Properties

Label 8048.2.a.y
Level $8048$
Weight $2$
Character orbit 8048.a
Self dual yes
Analytic conductor $64.264$
Analytic rank $0$
Dimension $33$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8048.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(0\)
Dimension: \(33\)
Twist minimal: no (minimal twist has level 4024)
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.

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

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 −3.29586 0 −1.31643 0 −2.99871 0 7.86271 0
1.2 0 −2.95302 0 0.296089 0 −1.50033 0 5.72032 0
1.3 0 −2.93503 0 3.00897 0 2.93938 0 5.61438 0
1.4 0 −2.66114 0 3.83009 0 −0.592406 0 4.08164 0
1.5 0 −2.60209 0 1.12945 0 1.15113 0 3.77086 0
1.6 0 −2.45195 0 0.279836 0 −3.64586 0 3.01204 0
1.7 0 −2.44174 0 −3.94731 0 −0.854513 0 2.96210 0
1.8 0 −1.79707 0 2.90936 0 −4.51295 0 0.229458 0
1.9 0 −1.66808 0 −3.27041 0 4.00229 0 −0.217521 0
1.10 0 −1.61089 0 −0.419657 0 5.20635 0 −0.405023 0
1.11 0 −1.23409 0 −1.43413 0 1.24533 0 −1.47702 0
1.12 0 −1.07783 0 −1.09164 0 −2.08785 0 −1.83829 0
1.13 0 −1.01188 0 3.66411 0 −1.84945 0 −1.97610 0
1.14 0 −0.368053 0 2.18272 0 −4.72026 0 −2.86454 0
1.15 0 −0.220191 0 1.20642 0 3.77303 0 −2.95152 0
1.16 0 −0.176667 0 2.93614 0 0.0214699 0 −2.96879 0
1.17 0 −0.0147975 0 −2.88853 0 1.61248 0 −2.99978 0
1.18 0 0.224625 0 −2.01216 0 −1.98253 0 −2.94954 0
1.19 0 0.254882 0 3.76559 0 2.29648 0 −2.93504 0
1.20 0 0.502871 0 −1.85170 0 −1.22131 0 −2.74712 0
See all 33 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.33
Significant digits:
Format:

Atkin-Lehner signs

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

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 8048.2.a.y 33
4.b odd 2 1 4024.2.a.f 33
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4024.2.a.f 33 4.b odd 2 1
8048.2.a.y 33 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8048))\):

\(T_{3}^{33} - \cdots\)
\(T_{5}^{33} - \cdots\)
\(T_{7}^{33} + \cdots\)
\(T_{13}^{33} - \cdots\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database