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Properties

Label 35.10.e.b
Level $35$
Weight $10$
Character orbit 35.e
Analytic conductor $18.026$
Analytic rank $0$
Dimension $26$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [35,10,Mod(11,35)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(35, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("35.11");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 35.e (of order \(3\), degree \(2\), 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: \(18.0262542657\)
Analytic rank: \(0\)
Dimension: \(26\)
Relative dimension: \(13\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 26 q + q^{2} - 268 q^{3} - 3563 q^{4} - 8125 q^{5} + 6080 q^{6} - 8462 q^{7} - 9390 q^{8} - 82107 q^{9} + 625 q^{10} - 129087 q^{11} - 356068 q^{12} + 71778 q^{13} + 828653 q^{14} + 335000 q^{15} - 1379187 q^{16}+ \cdots + 10532284198 q^{99}+O(q^{100}) \) 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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
11.1 −22.5253 − 39.0149i −82.8695 + 143.534i −758.777 + 1314.24i −312.500 − 541.266i 7466.64 −974.948 + 6277.19i 45300.8 −3893.21 − 6743.23i −14078.3 + 24384.3i
11.2 −17.9712 − 31.1270i 48.7106 − 84.3693i −389.927 + 675.374i −312.500 − 541.266i −3501.55 −2294.91 − 5923.43i 9627.32 5096.05 + 8826.62i −11232.0 + 19454.4i
11.3 −13.4978 − 23.3789i −20.4858 + 35.4825i −108.381 + 187.722i −312.500 − 541.266i 1106.05 5969.00 + 2173.62i −7970.10 9002.16 + 15592.2i −8436.13 + 14611.8i
11.4 −12.0438 − 20.8604i −128.396 + 222.388i −34.1047 + 59.0710i −312.500 − 541.266i 6185.48 −2990.00 − 5604.77i −10689.8 −23129.5 − 40061.5i −7527.35 + 13037.8i
11.5 −7.72146 − 13.3740i 23.1625 − 40.1186i 136.758 − 236.872i −312.500 − 541.266i −715.393 −6025.47 + 2011.79i −12130.7 8768.50 + 15187.5i −4825.91 + 8358.72i
11.6 −6.99651 − 12.1183i 127.747 − 221.265i 158.098 − 273.833i −312.500 − 541.266i −3575.14 −4480.30 + 4503.39i −11589.0 −22797.3 − 39486.1i −4372.82 + 7573.94i
11.7 1.28068 + 2.21821i −88.7779 + 153.768i 252.720 − 437.723i −312.500 − 541.266i −454.786 3039.46 + 5578.11i 2606.03 −5921.54 − 10256.4i 800.427 − 1386.38i
11.8 4.76014 + 8.24481i 87.7485 − 151.985i 210.682 − 364.912i −312.500 − 541.266i 1670.78 6348.81 − 214.845i 8885.89 −5558.10 − 9626.90i 2975.09 − 5153.00i
11.9 7.58976 + 13.1459i −22.9573 + 39.7632i 140.791 − 243.857i −312.500 − 541.266i −696.962 −6215.41 + 1312.34i 12046.2 8787.43 + 15220.3i 4743.60 − 8216.16i
11.10 10.6621 + 18.4672i −95.0320 + 164.600i 28.6405 − 49.6068i −312.500 − 541.266i −4052.95 −374.098 − 6341.42i 12139.4 −8220.66 − 14238.6i 6663.79 − 11542.0i
11.11 17.0642 + 29.5561i 64.1727 − 111.150i −326.375 + 565.298i −312.500 − 541.266i 4380.23 −1287.99 − 6220.51i −4803.59 1605.23 + 2780.35i 10665.1 − 18472.6i
11.12 18.2405 + 31.5936i 51.0946 − 88.4984i −409.435 + 709.163i −312.500 − 541.266i 3727.97 −772.002 + 6305.36i −11195.0 4620.19 + 8002.40i 11400.3 − 19746.0i
11.13 21.6586 + 37.5138i −98.1178 + 169.945i −682.188 + 1181.59i −312.500 − 541.266i −8500.37 5826.86 − 2530.08i −36922.6 −9412.70 − 16303.3i 13536.6 − 23446.1i
16.1 −22.5253 + 39.0149i −82.8695 − 143.534i −758.777 − 1314.24i −312.500 + 541.266i 7466.64 −974.948 − 6277.19i 45300.8 −3893.21 + 6743.23i −14078.3 − 24384.3i
16.2 −17.9712 + 31.1270i 48.7106 + 84.3693i −389.927 − 675.374i −312.500 + 541.266i −3501.55 −2294.91 + 5923.43i 9627.32 5096.05 − 8826.62i −11232.0 − 19454.4i
16.3 −13.4978 + 23.3789i −20.4858 − 35.4825i −108.381 − 187.722i −312.500 + 541.266i 1106.05 5969.00 − 2173.62i −7970.10 9002.16 − 15592.2i −8436.13 − 14611.8i
16.4 −12.0438 + 20.8604i −128.396 − 222.388i −34.1047 − 59.0710i −312.500 + 541.266i 6185.48 −2990.00 + 5604.77i −10689.8 −23129.5 + 40061.5i −7527.35 − 13037.8i
16.5 −7.72146 + 13.3740i 23.1625 + 40.1186i 136.758 + 236.872i −312.500 + 541.266i −715.393 −6025.47 − 2011.79i −12130.7 8768.50 − 15187.5i −4825.91 − 8358.72i
16.6 −6.99651 + 12.1183i 127.747 + 221.265i 158.098 + 273.833i −312.500 + 541.266i −3575.14 −4480.30 − 4503.39i −11589.0 −22797.3 + 39486.1i −4372.82 − 7573.94i
16.7 1.28068 − 2.21821i −88.7779 − 153.768i 252.720 + 437.723i −312.500 + 541.266i −454.786 3039.46 − 5578.11i 2606.03 −5921.54 + 10256.4i 800.427 + 1386.38i
See all 26 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 11.13
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.c even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 35.10.e.b ✓ 26
7.c even 3 1 inner 35.10.e.b ✓ 26
7.c even 3 1 245.10.a.m 13
7.d odd 6 1 245.10.a.l 13
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
35.10.e.b ✓ 26 1.a even 1 1 trivial
35.10.e.b ✓ 26 7.c even 3 1 inner
245.10.a.l 13 7.d odd 6 1
245.10.a.m 13 7.c even 3 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{26} - T_{2}^{25} + 5110 T_{2}^{24} - 1297 T_{2}^{23} + 16469162 T_{2}^{22} + \cdots + 93\!\cdots\!04 \) acting on \(S_{10}^{\mathrm{new}}(35, [\chi])\). Copy content Toggle raw display