Properties

Label 4024.2.a.g
Level 4024
Weight 2
Character orbit 4024.a
Self dual Yes
Analytic conductor 32.132
Analytic rank 0
Dimension 33
CM No

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Newspace parameters

Level: \( N \) = \( 4024 = 2^{3} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4024.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1318017734\)
Analytic rank: \(0\)
Dimension: \(33\)
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.

\(\operatorname{Tr}(f)(q) = \) \(33q \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 47q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(33q \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 47q^{9} \) \(\mathstrut +\mathstrut 22q^{11} \) \(\mathstrut -\mathstrut 17q^{13} \) \(\mathstrut +\mathstrut 22q^{15} \) \(\mathstrut +\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 6q^{21} \) \(\mathstrut +\mathstrut 36q^{23} \) \(\mathstrut +\mathstrut 47q^{25} \) \(\mathstrut +\mathstrut 34q^{27} \) \(\mathstrut +\mathstrut 13q^{29} \) \(\mathstrut +\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 14q^{33} \) \(\mathstrut +\mathstrut 33q^{35} \) \(\mathstrut -\mathstrut 55q^{37} \) \(\mathstrut +\mathstrut 37q^{39} \) \(\mathstrut +\mathstrut 42q^{41} \) \(\mathstrut +\mathstrut 23q^{43} \) \(\mathstrut +\mathstrut 5q^{45} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut +\mathstrut 55q^{49} \) \(\mathstrut +\mathstrut 53q^{51} \) \(\mathstrut -\mathstrut 32q^{53} \) \(\mathstrut +\mathstrut 35q^{55} \) \(\mathstrut +\mathstrut 21q^{57} \) \(\mathstrut +\mathstrut 20q^{59} \) \(\mathstrut -\mathstrut 15q^{61} \) \(\mathstrut +\mathstrut 48q^{63} \) \(\mathstrut +\mathstrut 34q^{65} \) \(\mathstrut +\mathstrut 66q^{67} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut +\mathstrut 61q^{71} \) \(\mathstrut +\mathstrut 19q^{73} \) \(\mathstrut +\mathstrut 59q^{75} \) \(\mathstrut +\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 62q^{79} \) \(\mathstrut +\mathstrut 77q^{81} \) \(\mathstrut +\mathstrut 36q^{83} \) \(\mathstrut -\mathstrut 14q^{85} \) \(\mathstrut +\mathstrut 43q^{87} \) \(\mathstrut +\mathstrut 34q^{89} \) \(\mathstrut +\mathstrut 41q^{91} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 61q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 98q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.28143 0 −3.08568 0 0.442605 0 7.76776 0
1.2 0 −2.94941 0 3.18881 0 1.60634 0 5.69904 0
1.3 0 −2.71136 0 −1.51865 0 −2.20669 0 4.35148 0
1.4 0 −2.52320 0 −3.79071 0 1.89288 0 3.36655 0
1.5 0 −2.39336 0 0.556589 0 4.72926 0 2.72817 0
1.6 0 −2.15460 0 −0.0166844 0 −4.51155 0 1.64231 0
1.7 0 −2.14143 0 2.09880 0 3.79183 0 1.58570 0
1.8 0 −2.13657 0 −1.27952 0 1.02417 0 1.56495 0
1.9 0 −1.65797 0 −0.641790 0 −1.04800 0 −0.251130 0
1.10 0 −1.02127 0 0.309055 0 −3.45255 0 −1.95700 0
1.11 0 −0.950380 0 3.01565 0 0.279316 0 −2.09678 0
1.12 0 −0.741660 0 −2.54437 0 −0.0722362 0 −2.44994 0
1.13 0 −0.648270 0 2.57860 0 −1.91468 0 −2.57975 0
1.14 0 −0.105343 0 −1.39521 0 −1.93153 0 −2.98890 0
1.15 0 0.221515 0 4.40155 0 5.16895 0 −2.95093 0
1.16 0 0.281703 0 −0.580455 0 2.82149 0 −2.92064 0
1.17 0 0.410265 0 −4.21207 0 3.36092 0 −2.83168 0
1.18 0 0.649284 0 −2.92377 0 −1.90965 0 −2.57843 0
1.19 0 0.885832 0 −0.282055 0 −2.95093 0 −2.21530 0
1.20 0 0.940347 0 2.53897 0 0.182218 0 −2.11575 0
See all 33 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.33
Significant digits:
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Inner twists

This newform does not have CM; other inner twists have not been computed.

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(503\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4024))\):

\(T_{3}^{33} - \cdots\)
\(T_{5}^{33} - \cdots\)
\(T_{7}^{33} - \cdots\)