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Properties

Label 275.3.f.c
Level $275$
Weight $3$
Character orbit 275.f
Analytic conductor $7.493$
Analytic rank $0$
Dimension $24$
Inner twists $4$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [275,3,Mod(232,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.232"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Level: \( N \) \(=\) \( 275 = 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 275.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24] 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: \(7.49320726991\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 8 q^{6} - 128 q^{16} - 88 q^{21} + 96 q^{26} + 360 q^{31} + 176 q^{36} - 152 q^{41} + 56 q^{46} - 512 q^{51} - 1048 q^{56} + 784 q^{61} - 440 q^{66} + 728 q^{71} + 1704 q^{76} - 568 q^{81} - 328 q^{86}+ \cdots + 1568 q^{96}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
232.1 −2.61911 − 2.61911i 3.50488 − 3.50488i 9.71948i 0 −18.3593 −6.89960 − 6.89960i 14.9800 − 14.9800i − 15.5684i 0
232.2 −2.31629 − 2.31629i −0.535688 + 0.535688i 6.73036i 0 2.48161 −2.25638 − 2.25638i 6.32430 − 6.32430i 8.42608i 0
232.3 −1.94573 − 1.94573i −2.32995 + 2.32995i 3.57173i 0 9.06691 −4.69739 − 4.69739i −0.833292 + 0.833292i − 1.85733i 0
232.4 −1.02070 − 1.02070i 0.314710 − 0.314710i − 1.91636i 0 −0.642447 6.75035 + 6.75035i −6.03880 + 6.03880i 8.80192i 0
232.5 −0.925034 − 0.925034i −3.86940 + 3.86940i − 2.28862i 0 7.15866 −2.48674 − 2.48674i −5.81719 + 5.81719i − 20.9446i 0
232.6 −0.302824 − 0.302824i 2.81582 − 2.81582i − 3.81659i 0 −1.70540 −3.80626 − 3.80626i −2.36706 + 2.36706i − 6.85771i 0
232.7 0.302824 + 0.302824i −2.81582 + 2.81582i − 3.81659i 0 −1.70540 3.80626 + 3.80626i 2.36706 − 2.36706i − 6.85771i 0
232.8 0.925034 + 0.925034i 3.86940 − 3.86940i − 2.28862i 0 7.15866 2.48674 + 2.48674i 5.81719 − 5.81719i − 20.9446i 0
232.9 1.02070 + 1.02070i −0.314710 + 0.314710i − 1.91636i 0 −0.642447 −6.75035 − 6.75035i 6.03880 − 6.03880i 8.80192i 0
232.10 1.94573 + 1.94573i 2.32995 − 2.32995i 3.57173i 0 9.06691 4.69739 + 4.69739i 0.833292 − 0.833292i − 1.85733i 0
232.11 2.31629 + 2.31629i 0.535688 − 0.535688i 6.73036i 0 2.48161 2.25638 + 2.25638i −6.32430 + 6.32430i 8.42608i 0
232.12 2.61911 + 2.61911i −3.50488 + 3.50488i 9.71948i 0 −18.3593 6.89960 + 6.89960i −14.9800 + 14.9800i − 15.5684i 0
243.1 −2.61911 + 2.61911i 3.50488 + 3.50488i − 9.71948i 0 −18.3593 −6.89960 + 6.89960i 14.9800 + 14.9800i 15.5684i 0
243.2 −2.31629 + 2.31629i −0.535688 − 0.535688i − 6.73036i 0 2.48161 −2.25638 + 2.25638i 6.32430 + 6.32430i − 8.42608i 0
243.3 −1.94573 + 1.94573i −2.32995 − 2.32995i − 3.57173i 0 9.06691 −4.69739 + 4.69739i −0.833292 − 0.833292i 1.85733i 0
243.4 −1.02070 + 1.02070i 0.314710 + 0.314710i 1.91636i 0 −0.642447 6.75035 − 6.75035i −6.03880 − 6.03880i − 8.80192i 0
243.5 −0.925034 + 0.925034i −3.86940 − 3.86940i 2.28862i 0 7.15866 −2.48674 + 2.48674i −5.81719 − 5.81719i 20.9446i 0
243.6 −0.302824 + 0.302824i 2.81582 + 2.81582i 3.81659i 0 −1.70540 −3.80626 + 3.80626i −2.36706 − 2.36706i 6.85771i 0
243.7 0.302824 − 0.302824i −2.81582 − 2.81582i 3.81659i 0 −1.70540 3.80626 − 3.80626i 2.36706 + 2.36706i 6.85771i 0
243.8 0.925034 − 0.925034i 3.86940 + 3.86940i 2.28862i 0 7.15866 2.48674 − 2.48674i 5.81719 + 5.81719i 20.9446i 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 232.12
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
5.c odd 4 2 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 275.3.f.c ✓ 24
5.b even 2 1 inner 275.3.f.c ✓ 24
5.c odd 4 2 inner 275.3.f.c ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
275.3.f.c ✓ 24 1.a even 1 1 trivial
275.3.f.c ✓ 24 5.b even 2 1 inner
275.3.f.c ✓ 24 5.c odd 4 2 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{24} + 368T_{2}^{20} + 41712T_{2}^{16} + 1532498T_{2}^{12} + 9581632T_{2}^{8} + 16119648T_{2}^{4} + 531441 \) acting on \(S_{3}^{\mathrm{new}}(275, [\chi])\). Copy content Toggle raw display