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Properties

Label 195.2.bm.a
Level $195$
Weight $2$
Character orbit 195.bm
Analytic conductor $1.557$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [195,2,Mod(7,195)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(195, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("195.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 195 = 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 195.bm (of order \(12\), degree \(4\), minimal)

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: no
Analytic conductor: \(1.55708283941\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 56 q + 28 q^{4} - 8 q^{5}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 56 q + 28 q^{4} - 8 q^{5} + 8 q^{11} + 16 q^{12} - 4 q^{15} - 28 q^{16} - 20 q^{17} - 8 q^{18} + 24 q^{19} - 8 q^{21} - 28 q^{22} - 8 q^{23} - 20 q^{25} - 8 q^{31} - 60 q^{32} + 12 q^{33} - 4 q^{34} - 20 q^{37} - 8 q^{39} + 24 q^{40} - 4 q^{41} - 60 q^{42} - 12 q^{43} - 40 q^{44} - 8 q^{45} - 8 q^{46} + 24 q^{47} + 16 q^{48} - 44 q^{49} - 124 q^{50} + 8 q^{52} + 4 q^{53} + 32 q^{55} + 72 q^{56} - 4 q^{58} + 64 q^{59} - 48 q^{60} + 16 q^{61} + 108 q^{62} - 56 q^{64} - 40 q^{65} - 16 q^{66} + 12 q^{68} - 8 q^{69} + 80 q^{70} - 16 q^{71} - 12 q^{72} - 36 q^{74} + 16 q^{75} + 112 q^{76} + 48 q^{77} - 8 q^{78} + 164 q^{80} + 28 q^{81} - 52 q^{82} + 104 q^{83} + 32 q^{84} + 16 q^{85} - 64 q^{86} + 36 q^{87} - 24 q^{88} + 12 q^{89} - 12 q^{90} - 40 q^{91} - 64 q^{92} + 24 q^{94} + 40 q^{95} - 108 q^{97} - 96 q^{98} - 8 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
7.1 −2.16879 − 1.25215i −0.258819 − 0.965926i 2.13577 + 3.69927i −2.22127 − 0.256829i −0.648162 + 2.41897i 1.31169 + 2.27192i − 5.68865i −0.866025 + 0.500000i 4.49588 + 3.33838i
7.2 −1.74222 − 1.00587i 0.258819 + 0.965926i 1.02355 + 1.77285i −1.53131 − 1.62945i 0.520677 − 1.94319i −0.0952740 − 0.165019i − 0.0947706i −0.866025 + 0.500000i 1.02886 + 4.37915i
7.3 −1.59037 − 0.918199i 0.258819 + 0.965926i 0.686179 + 1.18850i 1.22674 + 1.86952i 0.475295 − 1.77382i −1.31456 − 2.27688i 1.15260i −0.866025 + 0.500000i −0.234383 − 4.09962i
7.4 −1.47770 − 0.853152i −0.258819 − 0.965926i 0.455736 + 0.789358i 1.77617 + 1.35839i −0.441624 + 1.64816i 2.46357 + 4.26702i 1.85736i −0.866025 + 0.500000i −1.46573 − 3.52264i
7.5 −1.08442 − 0.626089i −0.258819 − 0.965926i −0.216026 − 0.374168i 1.49926 − 1.65898i −0.324087 + 1.20951i −1.37566 − 2.38272i 3.04536i −0.866025 + 0.500000i −2.66449 + 0.860357i
7.6 −0.545471 − 0.314928i 0.258819 + 0.965926i −0.801641 − 1.38848i −1.95424 + 1.08672i 0.163019 − 0.608393i 1.84227 + 3.19090i 2.26955i −0.866025 + 0.500000i 1.40822 + 0.0226678i
7.7 0.138788 + 0.0801292i 0.258819 + 0.965926i −0.987159 − 1.70981i −0.0607511 − 2.23524i −0.0414779 + 0.154798i −2.22106 − 3.84699i − 0.636918i −0.866025 + 0.500000i 0.170677 − 0.315092i
7.8 0.579821 + 0.334760i −0.258819 − 0.965926i −0.775871 − 1.34385i −2.09803 − 0.773477i 0.173285 − 0.646707i 0.0297909 + 0.0515993i − 2.37796i −0.866025 + 0.500000i −0.957554 − 1.15082i
