Properties

Label 6040.2.a.s
Level 6040
Weight 2
Character orbit 6040.a
Self dual Yes
Analytic conductor 48.230
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6040 = 2^{3} \cdot 5 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6040.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2296428209\)
Analytic rank: \(0\)
Dimension: \(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \(24q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 24q^{5} \) \(\mathstrut +\mathstrut 3q^{7} \) \(\mathstrut +\mathstrut 40q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(24q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 24q^{5} \) \(\mathstrut +\mathstrut 3q^{7} \) \(\mathstrut +\mathstrut 40q^{9} \) \(\mathstrut +\mathstrut 17q^{11} \) \(\mathstrut +\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 22q^{17} \) \(\mathstrut +\mathstrut 16q^{19} \) \(\mathstrut -\mathstrut q^{21} \) \(\mathstrut +\mathstrut 7q^{23} \) \(\mathstrut +\mathstrut 24q^{25} \) \(\mathstrut -\mathstrut 4q^{27} \) \(\mathstrut +\mathstrut 25q^{29} \) \(\mathstrut +\mathstrut 28q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut +\mathstrut 3q^{35} \) \(\mathstrut +\mathstrut 26q^{37} \) \(\mathstrut +\mathstrut 13q^{39} \) \(\mathstrut +\mathstrut 38q^{41} \) \(\mathstrut -\mathstrut 13q^{43} \) \(\mathstrut +\mathstrut 40q^{45} \) \(\mathstrut +\mathstrut 12q^{47} \) \(\mathstrut +\mathstrut 61q^{49} \) \(\mathstrut +\mathstrut 53q^{53} \) \(\mathstrut +\mathstrut 17q^{55} \) \(\mathstrut +\mathstrut 30q^{57} \) \(\mathstrut +\mathstrut 35q^{59} \) \(\mathstrut +\mathstrut 44q^{61} \) \(\mathstrut -\mathstrut 9q^{63} \) \(\mathstrut +\mathstrut 16q^{65} \) \(\mathstrut -\mathstrut 15q^{67} \) \(\mathstrut +\mathstrut 9q^{69} \) \(\mathstrut +\mathstrut 22q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 26q^{77} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 88q^{81} \) \(\mathstrut -\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 22q^{85} \) \(\mathstrut -\mathstrut 18q^{87} \) \(\mathstrut +\mathstrut 37q^{89} \) \(\mathstrut -\mathstrut 26q^{91} \) \(\mathstrut +\mathstrut 13q^{93} \) \(\mathstrut +\mathstrut 16q^{95} \) \(\mathstrut +\mathstrut 21q^{97} \) \(\mathstrut -\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.28894 0 1.00000 0 4.04677 0 7.81711 0
1.2 0 −3.20286 0 1.00000 0 −3.67370 0 7.25831 0
1.3 0 −3.03909 0 1.00000 0 −1.69120 0 6.23604 0
1.4 0 −2.50341 0 1.00000 0 −2.70762 0 3.26705 0
1.5 0 −2.45370 0 1.00000 0 −1.79083 0 3.02066 0
1.6 0 −2.29572 0 1.00000 0 4.99611 0 2.27034 0
1.7 0 −2.03886 0 1.00000 0 1.67649 0 1.15693 0
1.8 0 −1.08470 0 1.00000 0 4.94762 0 −1.82343 0
1.9 0 −0.875996 0 1.00000 0 −1.42220 0 −2.23263 0
1.10 0 −0.559764 0 1.00000 0 −0.837547 0 −2.68666 0
1.11 0 0.0496662 0 1.00000 0 1.60144 0 −2.99753 0
1.12 0 0.161432 0 1.00000 0 −4.19061 0 −2.97394 0
1.13 0 0.225898 0 1.00000 0 2.54851 0 −2.94897 0
1.14 0 0.549309 0 1.00000 0 −0.285162 0 −2.69826 0
1.15 0 0.568728 0 1.00000 0 −5.03281 0 −2.67655 0
1.16 0 1.21987 0 1.00000 0 0.325030 0 −1.51192 0
1.17 0 1.49843 0 1.00000 0 1.73584 0 −0.754697 0
1.18 0 1.94109 0 1.00000 0 3.18961 0 0.767827 0
1.19 0 2.40154 0 1.00000 0 4.37326 0 2.76742 0
1.20 0 2.57003 0 1.00000 0 −3.15345 0 3.60506 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.24
Significant digits:
Format:

Inner twists

This newform does not have CM; other inner twists have not been computed.

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(5\) \(-1\)
\(151\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6040))\):

\(T_{3}^{24} - \cdots\)
\(T_{7}^{24} - \cdots\)
\(T_{11}^{24} - \cdots\)