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Properties

Label 23.25.b.c
Level $23$
Weight $25$
Character orbit 23.b
Analytic conductor $83.942$
Analytic rank $0$
Dimension $44$
Inner twists $2$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [23,25,Mod(22,23)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(23, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 25, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("23.22"); S:= CuspForms(chi, 25); N := Newforms(S);
 
Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 25 \)
Character orbit: \([\chi]\) \(=\) 23.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [44] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(83.9424450193\)
Analytic rank: \(0\)
Dimension: \(44\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 44 q - 4232 q^{2} - 434562 q^{3} + 317760360 q^{4} - 8460029520 q^{6} - 198307023760 q^{8} + 4220041988298 q^{9} - 67439597688792 q^{12} + 5771152551358 q^{13} + 18\!\cdots\!92 q^{16} + 18\!\cdots\!68 q^{18}+ \cdots - 20\!\cdots\!92 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
22.1 −7585.13 776377. 4.07570e7 − 3.88802e8i −5.88892e9 7.00512e9i −1.81889e11 3.20332e11 2.94912e12i
22.2 −7585.13 776377. 4.07570e7 3.88802e8i −5.88892e9 − 7.00512e9i −1.81889e11 3.20332e11 − 2.94912e12i
22.3 −7352.04 −139223. 3.72753e7 − 1.97315e8i 1.02357e9 − 1.56753e10i −1.50703e11 −2.63047e11 1.45067e12i
22.4 −7352.04 −139223. 3.72753e7 1.97315e8i 1.02357e9 1.56753e10i −1.50703e11 −2.63047e11 − 1.45067e12i
22.5 −7217.83 −896325. 3.53199e7 2.65149e8i 6.46953e9 − 2.16086e10i −1.33838e11 5.20969e11 − 1.91380e12i
22.6 −7217.83 −896325. 3.53199e7 − 2.65149e8i 6.46953e9 2.16086e10i −1.33838e11 5.20969e11 1.91380e12i
22.7 −5488.94 236392. 1.33512e7 1.99463e8i −1.29754e9 − 1.19586e10i 1.88050e10 −2.26549e11 − 1.09484e12i
22.8 −5488.94 236392. 1.33512e7 − 1.99463e8i −1.29754e9 1.19586e10i 1.88050e10 −2.26549e11 1.09484e12i
22.9 −4898.68 −558886. 7.21988e6 − 3.44673e8i 2.73780e9 − 1.10267e10i 4.68184e10 2.99237e10 1.68844e12i
22.10 −4898.68 −558886. 7.21988e6 3.44673e8i 2.73780e9 1.10267e10i 4.68184e10 2.99237e10 − 1.68844e12i
22.11 −4488.28 914024. 3.36747e6 − 5.44878e7i −4.10240e9 − 2.39870e10i 6.01867e10 5.53011e11 2.44557e11i
22.12 −4488.28 914024. 3.36747e6 5.44878e7i −4.10240e9 2.39870e10i 6.01867e10 5.53011e11 − 2.44557e11i
22.13 −4410.99 −600091. 2.67964e6 − 2.08680e8i 2.64700e9 − 9.90757e8i 6.21843e10 7.76795e10 9.20488e11i
22.14 −4410.99 −600091. 2.67964e6 2.08680e8i 2.64700e9 9.90757e8i 6.21843e10 7.76795e10 − 9.20488e11i
22.15 −2772.08 573161. −9.09276e6 − 4.41675e8i −1.58885e9 − 1.06536e10i 7.17138e10 4.60840e10 1.22436e12i
22.16 −2772.08 573161. −9.09276e6 4.41675e8i −1.58885e9 1.06536e10i 7.17138e10 4.60840e10 − 1.22436e12i
22.17 −2739.52 −10954.6 −9.27226e6 2.86680e8i 3.00102e7 − 2.46062e10i 7.13630e10 −2.82310e11 − 7.85365e11i
22.18 −2739.52 −10954.6 −9.27226e6 − 2.86680e8i 3.00102e7 2.46062e10i 7.13630e10 −2.82310e11 7.85365e11i
22.19 −1213.58 142839. −1.53044e7 − 1.97797e8i −1.73346e8 − 6.84832e9i 3.89336e10 −2.62027e11 2.40042e11i
22.20 −1213.58 142839. −1.53044e7 1.97797e8i −1.73346e8 6.84832e9i 3.89336e10 −2.62027e11 − 2.40042e11i
See all 44 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 22.44
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 23.25.b.c ✓ 44
23.b odd 2 1 inner 23.25.b.c ✓ 44
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
23.25.b.c ✓ 44 1.a even 1 1 trivial
23.25.b.c ✓ 44 23.b odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{22} + 2116 T_{2}^{21} - 261750738 T_{2}^{20} - 500304430576 T_{2}^{19} + \cdots - 10\!\cdots\!00 \) acting on \(S_{25}^{\mathrm{new}}(23, [\chi])\). Copy content Toggle raw display