↑

Properties

Label 325.10.a.l
Level $325$
Weight $10$
Character orbit 325.a
Self dual yes
Analytic conductor $167.387$
Analytic rank $0$
Dimension $27$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [325,10,Mod(1,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 10, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.1"); S:= CuspForms(chi, 10); N := Newforms(S);
 
Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 325.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [27,48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(167.386646753\)
Analytic rank: \(0\)
Dimension: \(27\)
Twist minimal: no (minimal twist has level 65)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 27 q + 48 q^{2} + 324 q^{3} + 6570 q^{4} - 1786 q^{6} + 3736 q^{7} + 36864 q^{8} + 214173 q^{9} - 66096 q^{11} + 114398 q^{12} - 771147 q^{13} - 359458 q^{14} + 998622 q^{16} + 779040 q^{17} + 1709648 q^{18}+ \cdots + 2142297632 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −42.7441 150.605 1315.05 0 −6437.48 −6310.63 −34325.8 2998.94 0
1.2 −37.7638 38.5058 914.105 0 −1454.12 5545.47 −15185.0 −18200.3 0
1.3 −36.8725 −202.048 847.581 0 7450.01 12381.6 −12373.7 21140.4 0
1.4 −32.4943 −126.169 543.879 0 4099.76 665.951 −1035.88 −3764.48 0
1.5 −31.5965 215.398 486.336 0 −6805.80 −6275.94 810.890 26713.1 0
1.6 −26.7907 −196.147 205.742 0 5254.92 −4544.36 8204.87 18790.7 0
1.7 −25.1980 257.968 122.940 0 −6500.27 10915.8 9803.54 46864.3 0
1.8 −24.0061 127.628 64.2915 0 −3063.86 1056.77 10747.7 −3394.00 0
1.9 −18.1415 −10.3900 −182.888 0 188.489 −11293.6 12606.3 −19575.0 0
1.10 −9.91262 −218.926 −413.740 0 2170.13 −1909.27 9176.51 28245.4 0
1.11 −9.01531 −96.0448 −430.724 0 865.874 6689.08 8498.95 −10458.4 0
1.12 −7.88453 18.3933 −449.834 0 −145.022 3534.00 7583.61 −19344.7 0
1.13 −5.61283 84.3580 −480.496 0 −473.487 −1730.99 5570.71 −12566.7 0
1.14 3.55822 263.202 −499.339 0 936.531 −8747.23 −3598.56 49592.5 0
1.15 9.94975 −186.339 −413.003 0 −1854.02 −2543.77 −9203.54 15039.1 0
1.16 11.5026 50.8152 −379.691 0 584.504 11334.3 −10256.7 −17100.8 0
1.17 16.3195 195.494 −245.673 0 3190.36 −4181.36 −12364.9 18534.7 0
1.18 16.7669 −206.316 −230.871 0 −3459.29 7929.76 −12455.6 22883.5 0
1.19 20.8068 72.3996 −79.0763 0 1506.40 −5461.35 −12298.4 −14441.3 0
1.20 22.9877 40.8325 16.4339 0 938.645 −7844.21 −11391.9 −18015.7 0
See all 27 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.27
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \( -1 \)
\(13\) \( +1 \)

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 325.10.a.l 27
5.b even 2 1 325.10.a.k 27
5.c odd 4 2 65.10.b.a ✓ 54
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
65.10.b.a ✓ 54 5.c odd 4 2
325.10.a.k 27 5.b even 2 1
325.10.a.l 27 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{27} - 48 T_{2}^{26} - 9045 T_{2}^{25} + 442352 T_{2}^{24} + 35528421 T_{2}^{23} + \cdots + 28\!\cdots\!00 \) acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(325))\). Copy content Toggle raw display