Properties

Label 4024.2.a.f
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.

\(\operatorname{Tr}(f)(q) = \) \(33q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 43q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(33q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 43q^{9} \) \(\mathstrut +\mathstrut 22q^{11} \) \(\mathstrut +\mathstrut 25q^{13} \) \(\mathstrut -\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut +\mathstrut 18q^{21} \) \(\mathstrut +\mathstrut 16q^{23} \) \(\mathstrut +\mathstrut 47q^{25} \) \(\mathstrut -\mathstrut 20q^{27} \) \(\mathstrut +\mathstrut 47q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 19q^{35} \) \(\mathstrut +\mathstrut 75q^{37} \) \(\mathstrut +\mathstrut 21q^{39} \) \(\mathstrut +\mathstrut 22q^{41} \) \(\mathstrut -\mathstrut 5q^{43} \) \(\mathstrut +\mathstrut 33q^{45} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 31q^{49} \) \(\mathstrut +\mathstrut 9q^{51} \) \(\mathstrut +\mathstrut 64q^{53} \) \(\mathstrut -\mathstrut 3q^{55} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut +\mathstrut 28q^{59} \) \(\mathstrut +\mathstrut 49q^{61} \) \(\mathstrut -\mathstrut 10q^{63} \) \(\mathstrut +\mathstrut 46q^{65} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 30q^{69} \) \(\mathstrut +\mathstrut 35q^{71} \) \(\mathstrut +\mathstrut 19q^{73} \) \(\mathstrut -\mathstrut 33q^{75} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut -\mathstrut 12q^{79} \) \(\mathstrut +\mathstrut 57q^{81} \) \(\mathstrut +\mathstrut 82q^{85} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut -\mathstrut 15q^{91} \) \(\mathstrut +\mathstrut 55q^{93} \) \(\mathstrut +\mathstrut 33q^{95} \) \(\mathstrut +\mathstrut 4q^{97} \) \(\mathstrut +\mathstrut 22q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.25521 0 −2.40628 0 −4.10646 0 7.59642 0
1.2 0 −3.20822 0 2.09579 0 −1.61648 0 7.29270 0
1.3 0 −3.01200 0 3.98796 0 4.01800 0 6.07216 0
1.4 0 −2.91979 0 2.60605 0 −3.20806 0 5.52520 0
1.5 0 −2.88194 0 −1.00235 0 −1.34540 0 5.30561 0
1.6 0 −2.48200 0 −3.41370 0 3.75697 0 3.16033 0
1.7 0 −2.27275 0 2.37900 0 1.75584 0 2.16537 0
1.8 0 −2.23369 0 −1.90057 0 0.0272535 0 1.98935 0
1.9 0 −2.05859 0 3.84987 0 −4.00015 0 1.23779 0
1.10 0 −2.05780 0 −1.22779 0 1.00021 0 1.23452 0
1.11 0 −1.25385 0 2.99234 0 2.30060 0 −1.42787 0
1.12 0 −1.19201 0 −0.00829431 0 3.59968 0 −1.57911 0
1.13 0 −0.710131 0 −2.92884 0 −1.90024 0 −2.49571 0
1.14 0 −0.502871 0 −1.85170 0 1.22131 0 −2.74712 0
1.15 0 −0.254882 0 3.76559 0 −2.29648 0 −2.93504 0
1.16 0 −0.224625 0 −2.01216 0 1.98253 0 −2.94954 0
1.17 0 0.0147975 0 −2.88853 0 −1.61248 0 −2.99978 0
1.18 0 0.176667 0 2.93614 0 −0.0214699 0 −2.96879 0
1.19 0 0.220191 0 1.20642 0 −3.77303 0 −2.95152 0
1.20 0 0.368053 0 2.18272 0 4.72026 0 −2.86454 0
See all 33 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.33
Significant digits:
Format:

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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4024))\):

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