Properties

Label 8032.2.a.i
Level $8032$
Weight $2$
Character orbit 8032.a
Self dual yes
Analytic conductor $64.136$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8032 = 2^{5} \cdot 251 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8032.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.1358429035\)
Analytic rank: \(0\)
Dimension: \(30\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 30q + 3q^{3} + 13q^{7} + 35q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 30q + 3q^{3} + 13q^{7} + 35q^{9} + 13q^{11} - 7q^{13} + 28q^{15} - 9q^{17} - 17q^{19} - 6q^{21} + 43q^{23} + 34q^{25} + 12q^{27} - q^{29} + 39q^{31} + 17q^{35} - q^{37} + 48q^{39} - 3q^{41} - 19q^{43} + 66q^{47} + 25q^{49} - 14q^{51} + 3q^{53} + 50q^{55} - 14q^{57} + 27q^{59} + 15q^{61} + 75q^{63} - 6q^{65} + 8q^{67} + 18q^{69} + 64q^{71} - 15q^{73} + 9q^{75} + 71q^{79} + 6q^{81} + 60q^{83} + 15q^{85} + 64q^{87} - 32q^{89} - 26q^{91} - 4q^{93} + 72q^{95} - 4q^{97} + 13q^{99} + O(q^{100}) \)

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 −3.18079 0 −0.628547 0 2.91752 0 7.11746 0
1.2 0 −2.91073 0 −4.30087 0 1.78682 0 5.47235 0
1.3 0 −2.87266 0 1.81575 0 4.67512 0 5.25220 0
1.4 0 −2.63245 0 −1.53692 0 −2.44148 0 3.92982 0
1.5 0 −2.41377 0 −0.771409 0 0.588687 0 2.82630 0
1.6 0 −2.05220 0 −2.64875 0 −3.00423 0 1.21151 0
1.7 0 −1.95667 0 −3.45496 0 1.56067 0 0.828557 0
1.8 0 −1.70694 0 1.80279 0 −0.510098 0 −0.0863705 0
1.9 0 −1.69973 0 2.39251 0 −2.42748 0 −0.110913 0
1.10 0 −1.53827 0 2.32384 0 4.76077 0 −0.633727 0
1.11 0 −1.12351 0 0.837743 0 −0.914625 0 −1.73772 0
1.12 0 −0.797542 0 −1.59101 0 1.45275 0 −2.36393 0
1.13 0 −0.513479 0 3.65851 0 −0.146814 0 −2.73634 0
1.14 0 −0.0957135 0 3.87548 0 3.14340 0 −2.99084 0
1.15 0 −0.0692070 0 0.775693 0 −4.19948 0 −2.99521 0
1.16 0 0.486172 0 −3.69982 0 0.0825276 0 −2.76364 0
1.17 0 0.679540 0 −1.36350 0 −2.99119 0 −2.53823 0
1.18 0 0.700584 0 −3.32459 0 −0.693647 0 −2.50918 0
1.19 0 1.07677 0 −3.37253 0 5.03712 0 −1.84058 0
1.20 0 1.18444 0 −0.0964158 0 −1.78364 0 −1.59711 0
See all 30 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.30
Significant digits:
Format:

Atkin-Lehner signs

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

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 8032.2.a.i yes 30
4.b odd 2 1 8032.2.a.h 30
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8032.2.a.h 30 4.b odd 2 1
8032.2.a.i yes 30 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8032))\):

\(T_{3}^{30} - \cdots\)
\(T_{7}^{30} - \cdots\)
\(T_{11}^{30} - \cdots\)