Properties

Label 6036.2.a.h
Level 6036
Weight 2
Character orbit 6036.a
Self dual Yes
Analytic conductor 48.198
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.19770266\)
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.

\(\operatorname{Tr}(f)(q) = \) \(24q \) \(\mathstrut +\mathstrut 24q^{3} \) \(\mathstrut +\mathstrut 18q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(24q \) \(\mathstrut +\mathstrut 24q^{3} \) \(\mathstrut +\mathstrut 18q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 18q^{15} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut +\mathstrut 9q^{21} \) \(\mathstrut +\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 48q^{25} \) \(\mathstrut +\mathstrut 24q^{27} \) \(\mathstrut +\mathstrut 44q^{29} \) \(\mathstrut +\mathstrut 15q^{31} \) \(\mathstrut +\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut 3q^{35} \) \(\mathstrut +\mathstrut 18q^{37} \) \(\mathstrut +\mathstrut 7q^{39} \) \(\mathstrut +\mathstrut 37q^{41} \) \(\mathstrut -\mathstrut 8q^{43} \) \(\mathstrut +\mathstrut 18q^{45} \) \(\mathstrut +\mathstrut 24q^{47} \) \(\mathstrut +\mathstrut 63q^{49} \) \(\mathstrut +\mathstrut 12q^{51} \) \(\mathstrut +\mathstrut 59q^{53} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut -\mathstrut q^{57} \) \(\mathstrut +\mathstrut 44q^{59} \) \(\mathstrut +\mathstrut 33q^{61} \) \(\mathstrut +\mathstrut 9q^{63} \) \(\mathstrut +\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 13q^{67} \) \(\mathstrut +\mathstrut 22q^{69} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut +\mathstrut 28q^{73} \) \(\mathstrut +\mathstrut 48q^{75} \) \(\mathstrut +\mathstrut 19q^{77} \) \(\mathstrut +\mathstrut 12q^{79} \) \(\mathstrut +\mathstrut 24q^{81} \) \(\mathstrut +\mathstrut 17q^{83} \) \(\mathstrut +\mathstrut 31q^{85} \) \(\mathstrut +\mathstrut 44q^{87} \) \(\mathstrut +\mathstrut 41q^{89} \) \(\mathstrut -\mathstrut q^{91} \) \(\mathstrut +\mathstrut 15q^{93} \) \(\mathstrut +\mathstrut 58q^{95} \) \(\mathstrut +\mathstrut 51q^{97} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 1.00000 0 −3.64052 0 2.86228 0 1.00000 0
1.2 0 1.00000 0 −3.54344 0 −1.09625 0 1.00000 0
1.3 0 1.00000 0 −2.75869 0 −0.925607 0 1.00000 0
1.4 0 1.00000 0 −2.71451 0 −1.53717 0 1.00000 0
1.5 0 1.00000 0 −1.85882 0 5.16371 0 1.00000 0
1.6 0 1.00000 0 −1.66295 0 −0.368117 0 1.00000 0
1.7 0 1.00000 0 −1.40769 0 3.41112 0 1.00000 0
1.8 0 1.00000 0 −0.766960 0 −1.64718 0 1.00000 0
1.9 0 1.00000 0 −0.497428 0 −3.93416 0 1.00000 0
1.10 0 1.00000 0 −0.0279923 0 3.66780 0 1.00000 0
1.11 0 1.00000 0 0.357952 0 −4.62593 0 1.00000 0
1.12 0 1.00000 0 1.21459 0 5.16615 0 1.00000 0
1.13 0 1.00000 0 1.56884 0 1.63329 0 1.00000 0
1.14 0 1.00000 0 1.63100 0 0.968844 0 1.00000 0
1.15 0 1.00000 0 1.65069 0 1.03307 0 1.00000 0
1.16 0 1.00000 0 1.97211 0 2.26181 0 1.00000 0
1.17 0 1.00000 0 2.44705 0 −3.28775 0 1.00000 0
1.18 0 1.00000 0 2.55581 0 −4.67011 0 1.00000 0
1.19 0 1.00000 0 3.52243 0 1.80430 0 1.00000 0
1.20 0 1.00000 0 3.68154 0 2.26895 0 1.00000 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
\(2\) \(-1\)
\(3\) \(-1\)
\(503\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6036))\):

\(T_{5}^{24} - \cdots\)
\(T_{7}^{24} - \cdots\)