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Properties

Label 2252.2.a.b
Level $2252$
Weight $2$
Character orbit 2252.a
Self dual yes
Analytic conductor $17.982$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $1$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [2252,2,Mod(1,2252)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2252.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2252, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 2252 = 2^{2} \cdot 563 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2252.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [28] 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: yes
Analytic conductor: \(17.9823105352\)
Analytic rank: \(0\)
Dimension: \(28\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q + 10 q^{3} + q^{5} + 17 q^{7} + 38 q^{9} + 5 q^{11} - q^{13} + 24 q^{15} + 10 q^{17} + 22 q^{19} - q^{21} + 25 q^{23} + 57 q^{25} + 43 q^{27} + q^{29} + 19 q^{31} + 12 q^{33} + 20 q^{35} - 4 q^{37}+ \cdots + 38 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 0 −3.26098 0 −1.74626 0 1.26487 0 7.63400 0
1.2 0 −3.07697 0 −3.00276 0 1.74657 0 6.46775 0
1.3 0 −2.34165 0 0.552672 0 4.84134 0 2.48330 0
1.4 0 −2.20885 0 3.73737 0 1.43192 0 1.87903 0
1.5 0 −1.90092 0 1.82113 0 −0.376428 0 0.613488 0
1.6 0 −1.80731 0 −0.115653 0 −2.31875 0 0.266359 0
1.7 0 −1.77147 0 −1.20933 0 −3.09129 0 0.138106 0
1.8 0 −1.50995 0 −4.27752 0 4.38293 0 −0.720038 0
1.9 0 −1.02119 0 3.57966 0 3.45707 0 −1.95718 0
1.10 0 −0.881070 0 −0.903782 0 −3.75712 0 −2.22372 0
1.11 0 −0.711234 0 1.02497 0 −0.180408 0 −2.49415 0
1.12 0 0.0797074 0 −2.02448 0 1.49982 0 −2.99365 0
1.13 0 0.159995 0 −3.45292 0 −3.53424 0 −2.97440 0
1.14 0 0.362809 0 −2.21691 0 4.23250 0 −2.86837 0
1.15 0 0.619731 0 1.49532 0 0.504249 0 −2.61593 0
1.16 0 0.693758 0 −4.24703 0 −1.18399 0 −2.51870 0
1.17 0 0.804714 0 2.54534 0 −3.68207 0 −2.35244 0
1.18 0 0.928046 0 4.12820 0 2.41113 0 −2.13873 0
1.19 0 2.00262 0 2.80087 0 3.55210 0 1.01050 0
1.20 0 2.22329 0 0.861271 0 3.19083 0 1.94302 0
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.28
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(563\) \( +1 \)

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 2252.2.a.b ✓ 28
4.b odd 2 1 9008.2.a.v 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2252.2.a.b ✓ 28 1.a even 1 1 trivial
9008.2.a.v 28 4.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{28} - 10 T_{3}^{27} - 11 T_{3}^{26} + 409 T_{3}^{25} - 660 T_{3}^{24} - 6796 T_{3}^{23} + \cdots - 7499 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2252))\). Copy content Toggle raw display