Properties

Label 4025.2.a.be
Level 4025
Weight 2
Character orbit 4025.a
Self dual Yes
Analytic conductor 32.140
Analytic rank 0
Dimension 21
CM No

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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: \(21\)
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.

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

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 −2.80022 0.208644 5.84124 0 −0.584249 1.00000 −10.7563 −2.95647 0
1.2 −2.68001 −3.08395 5.18247 0 8.26504 1.00000 −8.52906 6.51078 0
1.3 −2.38755 1.09554 3.70041 0 −2.61567 1.00000 −4.05982 −1.79978 0
1.4 −2.20248 −2.83822 2.85093 0 6.25112 1.00000 −1.87416 5.05547 0
1.5 −1.67541 3.24787 0.806990 0 −5.44150 1.00000 1.99878 7.54864 0
1.6 −1.53505 −0.943091 0.356385 0 1.44769 1.00000 2.52303 −2.11058 0
1.7 −1.22234 1.28664 −0.505878 0 −1.57271 1.00000 3.06304 −1.34457 0
1.8 −0.685218 −1.12744 −1.53048 0 0.772540 1.00000 2.41915 −1.72889 0
1.9 −0.556064 −2.94180 −1.69079 0 1.63583 1.00000 2.05232 5.65418 0
1.10 −0.294301 3.07644 −1.91339 0 −0.905400 1.00000 1.15171 6.46449 0
1.11 −0.157646 0.829461 −1.97515 0 −0.130761 1.00000 0.626665 −2.31200 0
1.12 0.475047 −0.568069 −1.77433 0 −0.269859 1.00000 −1.79298 −2.67730 0
1.13 0.817573 1.89500 −1.33157 0 1.54930 1.00000 −2.72381 0.591014 0
1.14 1.30923 2.43985 −0.285909 0 3.19433 1.00000 −2.99279 2.95286 0
1.15 1.50084 −0.816695 0.252529 0 −1.22573 1.00000 −2.62268 −2.33301 0
1.16 1.61751 −2.88096 0.616354 0 −4.65999 1.00000 −2.23807 5.29992 0
1.17 2.11197 −1.59044 2.46043 0 −3.35897 1.00000 0.972410 −0.470497 0
1.18 2.35921 2.50751 3.56589 0 5.91575 1.00000 3.69426 3.28760 0
1.19 2.57149 0.285863 4.61257 0 0.735095 1.00000 6.71821 −2.91828 0
1.20 2.70441 1.97894 5.31383 0 5.35185 1.00000 8.96197 0.916187 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 have CM; other inner twists have not been computed.

Atkin-Lehner signs

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

Hecke kernels

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

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