Properties

Label 6044.2.a.b
Level 6044
Weight 2
Character orbit 6044.a
Self dual yes
Analytic conductor 48.262
Analytic rank 0
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: \(0\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 63q + 5q^{3} + 5q^{5} + 22q^{7} + 62q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 63q + 5q^{3} + 5q^{5} + 22q^{7} + 62q^{9} + 21q^{11} + 17q^{13} + 26q^{15} - 5q^{17} + 57q^{19} + 18q^{21} + 16q^{23} + 60q^{25} + 14q^{27} + 22q^{29} + 36q^{31} - q^{33} + 28q^{35} + 21q^{37} + 69q^{39} - 3q^{41} + 86q^{43} + 39q^{45} + 23q^{47} + 63q^{49} + 67q^{51} + 18q^{53} + 67q^{55} + 27q^{59} + 62q^{61} + 58q^{63} - 13q^{65} + 62q^{67} + 45q^{69} + 29q^{71} - q^{73} + 39q^{75} + 19q^{77} + 132q^{79} + 51q^{81} + 35q^{83} + 60q^{85} + 55q^{87} - 2q^{89} + 84q^{91} + 29q^{93} + 53q^{95} - 10q^{97} + 95q^{99} + O(q^{100}) \)

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 −3.44578 0 2.15177 0 0.876792 0 8.87339 0
1.2 0 −3.26383 0 −4.12384 0 −1.32793 0 7.65258 0
1.3 0 −2.94078 0 −0.581492 0 −3.80526 0 5.64819 0
1.4 0 −2.79559 0 1.54493 0 3.97273 0 4.81535 0
1.5 0 −2.69290 0 −2.32986 0 −1.27542 0 4.25169 0
1.6 0 −2.68247 0 0.714038 0 3.91380 0 4.19563 0
1.7 0 −2.63352 0 −1.02766 0 −1.79528 0 3.93544 0
1.8 0 −2.56682 0 0.554911 0 −3.08439 0 3.58855 0
1.9 0 −2.50519 0 −1.30564 0 3.79113 0 3.27598 0
1.10 0 −2.38781 0 2.32923 0 0.907839 0 2.70165 0
1.11 0 −2.30919 0 2.96511 0 1.31242 0 2.33234 0
1.12 0 −2.24731 0 0.981673 0 −2.98823 0 2.05038 0
1.13 0 −2.22958 0 −3.12332 0 0.924225 0 1.97105 0
1.14 0 −2.12225 0 −0.499336 0 −0.0909608 0 1.50393 0
1.15 0 −2.06433 0 4.18134 0 5.19775 0 1.26148 0
1.16 0 −1.67900 0 −4.00186 0 3.70926 0 −0.180962 0
1.17 0 −1.55218 0 −1.58422 0 −1.70170 0 −0.590736 0
1.18 0 −1.47185 0 −3.39845 0 2.90753 0 −0.833657 0
1.19 0 −1.08193 0 −0.304592 0 −4.98661 0 −1.82943 0
1.20 0 −1.07770 0 3.26525 0 −1.02333 0 −1.83857 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.b 63
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6044.2.a.b 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