Properties

Label 6028.2.a.c
Level 6028
Weight 2
Character orbit 6028.a
Self dual Yes
Analytic conductor 48.134
Analytic rank 1
Dimension 25
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: \(1\)
Dimension: \(25\)
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.

\(\operatorname{Tr}(f)(q) = \) \(25q \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(25q \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 25q^{11} \) \(\mathstrut -\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut -\mathstrut 19q^{17} \) \(\mathstrut -\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 8q^{21} \) \(\mathstrut -\mathstrut 31q^{23} \) \(\mathstrut -\mathstrut q^{25} \) \(\mathstrut -\mathstrut 44q^{27} \) \(\mathstrut -\mathstrut q^{29} \) \(\mathstrut -\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 14q^{37} \) \(\mathstrut -\mathstrut 18q^{39} \) \(\mathstrut -\mathstrut 5q^{41} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut -\mathstrut 15q^{45} \) \(\mathstrut -\mathstrut 41q^{47} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut +\mathstrut 10q^{51} \) \(\mathstrut +\mathstrut 4q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut -\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 35q^{59} \) \(\mathstrut -\mathstrut 4q^{61} \) \(\mathstrut -\mathstrut 45q^{63} \) \(\mathstrut -\mathstrut 28q^{65} \) \(\mathstrut -\mathstrut 30q^{67} \) \(\mathstrut -\mathstrut 3q^{69} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 7q^{73} \) \(\mathstrut -\mathstrut 18q^{75} \) \(\mathstrut -\mathstrut 9q^{77} \) \(\mathstrut -\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 29q^{81} \) \(\mathstrut -\mathstrut 72q^{83} \) \(\mathstrut -\mathstrut 33q^{87} \) \(\mathstrut -\mathstrut 30q^{89} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut +\mathstrut 7q^{93} \) \(\mathstrut +\mathstrut 9q^{95} \) \(\mathstrut -\mathstrut 37q^{97} \) \(\mathstrut +\mathstrut 18q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.38016 0 −2.49069 0 −4.68929 0 8.42547 0
1.2 0 −3.29075 0 0.224551 0 1.38599 0 7.82903 0
1.3 0 −3.18883 0 2.53247 0 −2.00866 0 7.16863 0
1.4 0 −2.50588 0 2.86844 0 −2.58862 0 3.27945 0
1.5 0 −2.33036 0 0.868912 0 2.53747 0 2.43060 0
1.6 0 −2.30272 0 −2.25624 0 −2.39335 0 2.30252 0
1.7 0 −2.18955 0 −1.45357 0 3.11023 0 1.79411 0
1.8 0 −1.95548 0 1.12146 0 3.14826 0 0.823884 0
1.9 0 −1.61432 0 −4.02092 0 2.29943 0 −0.393974 0
1.10 0 −1.44202 0 3.24879 0 −4.91695 0 −0.920583 0
1.11 0 −0.747609 0 −1.50988 0 −0.315514 0 −2.44108 0
1.12 0 −0.509200 0 1.39955 0 1.69458 0 −2.74071 0
1.13 0 −0.397686 0 −2.70688 0 −3.71101 0 −2.84185 0
1.14 0 −0.0987018 0 0.748865 0 1.53599 0 −2.99026 0
1.15 0 0.0141418 0 −1.21436 0 −2.15622 0 −2.99980 0
1.16 0 0.0317141 0 3.98776 0 −1.35146 0 −2.99899 0
1.17 0 0.594909 0 2.93206 0 −0.580702 0 −2.64608 0
1.18 0 0.615083 0 0.179847 0 1.85704 0 −2.62167 0
1.19 0 1.10804 0 −3.19726 0 3.64868 0 −1.77224 0
1.20 0 1.71464 0 0.0212259 0 3.28745 0 −0.0600233 0
See all 25 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.25
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6028))\):

\(T_{3}^{25} + \cdots\)
\(T_{5}^{25} + \cdots\)