Properties

Label 4024.2.a.d
Level 4024
Weight 2
Character orbit 4024.a
Self dual Yes
Analytic conductor 32.132
Analytic rank 1
Dimension 28
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: \(1\)
Dimension: \(28\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 28q + 2q^{3} - 12q^{5} + 18q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 28q + 2q^{3} - 12q^{5} + 18q^{9} - 14q^{11} - 31q^{13} - 2q^{15} - 9q^{17} - 8q^{19} - 28q^{21} - 4q^{23} + 22q^{25} - 4q^{27} - 47q^{29} - 5q^{31} - 26q^{33} - 13q^{35} - 67q^{37} - 9q^{39} - 28q^{41} + 15q^{43} - 57q^{45} - 10q^{47} + 20q^{49} - 11q^{51} - 58q^{53} + 15q^{55} - 31q^{57} - 32q^{59} - 55q^{61} - 16q^{63} - 44q^{65} + 22q^{67} - 44q^{69} - 47q^{71} - 5q^{73} - 25q^{75} - 50q^{77} - 14q^{79} - 28q^{81} - 16q^{83} - 78q^{85} - 11q^{87} - 20q^{89} - 15q^{91} - 83q^{93} - 27q^{95} - 8q^{97} - 70q^{99} + O(q^{100}) \)

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 −3.02746 0 −1.92479 0 4.18734 0 6.16549 0
1.2 0 −2.92644 0 0.124991 0 2.19824 0 5.56407 0
1.3 0 −2.80686 0 −3.33080 0 −2.85725 0 4.87847 0
1.4 0 −2.25613 0 2.34171 0 2.23682 0 2.09012 0
1.5 0 −2.22675 0 −3.90847 0 −0.127234 0 1.95840 0
1.6 0 −1.98770 0 0.688613 0 −1.63548 0 0.950962 0
1.7 0 −1.73728 0 2.58604 0 2.10260 0 0.0181326 0
1.8 0 −1.72455 0 0.586565 0 −2.46074 0 −0.0259209 0
1.9 0 −1.32661 0 −1.90684 0 −4.79236 0 −1.24010 0
1.10 0 −0.893789 0 −3.85908 0 3.77625 0 −2.20114 0
1.11 0 −0.667261 0 0.307121 0 4.25072 0 −2.55476 0
1.12 0 −0.596863 0 3.74289 0 1.10831 0 −2.64375 0
1.13 0 −0.447624 0 0.901345 0 −1.57888 0 −2.79963 0
1.14 0 −0.0730681 0 −4.10981 0 −1.52145 0 −2.99466 0
1.15 0 0.659121 0 0.997881 0 0.366743 0 −2.56556 0
1.16 0 0.682343 0 3.69511 0 −3.46637 0 −2.53441 0
1.17 0 0.799349 0 0.626001 0 −0.555593 0 −2.36104 0
1.18 0 0.823496 0 −2.12271 0 4.15456 0 −2.32185 0
1.19 0 1.49100 0 −1.09730 0 −0.799854 0 −0.776913 0
1.20 0 1.59308 0 2.75433 0 1.46360 0 −0.462108 0
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.28
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4024))\):

\(T_{3}^{28} - \cdots\)
\(T_{5}^{28} + \cdots\)
\(T_{7}^{28} - \cdots\)