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Properties

Label 2900.2.j.d
Level $2900$
Weight $2$
Character orbit 2900.j
Analytic conductor $23.157$
Analytic rank $0$
Dimension $30$
Inner twists $2$

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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] = [2900,2,Mod(1757,2900)] 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("2900.1757"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2900, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 3])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2900.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [30,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(23.1566165862\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(15\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 580)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 30 q - 38 q^{9} - 4 q^{11} - 6 q^{13} - 12 q^{17} - 4 q^{21} - 4 q^{31} + 4 q^{33} + 12 q^{39} + 10 q^{41} + 18 q^{53} + 24 q^{57} - 22 q^{61} + 24 q^{63} + 16 q^{67} + 8 q^{69} + 20 q^{73} - 20 q^{77}+ \cdots + 44 q^{93}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1757.1 0 − 3.33306i 0 0 0 −2.63647 − 2.63647i 0 −8.10929 0
1757.2 0 − 2.93055i 0 0 0 1.87865 + 1.87865i 0 −5.58815 0
1757.3 0 − 1.94358i 0 0 0 2.43648 + 2.43648i 0 −0.777490 0
1757.4 0 − 1.61432i 0 0 0 −1.96009 − 1.96009i 0 0.393986 0
1757.5 0 − 1.59876i 0 0 0 −2.73334 − 2.73334i 0 0.443956 0
1757.6 0 − 1.57681i 0 0 0 1.37454 + 1.37454i 0 0.513683 0
1757.7 0 − 0.357354i 0 0 0 1.34106 + 1.34106i 0 2.87230 0
1757.8 0 − 0.121921i 0 0 0 2.56056 + 2.56056i 0 2.98514 0
1757.9 0 0.548138i 0 0 0 −1.10894 − 1.10894i 0 2.69955 0
1757.10 0 0.938623i 0 0 0 −0.222978 − 0.222978i 0 2.11899 0
1757.11 0 0.993874i 0 0 0 −1.61651 − 1.61651i 0 2.01221 0
1757.12 0 2.30110i 0 0 0 2.56511 + 2.56511i 0 −2.29505 0
1757.13 0 2.68138i 0 0 0 −3.30434 − 3.30434i 0 −4.18982 0
1757.14 0 2.99066i 0 0 0 1.61250 + 1.61250i 0 −5.94404 0
1757.15 0 3.02258i 0 0 0 −0.186244 − 0.186244i 0 −6.13596 0
2593.1 0 − 3.02258i 0 0 0 −0.186244 + 0.186244i 0 −6.13596 0
2593.2 0 − 2.99066i 0 0 0 1.61250 − 1.61250i 0 −5.94404 0
2593.3 0 − 2.68138i 0 0 0 −3.30434 + 3.30434i 0 −4.18982 0
2593.4 0 − 2.30110i 0 0 0 2.56511 − 2.56511i 0 −2.29505 0
2593.5 0 − 0.993874i 0 0 0 −1.61651 + 1.61651i 0 2.01221 0
See all 30 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1757.15
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
145.j even 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2900.2.j.d 30
5.b even 2 1 580.2.j.a ✓ 30
5.c odd 4 1 580.2.s.a yes 30
5.c odd 4 1 2900.2.s.d 30
29.c odd 4 1 2900.2.s.d 30
145.e even 4 1 580.2.j.a ✓ 30
145.f odd 4 1 580.2.s.a yes 30
145.j even 4 1 inner 2900.2.j.d 30
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
580.2.j.a ✓ 30 5.b even 2 1
580.2.j.a ✓ 30 145.e even 4 1
580.2.s.a yes 30 5.c odd 4 1
580.2.s.a yes 30 145.f odd 4 1
2900.2.j.d 30 1.a even 1 1 trivial
2900.2.j.d 30 145.j even 4 1 inner
2900.2.s.d 30 5.c odd 4 1
2900.2.s.d 30 29.c odd 4 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(2900, [\chi])\):

\( T_{3}^{30} + 64 T_{3}^{28} + 1810 T_{3}^{26} + 29828 T_{3}^{24} + 318129 T_{3}^{22} + 2307580 T_{3}^{20} + \cdots + 9216 \) Copy content Toggle raw display
\( T_{7}^{30} - 32 T_{7}^{27} + 788 T_{7}^{26} - 584 T_{7}^{25} + 512 T_{7}^{24} - 15208 T_{7}^{23} + \cdots + 3159171072 \) Copy content Toggle raw display