Properties

Label 8048.2.a.v
Level 8048
Weight 2
Character orbit 8048.a
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

Related objects

Downloads

Learn more about

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: \(1\)
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.

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

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 −3.18633 0 −1.57145 0 3.06067 0 7.15268 0
1.2 0 −2.89723 0 −1.96349 0 −2.82850 0 5.39392 0
1.3 0 −2.84528 0 −2.72112 0 3.71681 0 5.09562 0
1.4 0 −2.31121 0 0.927476 0 1.63809 0 2.34167 0
1.5 0 −2.11208 0 2.26631 0 4.06526 0 1.46088 0
1.6 0 −1.95835 0 0.337153 0 −0.830729 0 0.835124 0
1.7 0 −1.67525 0 −2.92493 0 1.65914 0 −0.193522 0
1.8 0 −1.66428 0 −3.44274 0 −4.43077 0 −0.230172 0
1.9 0 −1.59308 0 2.75433 0 −1.46360 0 −0.462108 0
1.10 0 −1.49100 0 −1.09730 0 0.799854 0 −0.776913 0
1.11 0 −0.823496 0 −2.12271 0 −4.15456 0 −2.32185 0
1.12 0 −0.799349 0 0.626001 0 0.555593 0 −2.36104 0
1.13 0 −0.682343 0 3.69511 0 3.46637 0 −2.53441 0
1.14 0 −0.659121 0 0.997881 0 −0.366743 0 −2.56556 0
1.15 0 0.0730681 0 −4.10981 0 1.52145 0 −2.99466 0
1.16 0 0.447624 0 0.901345 0 1.57888 0 −2.79963 0
1.17 0 0.596863 0 3.74289 0 −1.10831 0 −2.64375 0
1.18 0 0.667261 0 0.307121 0 −4.25072 0 −2.55476 0
1.19 0 0.893789 0 −3.85908 0 −3.77625 0 −2.20114 0
1.20 0 1.32661 0 −1.90684 0 4.79236 0 −1.24010 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8048))\):

\(T_{3}^{28} + \cdots\)
\(T_{5}^{28} + \cdots\)
\(T_{7}^{28} - \cdots\)
\(T_{13}^{28} + \cdots\)