7.9 0.835096 + 0.482143i −0.258819 − 0.965926i −0.535077 − 0.926780i 2.23184 + 0.137372i 0.249575 − 0.931428i −0.676930 − 1.17248i − 2.96050i −0.866025 + 0.500000i 1.79757 + 1.19079i
7.10 0.975669 + 0.563303i 0.258819 + 0.965926i −0.365380 − 0.632856i 1.98502 − 1.02941i −0.291587 + 1.08822i 1.23258 + 2.13490i − 3.07649i −0.866025 + 0.500000i 2.51660 + 0.113800i
7.11 1.49213 + 0.861480i 0.258819 + 0.965926i 0.484294 + 0.838822i −0.0988139 + 2.23388i −0.445935 + 1.66425i 0.243108 + 0.421075i − 1.77708i −0.866025 + 0.500000i −2.07189 + 3.24811i
7.12 1.96880 + 1.13669i −0.258819 − 0.965926i 1.58411 + 2.74376i 0.165292 − 2.22995i 0.588392 − 2.19591i 1.06779 + 1.84947i 2.65581i −0.866025 + 0.500000i 2.86018 − 4.20244i
7.13 2.13750 + 1.23409i 0.258819 + 0.965926i 2.04594 + 3.54367i −1.63248 − 1.52807i −0.638810 + 2.38407i −0.204703 − 0.354557i 5.16311i −0.866025 + 0.500000i −1.60366 − 5.28088i
7.14 2.21322 + 1.27780i −0.258819 − 0.965926i 2.26557 + 3.92408i 0.444615 + 2.19142i 0.661440 − 2.46853i −2.30261 − 3.98824i 6.46858i −0.866025 + 0.500000i −1.81617 + 5.41823i
28.1 −2.16879 + 1.25215i −0.258819 + 0.965926i 2.13577 − 3.69927i −2.22127 + 0.256829i −0.648162 − 2.41897i 1.31169 − 2.27192i 5.68865i −0.866025 − 0.500000i 4.49588 − 3.33838i
28.2 −1.74222 + 1.00587i 0.258819 − 0.965926i 1.02355 − 1.77285i −1.53131 + 1.62945i 0.520677 + 1.94319i −0.0952740 + 0.165019i 0.0947706i −0.866025 − 0.500000i 1.02886 − 4.37915i
28.3 −1.59037 + 0.918199i 0.258819 − 0.965926i 0.686179 − 1.18850i 1.22674 − 1.86952i 0.475295 + 1.77382i −1.31456 + 2.27688i − 1.15260i −0.866025 − 0.500000i −0.234383 + 4.09962i
28.4 −1.47770 + 0.853152i −0.258819 + 0.965926i 0.455736 − 0.789358i 1.77617 − 1.35839i −0.441624 − 1.64816i 2.46357 − 4.26702i − 1.85736i −0.866025 − 0.500000i −1.46573 + 3.52264i
28.5 −1.08442 + 0.626089i −0.258819 + 0.965926i −0.216026 + 0.374168i 1.49926 + 1.65898i −0.324087 − 1.20951i −1.37566 + 2.38272i − 3.04536i −0.866025 − 0.500000i −2.66449 − 0.860357i
28.6 −0.545471 + 0.314928i 0.258819 − 0.965926i −0.801641 + 1.38848i −1.95424 − 1.08672i 0.163019 + 0.608393i 1.84227 − 3.19090i − 2.26955i −0.866025 − 0.500000i 1.40822 − 0.0226678i
See all 56 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 7.14
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
65.t even 12 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 195.2.bm.a yes 56
3.b odd 2 1 585.2.dp.c 56
5.b even 2 1 975.2.bu.i 56
5.c odd 4 1 195.2.bd.a ✓ 56
5.c odd 4 1 975.2.bl.i 56
13.f odd 12 1 195.2.bd.a ✓ 56
15.e even 4 1 585.2.cf.b 56
39.k even 12 1 585.2.cf.b 56
65.o even 12 1 975.2.bu.i 56
65.s odd 12 1 975.2.bl.i 56
65.t even 12 1 inner 195.2.bm.a yes 56
195.bc odd 12 1 585.2.dp.c 56
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
195.2.bd.a ✓ 56 5.c odd 4 1
195.2.bd.a ✓ 56 13.f odd 12 1
195.2.bm.a yes 56 1.a even 1 1 trivial
195.2.bm.a yes 56 65.t even 12 1 inner
585.2.cf.b 56 15.e even 4 1
585.2.cf.b 56 39.k even 12 1
585.2.dp.c 56 3.b odd 2 1
585.2.dp.c 56 195.bc odd 12 1
975.2.bl.i 56 5.c odd 4 1
975.2.bl.i 56 65.s odd 12 1
975.2.bu.i 56 5.b even 2 1
975.2.bu.i 56 65.o even 12 1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(195, [\chi])\).