Properties

Label 6044.2.a.a
Level 6044
Weight 2
Character orbit 6044.a
Self dual yes
Analytic conductor 48.262
Analytic rank 1
Dimension 63
CM no
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) \(=\) \( 6044 = 2^{2} \cdot 1511 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6044.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.2615829817\)
Analytic rank: \(1\)
Dimension: \(63\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 63q - 7q^{3} - 7q^{5} - 22q^{7} + 62q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 63q - 7q^{3} - 7q^{5} - 22q^{7} + 62q^{9} - 21q^{11} - 19q^{13} - 30q^{15} - 5q^{17} - 59q^{19} - 30q^{21} - 24q^{23} + 60q^{25} - 34q^{27} - 28q^{29} - 48q^{31} - q^{33} - 44q^{35} - 29q^{37} - 75q^{39} - 3q^{41} - 88q^{43} - 21q^{45} - 21q^{47} + 63q^{49} - 85q^{51} - 24q^{53} - 85q^{55} - 35q^{59} - 78q^{61} - 74q^{63} - 13q^{65} - 68q^{67} - 43q^{69} - 59q^{71} - q^{73} - 45q^{75} - 33q^{77} - 140q^{79} + 51q^{81} - 27q^{83} - 84q^{85} - 61q^{87} - 2q^{89} - 92q^{91} - 51q^{93} - 51q^{95} - 10q^{97} - 115q^{99} + O(q^{100}) \)

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 −3.43683 0 1.31396 0 2.97589 0 8.81178 0
1.2 0 −3.31051 0 0.0245297 0 −4.08379 0 7.95946 0
1.3 0 −3.15665 0 −3.22660 0 1.21507 0 6.96442 0
1.4 0 −3.10897 0 4.27127 0 −2.96851 0 6.66567 0
1.5 0 −3.06921 0 2.30904 0 −0.616615 0 6.42006 0
1.6 0 −2.97134 0 −2.23756 0 4.75272 0 5.82886 0
1.7 0 −2.95257 0 −0.800433 0 −2.68929 0 5.71766 0
1.8 0 −2.59590 0 −0.0339717 0 0.331169 0 3.73871 0
1.9 0 −2.53520 0 −2.05681 0 1.80178 0 3.42722 0
1.10 0 −2.53490 0 4.14677 0 1.26365 0 3.42570 0
1.11 0 −2.46300 0 −1.99757 0 3.35645 0 3.06637 0
1.12 0 −2.40035 0 2.30377 0 −2.94550 0 2.76170 0
1.13 0 −2.33939 0 2.09632 0 1.25063 0 2.47276 0
1.14 0 −1.98161 0 −3.75516 0 −4.03693 0 0.926797 0
1.15 0 −1.75230 0 −3.12629 0 −3.74178 0 0.0705422 0
1.16 0 −1.69210 0 −3.14690 0 −4.59556 0 −0.136814 0
1.17 0 −1.68302 0 3.28650 0 −4.68087 0 −0.167449 0
1.18 0 −1.59751 0 1.94100 0 −3.58958 0 −0.447960 0
1.19 0 −1.58770 0 −0.675402 0 −1.82211 0 −0.479212 0
1.20 0 −1.57704 0 3.78585 0 1.51605 0 −0.512930 0
See all 63 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.63
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 6044.2.a.a 63
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6044.2.a.a 63 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(1511\) \(-1\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database