0.641208 1.00000 −2.49700 2.31698 −3.07878 1.58864 1.16567
1.19 1.63303 1.09031 0.666789 1.00000 1.78051 −3.70753 −2.17717 −1.81123 1.63303
1.20 1.85209 −0.618919 1.43023 1.00000 −1.14629 −4.05373 −1.05527 −2.61694 1.85209
See all 27 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.27
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.bh yes 27
13.b even 2 1 9295.2.a.bg ✓ 27
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
9295.2.a.bg ✓ 27 13.b even 2 1
9295.2.a.bh yes 27 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(9295))\):

\( T_{2}^{27} - 8 T_{2}^{26} - 5 T_{2}^{25} + 193 T_{2}^{24} - 272 T_{2}^{23} - 1894 T_{2}^{22} + 4600 T_{2}^{21} + \cdots - 43 \) Copy content Toggle raw display
\( T_{3}^{27} - 52 T_{3}^{25} - 2 T_{3}^{24} + 1187 T_{3}^{23} + 76 T_{3}^{22} - 15670 T_{3}^{21} + \cdots - 57863 \) Copy content Toggle raw display