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Properties

Label 696.2.y.c
Level $696$
Weight $2$
Character orbit 696.y
Analytic conductor $5.558$
Analytic rank $0$
Dimension $24$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [696,2,Mod(25,696)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(696, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("696.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 696 = 2^{3} \cdot 3 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 696.y (of order \(7\), degree \(6\), 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: \(5.55758798068\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{7})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 4 q^{3} + q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 4 q^{3} + q^{5} + 4 q^{7} - 4 q^{9} - 12 q^{11} + 7 q^{13} + q^{15} - 38 q^{17} - 18 q^{19} + 4 q^{21} - 6 q^{23} - 19 q^{25} - 4 q^{27} + 5 q^{29} - 2 q^{31} + 2 q^{33} + 21 q^{35} - 18 q^{37} + 7 q^{39} - 70 q^{41} - q^{43} + q^{45} + 23 q^{47} + 8 q^{49} + 11 q^{51} + 26 q^{53} - 17 q^{55} + 10 q^{57} - 4 q^{59} + 10 q^{61} - 3 q^{63} + 43 q^{65} + 2 q^{67} + 8 q^{69} + 16 q^{71} + 8 q^{73} + 30 q^{75} - 36 q^{77} + 45 q^{79} - 4 q^{81} - 10 q^{83} - 53 q^{85} - 16 q^{87} + 10 q^{89} + 57 q^{91} - 2 q^{93} - 34 q^{95} + 96 q^{97} + 2 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
25.1 0 −0.900969 + 0.433884i 0 −0.650578 + 2.85037i 0 2.75146 − 1.32503i 0 0.623490 − 0.781831i 0
25.2 0 −0.900969 + 0.433884i 0 −0.301797 + 1.32226i 0 −1.69408 + 0.815825i 0 0.623490 − 0.781831i 0
25.3 0 −0.900969 + 0.433884i 0 0.578049 − 2.53260i 0 −3.37334 + 1.62452i 0 0.623490 − 0.781831i 0
25.4 0 −0.900969 + 0.433884i 0 0.596848 − 2.61496i 0 3.71693 − 1.78998i 0 0.623490 − 0.781831i 0
49.1 0 0.623490 + 0.781831i 0 −1.90319 + 0.916530i 0 −1.94859 − 2.44345i 0 −0.222521 + 0.974928i 0
49.2 0 0.623490 + 0.781831i 0 −0.697550 + 0.335922i 0 1.08688 + 1.36290i 0 −0.222521 + 0.974928i 0
49.3 0 0.623490 + 0.781831i 0 0.546465 − 0.263164i 0 −1.49416 − 1.87362i 0 −0.222521 + 0.974928i 0
49.4 0 0.623490 + 0.781831i 0 2.95525 − 1.42317i 0 2.23238 + 2.79932i 0 −0.222521 + 0.974928i 0
169.1 0 −0.222521 − 0.974928i 0 −2.47254 − 3.10047i 0 −0.654567 − 2.86785i 0 −0.900969 + 0.433884i 0
169.2 0 −0.222521 − 0.974928i 0 −0.629035 − 0.788784i 0 1.08686 + 4.76183i 0 −0.900969 + 0.433884i 0
169.3 0 −0.222521 − 0.974928i 0 −0.143868 − 0.180405i 0 0.241011 + 1.05594i 0 −0.900969 + 0.433884i 0
169.4 0 −0.222521 − 0.974928i 0 2.62195 + 3.28782i 0 0.0492213 + 0.215653i 0 −0.900969 + 0.433884i 0
313.1 0 −0.222521 + 0.974928i 0 −2.47254 + 3.10047i 0 −0.654567 + 2.86785i 0 −0.900969 − 0.433884i 0
313.2 0 −0.222521 + 0.974928i 0 −0.629035 + 0.788784i 0 1.08686 − 4.76183i 0 −0.900969 − 0.433884i 0
313.3 0 −0.222521 + 0.974928i 0 −0.143868 + 0.180405i 0 0.241011 − 1.05594i 0 −0.900969 − 0.433884i 0
313.4 0 −0.222521 + 0.974928i 0 2.62195 − 3.28782i 0 0.0492213 − 0.215653i 0 −0.900969 − 0.433884i 0
529.1 0 −0.900969 − 0.433884i 0 −0.650578 − 2.85037i 0 2.75146 + 1.32503i 0 0.623490 + 0.781831i 0
529.2 0 −0.900969 − 0.433884i 0 −0.301797 − 1.32226i 0 −1.69408 − 0.815825i 0 0.623490 + 0.781831i 0
529.3 0 −0.900969 − 0.433884i 0 0.578049 + 2.53260i 0 −3.37334 − 1.62452i 0 0.623490 + 0.781831i 0
529.4 0 −0.900969 − 0.433884i 0 0.596848 + 2.61496i 0 3.71693 + 1.78998i 0 0.623490 + 0.781831i 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 25.4
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
29.d even 7 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 696.2.y.c ✓ 24
29.d even 7 1 inner 696.2.y.c ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
696.2.y.c ✓ 24 1.a even 1 1 trivial
696.2.y.c ✓ 24 29.d even 7 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{24} - T_{5}^{23} + 20 T_{5}^{22} - 13 T_{5}^{21} + 407 T_{5}^{20} - 174 T_{5}^{19} + \cdots + 121801 \) acting on \(S_{2}^{\mathrm{new}}(696, [\chi])\). Copy content Toggle raw display