Properties

Label 6027.2.a.bn
Level 6027
Weight 2
Character orbit 6027.a
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
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.

\(\operatorname{Tr}(f)(q) = \) \(24q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 24q^{3} \) \(\mathstrut +\mathstrut 32q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(24q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 24q^{3} \) \(\mathstrut +\mathstrut 32q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 32q^{12} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 44q^{16} \) \(\mathstrut -\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 8q^{18} \) \(\mathstrut +\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 28q^{20} \) \(\mathstrut +\mathstrut 16q^{22} \) \(\mathstrut +\mathstrut 20q^{23} \) \(\mathstrut -\mathstrut 24q^{24} \) \(\mathstrut +\mathstrut 48q^{25} \) \(\mathstrut -\mathstrut 32q^{26} \) \(\mathstrut -\mathstrut 24q^{27} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut -\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 36q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 16q^{34} \) \(\mathstrut +\mathstrut 32q^{36} \) \(\mathstrut +\mathstrut 64q^{37} \) \(\mathstrut -\mathstrut 20q^{38} \) \(\mathstrut +\mathstrut 48q^{40} \) \(\mathstrut +\mathstrut 24q^{41} \) \(\mathstrut +\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 48q^{44} \) \(\mathstrut -\mathstrut 4q^{45} \) \(\mathstrut +\mathstrut 28q^{46} \) \(\mathstrut -\mathstrut 32q^{47} \) \(\mathstrut -\mathstrut 44q^{48} \) \(\mathstrut -\mathstrut 20q^{50} \) \(\mathstrut +\mathstrut 8q^{51} \) \(\mathstrut +\mathstrut 76q^{53} \) \(\mathstrut -\mathstrut 8q^{54} \) \(\mathstrut +\mathstrut 24q^{55} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 28q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut +\mathstrut 28q^{60} \) \(\mathstrut +\mathstrut 28q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut +\mathstrut 48q^{64} \) \(\mathstrut +\mathstrut 28q^{65} \) \(\mathstrut -\mathstrut 16q^{66} \) \(\mathstrut +\mathstrut 44q^{67} \) \(\mathstrut +\mathstrut 32q^{68} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 20q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut +\mathstrut 16q^{73} \) \(\mathstrut +\mathstrut 44q^{74} \) \(\mathstrut -\mathstrut 48q^{75} \) \(\mathstrut +\mathstrut 16q^{76} \) \(\mathstrut +\mathstrut 32q^{78} \) \(\mathstrut +\mathstrut 4q^{79} \) \(\mathstrut -\mathstrut 44q^{80} \) \(\mathstrut +\mathstrut 24q^{81} \) \(\mathstrut +\mathstrut 8q^{82} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut +\mathstrut 28q^{85} \) \(\mathstrut +\mathstrut 56q^{86} \) \(\mathstrut -\mathstrut 24q^{87} \) \(\mathstrut +\mathstrut 60q^{88} \) \(\mathstrut -\mathstrut 60q^{89} \) \(\mathstrut +\mathstrut 4q^{90} \) \(\mathstrut +\mathstrut 60q^{92} \) \(\mathstrut -\mathstrut 4q^{93} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut +\mathstrut 28q^{95} \) \(\mathstrut -\mathstrut 36q^{96} \) \(\mathstrut +\mathstrut 48q^{97} \) \(\mathstrut +\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.69245 −1.00000 5.24930 −3.40876 2.69245 0 −8.74860 1.00000 9.17792
1.2 −2.37986 −1.00000 3.66372 −3.68734 2.37986 0 −3.95941 1.00000 8.77534
1.3 −2.22021 −1.00000 2.92934 −0.165927 2.22021 0 −2.06334 1.00000 0.368393
1.4 −1.96907 −1.00000 1.87725 4.10878 1.96907 0 0.241710 1.00000 −8.09048
1.5 −1.80081 −1.00000 1.24292 2.17778 1.80081 0 1.36336 1.00000 −3.92176
1.6 −1.32413 −1.00000 −0.246682 −4.03355 1.32413 0 2.97490 1.00000 5.34094
1.7 −1.25316 −1.00000 −0.429590 1.76265 1.25316 0 3.04466 1.00000 −2.20889
1.8 −0.844195 −1.00000 −1.28734 1.91229 0.844195 0 2.77515 1.00000 −1.61434
1.9 −0.423828 −1.00000 −1.82037 −3.41632 0.423828 0 1.61918 1.00000 1.44793
1.10 −0.308797 −1.00000 −1.90464 0.898648 0.308797 0 1.20574 1.00000 −0.277499
1.11 −0.0650408 −1.00000 −1.99577 2.65358 0.0650408 0 0.259888 1.00000 −0.172591
1.12 0.154130 −1.00000 −1.97624 −1.29015 −0.154130 0 −0.612860 1.00000 −0.198852
1.13 0.368135 −1.00000 −1.86448 0.572097 −0.368135 0 −1.42265 1.00000 0.210609
1.14 1.11646 −1.00000 −0.753512 0.900581 −1.11646 0 −3.07419 1.00000 1.00546
1.15 1.33013 −1.00000 −0.230742 3.44355 −1.33013 0 −2.96719 1.00000 4.58038
1.16 1.50751 −1.00000 0.272577 −1.10903 −1.50751 0 −2.60410 1.00000 −1.67187
1.17 1.64420 −1.00000 0.703405 −3.28206 −1.64420 0 −2.13187 1.00000 −5.39638
1.18 1.95065 −1.00000 1.80504 −2.46699 −1.95065 0 −0.380308 1.00000 −4.81223
1.19 2.26259 −1.00000 3.11931 −3.51535 −2.26259 0 2.53253 1.00000 −7.95379
1.20 2.37367 −1.00000 3.63432 3.47491 −2.37367 0 3.87933 1.00000 8.24830
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
\(3\) \(1\)
\(7\) \(1\)
\(41\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6027))\):

\(T_{2}^{24} - \cdots\)
\(T_{5}^{24} + \cdots\)
\(T_{13}^{24} - \cdots\)