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

Related objects

Downloads

Learn more about

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 −2.72900 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 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4025))\):

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