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Properties

Label 595.2.k.a
Level $595$
Weight $2$
Character orbit 595.k
Analytic conductor $4.751$
Analytic rank $0$
Dimension $28$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [595,2,Mod(106,595)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(595, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("595.106");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 595 = 5 \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 595.k (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: \(4.75109892027\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q + 4 q^{3} - 16 q^{4}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 28 q + 4 q^{3} - 16 q^{4} + 4 q^{10} + 8 q^{11} + 8 q^{12} + 36 q^{13} - 4 q^{14} - 12 q^{17} - 32 q^{18} + 8 q^{21} - 16 q^{22} - 8 q^{24} - 8 q^{27} + 16 q^{29} + 16 q^{30} - 16 q^{31} - 8 q^{33} - 40 q^{34} + 28 q^{35} + 8 q^{37} - 24 q^{38} - 12 q^{39} + 8 q^{40} + 40 q^{41} - 16 q^{44} + 44 q^{46} + 36 q^{47} - 64 q^{48} - 8 q^{50} + 28 q^{51} - 64 q^{52} + 40 q^{54} + 16 q^{55} - 8 q^{56} - 8 q^{57} - 40 q^{58} - 40 q^{61} + 36 q^{62} + 40 q^{64} - 16 q^{65} - 56 q^{67} - 16 q^{68} - 72 q^{69} + 48 q^{71} - 8 q^{72} + 52 q^{73} - 28 q^{74} - 4 q^{75} + 56 q^{78} + 20 q^{79} + 44 q^{81} - 28 q^{82} + 40 q^{84} - 40 q^{86} + 8 q^{88} + 16 q^{89} + 12 q^{90} - 16 q^{91} + 24 q^{92} - 4 q^{95} + 104 q^{96} - 12 q^{97} + 8 q^{98} - 112 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
106.1 − 2.59592i −1.66674 + 1.66674i −4.73883 0.707107 − 0.707107i 4.32674 + 4.32674i 0.707107 + 0.707107i 7.10979i − 2.55607i −1.83560 − 1.83560i
106.2 − 2.44130i −0.475689 + 0.475689i −3.95993 −0.707107 + 0.707107i 1.16130 + 1.16130i −0.707107 − 0.707107i 4.78478i 2.54744i 1.72626 + 1.72626i
106.3 − 2.23371i 1.74985 − 1.74985i −2.98946 −0.707107 + 0.707107i −3.90866 − 3.90866i −0.707107 − 0.707107i 2.21018i − 3.12394i 1.57947 + 1.57947i
106.4 − 1.83120i 1.53701 − 1.53701i −1.35329 0.707107 − 0.707107i −2.81456 − 2.81456i 0.707107 + 0.707107i − 1.18425i − 1.72477i −1.29485 − 1.29485i
106.5 − 0.929487i 1.54570 − 1.54570i 1.13605 −0.707107 + 0.707107i −1.43671 − 1.43671i −0.707107 − 0.707107i − 2.91492i − 1.77836i 0.657247 + 0.657247i
106.6 − 0.719783i 0.0792478 − 0.0792478i 1.48191 0.707107 − 0.707107i −0.0570412 − 0.0570412i 0.707107 + 0.707107i − 2.50622i 2.98744i −0.508963 − 0.508963i
106.7 − 0.658517i −2.21796 + 2.21796i 1.56636 −0.707107 + 0.707107i 1.46057 + 1.46057i −0.707107 − 0.707107i − 2.34850i − 6.83873i 0.465642 + 0.465642i
106.8 − 0.407696i −1.05784 + 1.05784i 1.83378 −0.707107 + 0.707107i 0.431276 + 0.431276i −0.707107 − 0.707107i − 1.56302i 0.761959i 0.288285 + 0.288285i
106.9 0.0599808i 1.67516 − 1.67516i 1.99640 0.707107 − 0.707107i 0.100478 + 0.100478i 0.707107 + 0.707107i 0.239707i − 2.61235i 0.0424128 + 0.0424128i
106.10 0.872845i −0.286859 + 0.286859i 1.23814 0.707107 − 0.707107i −0.250383 − 0.250383i 0.707107 + 0.707107i 2.82640i 2.83542i 0.617195 + 0.617195i
106.11 1.25114i 0.821899 − 0.821899i 0.434654 −0.707107 + 0.707107i 1.02831 + 1.02831i −0.707107 − 0.707107i 3.04609i 1.64896i −0.884688 − 0.884688i
106.12 1.66911i 2.01900 − 2.01900i −0.785922 0.707107 − 0.707107i 3.36992 + 3.36992i 0.707107 + 0.707107i 2.02643i − 5.15270i 1.18024 + 1.18024i
106.13 1.95919i −0.942598 + 0.942598i −1.83841 0.707107 − 0.707107i −1.84673 − 1.84673i 0.707107 + 0.707107i 0.316577i 1.22302i 1.38535 + 1.38535i
106.14 2.00536i −0.780168 + 0.780168i −2.02145 −0.707107 + 0.707107i −1.56452 − 1.56452i −0.707107 − 0.707107i − 0.0430212i 1.78267i −1.41800 − 1.41800i
421.1 − 2.00536i −0.780168 − 0.780168i −2.02145 −0.707107 − 0.707107i −1.56452 + 1.56452i −0.707107 + 0.707107i 0.0430212i − 1.78267i −1.41800 + 1.41800i
421.2 − 1.95919i −0.942598 − 0.942598i −1.83841 0.707107 + 0.707107i −1.84673 + 1.84673i 0.707107 − 0.707107i − 0.316577i − 1.22302i 1.38535 − 1.38535i
421.3 − 1.66911i 2.01900 + 2.01900i −0.785922 0.707107 + 0.707107i 3.36992 − 3.36992i 0.707107 − 0.707107i − 2.02643i 5.15270i 1.18024 − 1.18024i
421.4 − 1.25114i 0.821899 + 0.821899i 0.434654 −0.707107 − 0.707107i 1.02831 − 1.02831i −0.707107 + 0.707107i − 3.04609i − 1.64896i −0.884688 + 0.884688i
421.5 − 0.872845i −0.286859 − 0.286859i 1.23814 0.707107 + 0.707107i −0.250383 + 0.250383i 0.707107 − 0.707107i − 2.82640i − 2.83542i 0.617195 − 0.617195i
421.6 − 0.0599808i 1.67516 + 1.67516i 1.99640 0.707107 + 0.707107i 0.100478 − 0.100478i 0.707107 − 0.707107i − 0.239707i 2.61235i 0.0424128 − 0.0424128i
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 106.14
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 595.2.k.a ✓ 28
17.c even 4 1 inner 595.2.k.a ✓ 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
595.2.k.a ✓ 28 1.a even 1 1 trivial
595.2.k.a ✓ 28 17.c even 4 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{28} + 36 T_{2}^{26} + 568 T_{2}^{24} + 5172 T_{2}^{22} + 30126 T_{2}^{20} + 117628 T_{2}^{18} + \cdots + 4 \) acting on \(S_{2}^{\mathrm{new}}(595, [\chi])\). Copy content Toggle raw display