Properties

Label 6028.2.a.f
Level 6028
Weight 2
Character orbit 6028.a
Self dual Yes
Analytic conductor 48.134
Analytic rank 0
Dimension 29
CM No

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Newspace parameters

Level: \( N \) = \( 6028 = 2^{2} \cdot 11 \cdot 137 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6028.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1338223384\)
Analytic rank: \(0\)
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.

\(\operatorname{Tr}(f)(q) = \) \(29q \) \(\mathstrut +\mathstrut 14q^{3} \) \(\mathstrut +\mathstrut 9q^{5} \) \(\mathstrut +\mathstrut 14q^{7} \) \(\mathstrut +\mathstrut 43q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(29q \) \(\mathstrut +\mathstrut 14q^{3} \) \(\mathstrut +\mathstrut 9q^{5} \) \(\mathstrut +\mathstrut 14q^{7} \) \(\mathstrut +\mathstrut 43q^{9} \) \(\mathstrut +\mathstrut 29q^{11} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 29q^{17} \) \(\mathstrut +\mathstrut 7q^{19} \) \(\mathstrut +\mathstrut 2q^{21} \) \(\mathstrut +\mathstrut 36q^{23} \) \(\mathstrut +\mathstrut 36q^{25} \) \(\mathstrut +\mathstrut 50q^{27} \) \(\mathstrut +\mathstrut 9q^{29} \) \(\mathstrut +\mathstrut 28q^{31} \) \(\mathstrut +\mathstrut 14q^{33} \) \(\mathstrut +\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 25q^{37} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut +\mathstrut 19q^{41} \) \(\mathstrut +\mathstrut 23q^{43} \) \(\mathstrut +\mathstrut 5q^{45} \) \(\mathstrut +\mathstrut 27q^{47} \) \(\mathstrut +\mathstrut 27q^{49} \) \(\mathstrut +\mathstrut 13q^{51} \) \(\mathstrut +\mathstrut 4q^{53} \) \(\mathstrut +\mathstrut 9q^{55} \) \(\mathstrut +\mathstrut 14q^{57} \) \(\mathstrut +\mathstrut 40q^{59} \) \(\mathstrut +\mathstrut 20q^{61} \) \(\mathstrut -\mathstrut 17q^{63} \) \(\mathstrut +\mathstrut 9q^{65} \) \(\mathstrut +\mathstrut 59q^{67} \) \(\mathstrut +\mathstrut 30q^{69} \) \(\mathstrut +\mathstrut 29q^{71} \) \(\mathstrut -\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 46q^{75} \) \(\mathstrut +\mathstrut 14q^{77} \) \(\mathstrut +\mathstrut 29q^{79} \) \(\mathstrut +\mathstrut 61q^{81} \) \(\mathstrut +\mathstrut 35q^{83} \) \(\mathstrut -\mathstrut 57q^{85} \) \(\mathstrut +\mathstrut 45q^{87} \) \(\mathstrut +\mathstrut 39q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut -\mathstrut 8q^{93} \) \(\mathstrut +\mathstrut q^{95} \) \(\mathstrut +\mathstrut 55q^{97} \) \(\mathstrut +\mathstrut 43q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.97866 0 −3.46603 0 0.700745 0 5.87240 0
1.2 0 −2.90851 0 0.776599 0 −2.27589 0 5.45943 0
1.3 0 −2.65731 0 2.47175 0 0.711504 0 4.06129 0
1.4 0 −2.38462 0 −1.71860 0 3.80618 0 2.68641 0
1.5 0 −2.00219 0 0.977497 0 −3.03319 0 1.00878 0
1.6 0 −1.84910 0 −0.463178 0 −1.96260 0 0.419175 0
1.7 0 −1.36461 0 2.36459 0 1.37904 0 −1.13783 0
1.8 0 −1.28547 0 2.42568 0 5.14778 0 −1.34758 0
1.9 0 −1.14725 0 4.20688 0 −0.775275 0 −1.68381 0
1.10 0 −0.886923 0 −0.640762 0 1.27780 0 −2.21337 0
1.11 0 −0.774336 0 −2.66500 0 0.769081 0 −2.40040 0
1.12 0 −0.191141 0 −3.65958 0 2.84676 0 −2.96346 0
1.13 0 0.213524 0 2.27425 0 4.54069 0 −2.95441 0
1.14 0 0.780624 0 0.801470 0 −4.30496 0 −2.39063 0
1.15 0 0.785650 0 1.28190 0 −3.55486 0 −2.38275 0
1.16 0 1.04417 0 −2.78682 0 −0.254204 0 −1.90970 0
1.17 0 1.09615 0 3.71316 0 3.72361 0 −1.79846 0
1.18 0 1.58135 0 3.56375 0 0.0558785 0 −0.499338 0
1.19 0 1.60026 0 −1.38303 0 0.488214 0 −0.439167 0
1.20 0 1.76391 0 −2.22231 0 2.22847 0 0.111381 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
\(2\) \(-1\)
\(11\) \(-1\)
\(137\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6028))\):

\(T_{3}^{29} - \cdots\)
\(T_{5}^{29} - \cdots\)