Properties

Label 2008.2.a.d
Level 2008
Weight 2
Character orbit 2008.a
Self dual yes
Analytic conductor 16.034
Analytic rank 0
Dimension 23
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 2008 = 2^{3} \cdot 251 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2008.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(16.0339607259\)
Analytic rank: \(0\)
Dimension: \(23\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 23q + 2q^{3} + 8q^{5} + 2q^{7} + 45q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 23q + 2q^{3} + 8q^{5} + 2q^{7} + 45q^{9} + 8q^{11} + 8q^{13} + 7q^{15} + 19q^{17} - 9q^{19} + 9q^{21} + 21q^{23} + 65q^{25} + 5q^{27} + 10q^{29} - 9q^{31} + 34q^{33} + 12q^{35} + 11q^{37} - 9q^{39} + 35q^{41} - 9q^{43} + 29q^{45} + 37q^{47} + 77q^{49} - 17q^{51} + 38q^{53} - 20q^{55} + 51q^{57} + 17q^{59} + 22q^{63} + 41q^{65} + 9q^{67} + 8q^{69} + 13q^{71} + 41q^{73} + 25q^{75} + 36q^{77} - 36q^{79} + 127q^{81} + 29q^{83} + 34q^{85} + 10q^{87} + 36q^{89} - 6q^{91} + 36q^{93} + 25q^{95} + 40q^{97} + 19q^{99} + O(q^{100}) \)

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.

Label \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 0 −3.39399 0 −1.84335 0 −1.40053 0 8.51918 0
1.2 0 −3.22331 0 3.75978 0 2.77250 0 7.38975 0
1.3 0 −3.19806 0 −2.92729 0 4.80027 0 7.22760 0
1.4 0 −2.74485 0 2.14962 0 −3.54966 0 4.53421 0
1.5 0 −2.21536 0 3.09704 0 −4.67984 0 1.90784 0
1.6 0 −2.13165 0 0.257423 0 0.578263 0 1.54395 0
1.7 0 −1.28390 0 3.72143 0 −0.978625 0 −1.35160 0
1.8 0 −1.19399 0 −1.76720 0 −4.20476 0 −1.57440 0
1.9 0 −1.15579 0 −4.09592 0 −0.621313 0 −1.66414 0
1.10 0 −0.347951 0 −1.66668 0 3.92094 0 −2.87893 0
1.11 0 −0.201914 0 −1.79819 0 3.34181 0 −2.95923 0
1.12 0 −0.0812979 0 4.08000 0 4.55548 0 −2.99339 0
1.13 0 0.259421 0 −1.96371 0 −4.76268 0 −2.93270 0
1.14 0 0.452441 0 1.91039 0 1.96124 0 −2.79530 0
1.15 0 1.39383 0 −3.54571 0 −3.34862 0 −1.05724 0
1.16 0 1.63778 0 2.87336 0 −2.53418 0 −0.317671 0
1.17 0 1.96174 0 0.807414 0 3.34299 0 0.848432 0
1.18 0 2.51727 0 −0.472191 0 4.16870 0 3.33662 0
1.19 0 2.53334 0 1.50187 0 0.478852 0 3.41783 0
1.20 0 2.67736 0 4.29688 0 −4.01755 0 4.16827 0
See all 23 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.23
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2008.2.a.d 23
4.b odd 2 1 4016.2.a.m 23
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2008.2.a.d 23 1.a even 1 1 trivial
4016.2.a.m 23 4.b odd 2 1

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(251\) \(1\)

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{3}^{23} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2008))\).

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database