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Properties

Label 276.7.d.a
Level $276$
Weight $7$
Character orbit 276.d
Analytic conductor $63.495$
Analytic rank $0$
Dimension $44$
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] = [276,7,Mod(185,276)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(276, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("276.185");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 276.d (of order \(2\), degree \(1\), 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: \(63.4949270791\)
Analytic rank: \(0\)
Dimension: \(44\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 44 q - 20 q^{3} - 968 q^{7} + 1292 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 44 q - 20 q^{3} - 968 q^{7} + 1292 q^{9} - 8648 q^{13} + 7696 q^{15} - 19304 q^{19} - 6416 q^{21} - 121972 q^{25} - 14804 q^{27} + 95752 q^{31} - 26688 q^{33} - 20456 q^{37} - 153168 q^{39} - 83000 q^{43} - 245264 q^{45} + 370212 q^{49} + 540032 q^{51} - 775440 q^{55} + 113336 q^{57} - 318152 q^{61} + 392832 q^{63} + 571144 q^{67} + 941464 q^{73} - 7468 q^{75} + 230440 q^{79} - 2079724 q^{81} + 3819120 q^{85} - 1133296 q^{87} - 3518560 q^{91} + 1630224 q^{93} - 1206728 q^{97} + 902040 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
185.1 0 −26.8446 − 2.89270i 0 − 153.558i 0 −72.8684 0 712.265 + 155.307i 0
185.2 0 −26.8446 + 2.89270i 0 153.558i 0 −72.8684 0 712.265 − 155.307i 0
185.3 0 −26.5400 − 4.96256i 0 166.980i 0 132.275 0 679.746 + 263.413i 0
185.4 0 −26.5400 + 4.96256i 0 − 166.980i 0 132.275 0 679.746 − 263.413i 0
185.5 0 −25.3192 − 9.37745i 0 − 96.1831i 0 564.886 0 553.127 + 474.859i 0
185.6 0 −25.3192 + 9.37745i 0 96.1831i 0 564.886 0 553.127 − 474.859i 0
185.7 0 −25.1636 − 9.78738i 0 − 51.2257i 0 −310.407 0 537.414 + 492.572i 0
185.8 0 −25.1636 + 9.78738i 0 51.2257i 0 −310.407 0 537.414 − 492.572i 0
185.9 0 −22.2086 − 15.3551i 0 153.276i 0 −253.836 0 257.443 + 682.029i 0
185.10 0 −22.2086 + 15.3551i 0 − 153.276i 0 −253.836 0 257.443 − 682.029i 0
185.11 0 −17.8660 − 20.2437i 0 25.4361i 0 −563.487 0 −90.6142 + 723.346i 0
185.12 0 −17.8660 + 20.2437i 0 − 25.4361i 0 −563.487 0 −90.6142 − 723.346i 0
185.13 0 −16.4896 − 21.3797i 0 − 60.5967i 0 324.497 0 −185.187 + 705.086i 0
185.14 0 −16.4896 + 21.3797i 0 60.5967i 0 324.497 0 −185.187 − 705.086i 0
185.15 0 −14.0854 − 23.0348i 0 − 238.897i 0 −384.130 0 −332.204 + 648.908i 0
185.16 0 −14.0854 + 23.0348i 0 238.897i 0 −384.130 0 −332.204 − 648.908i 0
185.17 0 −13.2946 − 23.5001i 0 158.820i 0 273.950 0 −375.509 + 624.847i 0
185.18 0 −13.2946 + 23.5001i 0 − 158.820i 0 273.950 0 −375.509 − 624.847i 0
185.19 0 −12.7008 − 23.8262i 0 134.449i 0 353.743 0 −406.378 + 605.226i 0
185.20 0 −12.7008 + 23.8262i 0 − 134.449i 0 353.743 0 −406.378 − 605.226i 0
See all 44 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 185.44
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 276.7.d.a ✓ 44
3.b odd 2 1 inner 276.7.d.a ✓ 44
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
276.7.d.a ✓ 44 1.a even 1 1 trivial
276.7.d.a ✓ 44 3.b odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{7}^{\mathrm{new}}(276, [\chi])\).