Properties

Label 4024.2.a.e
Level 4024
Weight 2
Character orbit 4024.a
Self dual Yes
Analytic conductor 32.132
Analytic rank 1
Dimension 29
CM No

Related objects

Downloads

Learn more about

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: \(1\)
Dimension: \(29\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 29q - 7q^{3} - 4q^{5} - 13q^{7} + 20q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 29q - 7q^{3} - 4q^{5} - 13q^{7} + 20q^{9} - 27q^{11} + 16q^{13} - 14q^{15} - 15q^{17} - 14q^{19} + q^{21} - 25q^{23} + 21q^{25} - 25q^{27} - 13q^{29} - 27q^{31} - 9q^{33} - 29q^{35} + 35q^{37} - 38q^{39} - 30q^{41} - 38q^{43} + q^{45} - 35q^{47} + 14q^{49} - 21q^{51} + 2q^{53} - 25q^{55} - 25q^{57} - 40q^{59} + 10q^{61} - 56q^{63} - 50q^{65} - 31q^{67} + 11q^{69} - 65q^{71} - 23q^{73} - 32q^{75} + 13q^{77} - 44q^{79} - 7q^{81} - 41q^{83} + 26q^{85} - 25q^{87} - 48q^{89} - 44q^{91} + 25q^{93} - 75q^{95} - 18q^{97} - 80q^{99} + O(q^{100}) \)

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 −3.34526 0 −0.499712 0 1.77499 0 8.19075 0
1.2 0 −3.05929 0 0.773308 0 −3.93634 0 6.35923 0
1.3 0 −2.89251 0 3.16304 0 −0.0867661 0 5.36660 0
1.4 0 −2.70977 0 2.99505 0 −2.81033 0 4.34283 0
1.5 0 −2.46401 0 −4.08257 0 −4.62698 0 3.07134 0
1.6 0 −2.34298 0 −1.32410 0 0.439798 0 2.48955 0
1.7 0 −2.20984 0 −0.810761 0 4.21793 0 1.88340 0
1.8 0 −1.85667 0 2.88879 0 1.11301 0 0.447227 0
1.9 0 −1.79909 0 0.0213618 0 −3.47965 0 0.236734 0
1.10 0 −1.15550 0 −3.26045 0 −1.92982 0 −1.66482 0
1.11 0 −1.10456 0 −2.70098 0 3.17910 0 −1.77994 0
1.12 0 −0.795174 0 3.83818 0 0.297725 0 −2.36770 0
1.13 0 −0.782310 0 2.74195 0 −3.13445 0 −2.38799 0
1.14 0 −0.582422 0 −3.18976 0 −3.00819 0 −2.66078 0
1.15 0 −0.502218 0 −3.38571 0 3.39706 0 −2.74778 0
1.16 0 −0.278789 0 −0.533193 0 1.93823 0 −2.92228 0
1.17 0 −0.137144 0 1.57958 0 4.44075 0 −2.98119 0
1.18 0 0.454325 0 0.622756 0 −4.14589 0 −2.79359 0
1.19 0 0.936010 0 1.25557 0 0.290471 0 −2.12388 0
1.20 0 1.28849 0 −1.09309 0 0.799248 0 −1.33979 0
See all 29 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.29
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4024))\):

\(T_{3}^{29} + \cdots\)
\(T_{5}^{29} + \cdots\)
\(T_{7}^{29} + \cdots\)