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Properties

Label 2252.4.a.b
Level $2252$
Weight $4$
Character orbit 2252.a
Self dual yes
Analytic conductor $132.872$
Analytic rank $0$
Dimension $75$
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] = [2252,4,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, 4); 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, 4, names="a")
 
Level: \( N \) \(=\) \( 2252 = 2^{2} \cdot 563 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2252.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [75] 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: \(132.872301333\)
Analytic rank: \(0\)
Dimension: \(75\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 75 q + 28 q^{3} - 5 q^{5} + 99 q^{7} + 781 q^{9} + 116 q^{11} + 4 q^{13} + 278 q^{15} + 181 q^{17} + 316 q^{19} + 56 q^{21} + 559 q^{23} + 2508 q^{25} + 940 q^{27} - 121 q^{29} + 822 q^{31} + 498 q^{33}+ \cdots + 4658 q^{99}+O(q^{100}) \) 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 −9.64281 0 −15.6607 0 2.82485 0 65.9838 0
1.2 0 −9.33422 0 15.5540 0 32.5722 0 60.1277 0
1.3 0 −9.13371 0 11.5781 0 −15.3092 0 56.4247 0
1.4 0 −9.07530 0 9.17507 0 10.8791 0 55.3610 0
1.5 0 −9.06971 0 −20.8423 0 8.58426 0 55.2597 0
1.6 0 −8.99758 0 −11.4289 0 −10.3862 0 53.9564 0
1.7 0 −8.54362 0 −3.19613 0 −33.5137 0 45.9935 0
1.8 0 −7.68821 0 −4.06371 0 21.8688 0 32.1085 0
1.9 0 −7.62710 0 −20.0306 0 −14.4715 0 31.1727 0
1.10 0 −7.44864 0 13.9758 0 16.6542 0 28.4823 0
1.11 0 −7.41771 0 19.9041 0 −11.4807 0 28.0224 0
1.12 0 −7.37912 0 −2.57990 0 −10.8489 0 27.4515 0
1.13 0 −7.00602 0 −8.96645 0 25.9512 0 22.0843 0
1.14 0 −6.71988 0 −1.04655 0 −4.95764 0 18.1568 0
1.15 0 −6.71365 0 6.08579 0 −11.0018 0 18.0731 0
1.16 0 −6.66999 0 −15.3660 0 −19.4853 0 17.4887 0
1.17 0 −5.71585 0 14.0490 0 23.6900 0 5.67090 0
1.18 0 −5.53559 0 −19.8247 0 30.8799 0 3.64280 0
1.19 0 −5.53493 0 4.32495 0 −17.7350 0 3.63546 0
1.20 0 −5.27327 0 8.83580 0 13.8431 0 0.807418 0
See all 75 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.75
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 2252.4.a.b ✓ 75
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2252.4.a.b ✓ 75 1.a even 1 1 trivial