Properties

Label 5.33.c.a
Level $5$
Weight $33$
Character orbit 5.c
Analytic conductor $32.433$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5,33,Mod(2,5)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 33, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5.2");
 
S:= CuspForms(chi, 33);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 33 \)
Character orbit: \([\chi]\) \(=\) 5.c (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(32.4333275711\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(15\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 30 q - 2 q^{2} - 2792232 q^{3} + 229266409900 q^{5} - 645476451240 q^{6} + 21807690136848 q^{7} + 340768936037220 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 30 q - 2 q^{2} - 2792232 q^{3} + 229266409900 q^{5} - 645476451240 q^{6} + 21807690136848 q^{7} + 340768936037220 q^{8} - 17\!\cdots\!50 q^{10}+ \cdots + 12\!\cdots\!02 q^{98}+O(q^{100}) \) 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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2.1 −86676.0 86676.0i 3.32299e7 3.32299e7i 1.07305e10i 1.18818e11 + 9.57363e10i −5.76047e12 −3.06435e13 3.06435e13i 5.57804e14 5.57804e14i 3.55432e14i −2.00059e15 1.85967e16i
2.2 −73528.8 73528.8i −4.29377e6 + 4.29377e6i 6.51799e9i −1.18376e11 9.62823e10i 6.31431e11 1.36489e13 + 1.36489e13i 1.63456e14 1.63456e14i 1.81615e15i 1.62449e15 + 1.57835e16i
2.3 −70960.9 70960.9i −4.83700e7 + 4.83700e7i 5.77593e9i 1.51118e11 + 2.11291e10i 6.86476e12 2.09740e13 + 2.09740e13i 1.05090e14 1.05090e14i 2.82629e15i −9.22412e15 1.22228e16i
2.4 −42029.2 42029.2i −2.23370e7 + 2.23370e7i 7.62067e8i −7.62027e10 + 1.32198e11i 1.87761e12 −2.39791e13 2.39791e13i −2.12543e14 + 2.12543e14i 8.55140e14i 8.75889e15 2.35342e15i
2.5 −39535.2 39535.2i 4.69567e7 4.69567e7i 1.16890e9i −7.61848e10 + 1.32208e11i −3.71289e12 2.85172e13 + 2.85172e13i −2.16015e14 + 2.16015e14i 2.55684e15i 8.23885e15 2.21489e15i
2.6 −37971.9 37971.9i 3.04306e7 3.04306e7i 1.41124e9i 7.42414e10 1.33309e11i −2.31101e12 −9.26812e12 9.26812e12i −2.16675e14 + 2.16675e14i 9.78102e11i −7.88108e15 + 2.24291e15i
2.7 −7096.95 7096.95i −4.70380e7 + 4.70380e7i 4.19423e9i −3.87281e10 1.47591e11i 6.67652e11 −3.04405e13 3.04405e13i −6.02475e13 + 6.02475e13i 2.57212e15i −7.72597e14 + 1.32230e15i
2.8 −5100.58 5100.58i −7.18185e6 + 7.18185e6i 4.24294e9i 1.52141e11 + 1.16729e10i 7.32632e10 2.17171e13 + 2.17171e13i −4.35482e13 + 4.35482e13i 1.74986e15i −7.16467e14 8.35545e14i
2.9 24352.5 + 24352.5i −2.67962e7 + 2.67962e7i 3.10888e9i −1.49880e11 + 2.86196e10i −1.30511e12 4.33877e13 + 4.33877e13i 1.80302e14 1.80302e14i 4.16950e14i −4.34691e15 2.95300e15i
2.10 25524.4 + 25524.4i 3.82280e7 3.82280e7i 2.99198e9i −1.26030e11 8.60210e10i 1.95149e12 −1.22489e13 1.22489e13i 1.85995e14 1.85995e14i 1.06974e15i −1.02119e15 5.41245e15i
2.11 32395.0 + 32395.0i 1.63684e7 1.63684e7i 2.19610e9i 5.30856e10 + 1.43056e11i 1.06051e12 −2.79912e13 2.79912e13i 2.10278e14 2.10278e14i 1.31717e15i −2.91458e15 + 6.35400e15i
2.12 61735.6 + 61735.6i −5.69775e7 + 5.69775e7i 3.32760e9i 7.47335e10 + 1.33034e11i −7.03508e12 −1.03601e13 1.03601e13i 5.97211e13 5.97211e13i 4.63985e15i −3.59920e15 + 1.28266e16i
2.13 65410.6 + 65410.6i −1.37699e7 + 1.37699e7i 4.26212e9i 5.68539e10 1.41600e11i −1.80139e12 −2.41000e12 2.41000e12i 2.14856e12 2.14856e12i 1.47380e15i 1.29810e16 5.54333e15i
2.14 68938.0 + 68938.0i 5.43018e7 5.43018e7i 5.20993e9i 1.52114e11 + 1.20131e10i 7.48691e12 3.40627e13 + 3.40627e13i −6.30755e13 + 6.30755e13i 4.04435e15i 9.65829e15 + 1.13146e16i
2.15 84542.4 + 84542.4i 5.85262e6 5.85262e6i 9.99987e9i −1.33071e11 + 7.46670e10i 9.89589e11 −4.06221e12 4.06221e12i −4.82306e14 + 4.82306e14i 1.78451e15i −1.75627e16 4.93762e15i
3.1 −86676.0 + 86676.0i 3.32299e7 + 3.32299e7i 1.07305e10i 1.18818e11 9.57363e10i −5.76047e12 −3.06435e13 + 3.06435e13i 5.57804e14 + 5.57804e14i 3.55432e14i −2.00059e15 + 1.85967e16i
3.2 −73528.8 + 73528.8i −4.29377e6 4.29377e6i 6.51799e9i −1.18376e11 + 9.62823e10i 6.31431e11 1.36489e13 1.36489e13i 1.63456e14 + 1.63456e14i 1.81615e15i 1.62449e15 1.57835e16i
3.3 −70960.9 + 70960.9i −4.83700e7 4.83700e7i 5.77593e9i 1.51118e11 2.11291e10i 6.86476e12 2.09740e13 2.09740e13i 1.05090e14 + 1.05090e14i 2.82629e15i −9.22412e15 + 1.22228e16i
3.4 −42029.2 + 42029.2i −2.23370e7 2.23370e7i 7.62067e8i −7.62027e10 1.32198e11i 1.87761e12 −2.39791e13 + 2.39791e13i −2.12543e14 2.12543e14i 8.55140e14i 8.75889e15 + 2.35342e15i
3.5 −39535.2 + 39535.2i 4.69567e7 + 4.69567e7i 1.16890e9i −7.61848e10 1.32208e11i −3.71289e12 2.85172e13 2.85172e13i −2.16015e14 2.16015e14i 2.55684e15i 8.23885e15 + 2.21489e15i
See all 30 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2.15
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5.33.c.a 30
5.b even 2 1 25.33.c.b 30
5.c odd 4 1 inner 5.33.c.a 30
5.c odd 4 1 25.33.c.b 30
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
5.33.c.a 30 1.a even 1 1 trivial
5.33.c.a 30 5.c odd 4 1 inner
25.33.c.b 30 5.b even 2 1
25.33.c.b 30 5.c odd 4 1

Hecke kernels

This newform subspace is the entire newspace \(S_{33}^{\mathrm{new}}(5, [\chi])\).