Properties

Label 4025.2.a.bd
Level 4025
Weight 2
Character orbit 4025.a
Self dual yes
Analytic conductor 32.140
Analytic rank 0
Dimension 21
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4025.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1397868136\)
Analytic rank: \(0\)
Dimension: \(21\)
Coefficient ring index: multiple of None
Twist minimal: no (minimal twist has level 805)
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.

\(\operatorname{Tr}(f)(q) = \) \( 21q - 2q^{2} + q^{3} + 30q^{4} + 6q^{6} - 21q^{7} - 6q^{8} + 30q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 21q - 2q^{2} + q^{3} + 30q^{4} + 6q^{6} - 21q^{7} - 6q^{8} + 30q^{9} + 7q^{11} + 22q^{12} + 3q^{13} + 2q^{14} + 56q^{16} - 7q^{17} + 24q^{19} - q^{21} - 4q^{22} - 21q^{23} + 24q^{24} - 2q^{26} + 19q^{27} - 30q^{28} + 11q^{29} + 46q^{31} + 6q^{32} + 3q^{33} + 28q^{34} + 58q^{36} - 24q^{37} + 4q^{38} + 31q^{39} + 14q^{41} - 6q^{42} - 18q^{43} + 12q^{44} + 2q^{46} + 25q^{47} + 36q^{48} + 21q^{49} + 17q^{51} + 8q^{52} - 22q^{53} - 6q^{54} + 6q^{56} - 40q^{57} - 6q^{58} + 10q^{59} + 38q^{61} + 54q^{62} - 30q^{63} + 100q^{64} + 38q^{66} - 12q^{67} - 18q^{68} - q^{69} + 56q^{71} - 42q^{72} + 40q^{73} - 20q^{74} + 60q^{76} - 7q^{77} - 38q^{78} + 49q^{79} + 57q^{81} - 16q^{82} + 2q^{83} - 22q^{84} + 16q^{86} + 23q^{87} - 12q^{88} + 28q^{89} - 3q^{91} - 30q^{92} + 30q^{93} + 66q^{94} + 46q^{96} + q^{97} - 2q^{98} - 2q^{99} + O(q^{100}) \)

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 −2.72900 3.06108 5.44746 0 −8.35371 −1.00000 −9.40815 6.37023 0
1.2 −2.70441 −1.97894 5.31383 0 5.35185 −1.00000 −8.96197 0.916187 0
1.3 −2.57149 −0.285863 4.61257 0 0.735095 −1.00000 −6.71821 −2.91828 0
1.4 −2.35921 −2.50751 3.56589 0 5.91575 −1.00000 −3.69426 3.28760 0
1.5 −2.11197 1.59044 2.46043 0 −3.35897 −1.00000 −0.972410 −0.470497 0
1.6 −1.61751 2.88096 0.616354 0 −4.65999 −1.00000 2.23807 5.29992 0
1.7 −1.50084 0.816695 0.252529 0 −1.22573 −1.00000 2.62268 −2.33301 0
1.8 −1.30923 −2.43985 −0.285909 0 3.19433 −1.00000 2.99279 2.95286 0
1.9 −0.817573 −1.89500 −1.33157 0 1.54930 −1.00000 2.72381 0.591014 0
1.10 −0.475047 0.568069 −1.77433 0 −0.269859 −1.00000 1.79298 −2.67730 0
1.11 0.157646 −0.829461 −1.97515 0 −0.130761 −1.00000 −0.626665 −2.31200 0
1.12 0.294301 −3.07644 −1.91339 0 −0.905400 −1.00000 −1.15171 6.46449 0
1.13 0.556064 2.94180 −1.69079 0 1.63583 −1.00000 −2.05232 5.65418 0
1.14 0.685218 1.12744 −1.53048 0 0.772540 −1.00000 −2.41915 −1.72889 0
1.15 1.22234 −1.28664 −0.505878 0 −1.57271 −1.00000 −3.06304 −1.34457 0
1.16 1.53505 0.943091 0.356385 0 1.44769 −1.00000 −2.52303 −2.11058 0
1.17 1.67541 −3.24787 0.806990 0 −5.44150 −1.00000 −1.99878 7.54864 0
1.18 2.20248 2.83822 2.85093 0 6.25112 −1.00000 1.87416 5.05547 0
1.19 2.38755 −1.09554 3.70041 0 −2.61567 −1.00000 4.05982 −1.79978 0
1.20 2.68001 3.08395 5.18247 0 8.26504 −1.00000 8.52906 6.51078 0
See all 21 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.21
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 4025.2.a.bd 21
5.b even 2 1 4025.2.a.be 21
5.c odd 4 2 805.2.c.c 42
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
805.2.c.c 42 5.c odd 4 2
4025.2.a.bd 21 1.a even 1 1 trivial
4025.2.a.be 21 5.b even 2 1

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(7\) \(1\)
\(23\) \(1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4025))\):

\(T_{2}^{21} + \cdots\)
\(T_{3}^{21} - \cdots\)
\(T_{11}^{21} - \cdots\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database