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Properties

Label 7595.2.a.bf
Level $7595$
Weight $2$
Character orbit 7595.a
Self dual yes
Analytic conductor $60.646$
Analytic rank $1$
Dimension $21$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7595,2,Mod(1,7595)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7595, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7595.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7595 = 5 \cdot 7^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7595.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(60.6463803352\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: no (minimal twist has level 1085)
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.

\(\operatorname{Tr}(f)(q) = \) \( 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9} - 4 q^{10} - 4 q^{11} - 21 q^{12} - 24 q^{13} - 5 q^{15} + 20 q^{16} - 18 q^{17} - 16 q^{18} - 17 q^{19} + 22 q^{20} + 9 q^{22} - 19 q^{23} - 21 q^{24} + 21 q^{25} - 16 q^{26} - 17 q^{27} - 4 q^{29} - 6 q^{30} - 21 q^{31} - 18 q^{32} - 27 q^{33} + 2 q^{34} + 52 q^{36} - 19 q^{37} + 10 q^{38} + 21 q^{39} - 12 q^{40} - 5 q^{41} - 15 q^{43} - 11 q^{44} + 20 q^{45} + 6 q^{46} - 4 q^{47} - 19 q^{48} - 4 q^{50} + 35 q^{51} - 66 q^{52} - 19 q^{53} - 11 q^{54} - 4 q^{55} - 27 q^{57} - q^{58} + q^{59} - 21 q^{60} - 60 q^{61} + 4 q^{62} - 10 q^{64} - 24 q^{65} - 64 q^{66} + 2 q^{67} - 11 q^{68} - 18 q^{69} - q^{71} - 37 q^{72} - 51 q^{73} + 11 q^{74} - 5 q^{75} - 13 q^{76} - 40 q^{78} + q^{79} + 20 q^{80} + 21 q^{81} + 2 q^{82} - 38 q^{83} - 18 q^{85} + 26 q^{86} - 32 q^{87} + 5 q^{88} - 2 q^{89} - 16 q^{90} - 86 q^{92} + 5 q^{93} - 67 q^{94} - 17 q^{95} + 56 q^{96} - 42 q^{97} - 35 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.64279 −0.623799 4.98432 1.00000 1.64857 0 −7.88694 −2.61087 −2.64279
1.2 −2.60530 −3.29842 4.78761 1.00000 8.59339 0 −7.26258 7.87957 −2.60530
1.3 −2.44160 3.13328 3.96139 1.00000 −7.65019 0 −4.78892 6.81741 −2.44160
1.4 −2.35322 1.38217 3.53763 1.00000 −3.25254 0 −3.61837 −1.08961 −2.35322
1.5 −2.08101 −0.506466 2.33062 1.00000 1.05396 0 −0.688024 −2.74349 −2.08101
1.6 −1.76366 1.51231 1.11050 1.00000 −2.66720 0 1.56878 −0.712912 −1.76366
1.7 −1.54789 −2.28009 0.395964 1.00000 3.52934 0 2.48287 2.19883 −1.54789
1.8 −1.10593 −2.59668 −0.776930 1.00000 2.87173 0 3.07108 3.74273 −1.10593
1.9 −0.686868 1.42521 −1.52821 1.00000 −0.978928 0 2.42342 −0.968789 −0.686868
1.10 −0.628452 −1.52512 −1.60505 1.00000 0.958466 0 2.26560 −0.674002 −0.628452
1.11 −0.0974727 2.80957 −1.99050 1.00000 −0.273856 0 0.388965 4.89367 −0.0974727
1.12 −0.0843633 −1.56695 −1.99288 1.00000 0.132193 0 0.336853 −0.544660 −0.0843633
1.13 0.239569 1.70292 −1.94261 1.00000 0.407968 0 −0.944527 −0.100048 0.239569
1.14 0.662091 −0.772226 −1.56164 1.00000 −0.511284 0 −2.35813 −2.40367 0.662091
1.15 1.17555 1.97842 −0.618087 1.00000 2.32573 0 −3.07769 0.914144 1.17555
1.16 1.42068 −0.0109751 0.0183294 1.00000 −0.0155920 0 −2.81532 −2.99988 1.42068
1.17 1.54185 −2.55402 0.377298 1.00000 −3.93792 0 −2.50196 3.52303 1.54185
1.18 2.00699 1.95367 2.02800 1.00000 3.92099 0 0.0561989 0.816828 2.00699
1.19 2.05811 −0.485171 2.23583 1.00000 −0.998537 0 0.485366 −2.76461 2.05811
1.20 2.26981 −3.30996 3.15205 1.00000 −7.51299 0 2.61493 7.95585 2.26981
See all 21 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.21
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(7\) \(-1\)
\(31\) \(1\)

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 7595.2.a.bf 21
7.b odd 2 1 7595.2.a.bg 21
7.d odd 6 2 1085.2.j.d ✓ 42
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1085.2.j.d ✓ 42 7.d odd 6 2
7595.2.a.bf 21 1.a even 1 1 trivial
7595.2.a.bg 21 7.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7595))\):

\( T_{2}^{21} + 4 T_{2}^{20} - 24 T_{2}^{19} - 108 T_{2}^{18} + 224 T_{2}^{17} + 1210 T_{2}^{16} - 981 T_{2}^{15} + \cdots - 9 \) Copy content Toggle raw display
\( T_{3}^{21} + 5 T_{3}^{20} - 29 T_{3}^{19} - 171 T_{3}^{18} + 302 T_{3}^{17} + 2395 T_{3}^{16} + \cdots + 121 \) Copy content Toggle raw display
\( T_{11}^{21} + 4 T_{11}^{20} - 125 T_{11}^{19} - 623 T_{11}^{18} + 5979 T_{11}^{17} + 38296 T_{11}^{16} + \cdots - 175277664 \) Copy content Toggle raw display