Properties

Label 49.26.a.h
Level $49$
Weight $26$
Character orbit 49.a
Self dual yes
Analytic conductor $194.038$
Analytic rank $1$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 26 \)
Character orbit: \([\chi]\) \(=\) 49.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(194.038422177\)
Analytic rank: \(1\)
Dimension: \(24\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 16290 q^{2} + 333378474 q^{4} - 798202294830 q^{8} + 5073152845720 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 16290 q^{2} + 333378474 q^{4} - 798202294830 q^{8} + 5073152845720 q^{9} - 29647806315264 q^{11} + 13\!\cdots\!04 q^{15}+ \cdots - 25\!\cdots\!24 q^{99}+O(q^{100}) \) 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.

Label \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −9947.40 −1.77441e6 6.53963e7 −5.10763e8 1.76507e10 0 −3.16744e11 2.30123e12 5.08076e12
1.2 −9947.40 1.77441e6 6.53963e7 5.10763e8 −1.76507e10 0 −3.16744e11 2.30123e12 −5.08076e12
1.3 −9621.83 −44215.1 5.90252e7 9.55920e8 4.25430e8 0 −2.45075e11 −8.45334e11 −9.19770e12
1.4 −9621.83 44215.1 5.90252e7 −9.55920e8 −4.25430e8 0 −2.45075e11 −8.45334e11 9.19770e12
1.5 −9304.30 −644120. 5.30155e7 5.39746e8 5.99309e9 0 −1.81072e11 −4.32397e11 −5.02196e12
1.6 −9304.30 644120. 5.30155e7 −5.39746e8 −5.99309e9 0 −1.81072e11 −4.32397e11 5.02196e12
1.7 −4742.65 −1.50280e6 −1.10617e7 −3.39227e8 7.12727e9 0 2.11599e11 1.41112e12 1.60884e12
1.8 −4742.65 1.50280e6 −1.10617e7 3.39227e8 −7.12727e9 0 2.11599e11 1.41112e12 −1.60884e12
1.9 −4573.51 −853606. −1.26374e7 3.17192e8 3.90397e9 0 2.11259e11 −1.18646e11 −1.45068e12
1.10 −4573.51 853606. −1.26374e7 −3.17192e8 −3.90397e9 0 2.11259e11 −1.18646e11 1.45068e12
1.11 −3011.53 −462530. −2.44851e7 −4.78350e8 1.39292e9 0 1.74788e11 −6.33355e11 1.44057e12
1.12 −3011.53 462530. −2.44851e7 4.78350e8 −1.39292e9 0 1.74788e11 −6.33355e11 −1.44057e12
1.13 1174.18 −942587. −3.21757e7 4.94390e8 −1.10677e9 0 −7.71793e10 4.11813e10 5.80505e11
1.14 1174.18 942587. −3.21757e7 −4.94390e8 1.10677e9 0 −7.71793e10 4.11813e10 −5.80505e11
1.15 3451.49 −304783. −2.16417e7 −7.74843e8 −1.05195e9 0 −1.90509e11 −7.54396e11 −2.67436e12
1.16 3451.49 304783. −2.16417e7 7.74843e8 1.05195e9 0 −1.90509e11 −7.54396e11 2.67436e12
1.17 3683.76 −1.60504e6 −1.99843e7 2.32545e8 −5.91257e9 0 −1.97224e11 1.72885e12 8.56642e11
1.18 3683.76 1.60504e6 −1.99843e7 −2.32545e8 5.91257e9 0 −1.97224e11 1.72885e12 −8.56642e11
1.19 6114.28 −603398. 3.83000e6 −9.40230e8 −3.68934e9 0 −1.81744e11 −4.83200e11 −5.74883e12
1.20 6114.28 603398. 3.83000e6 9.40230e8 3.68934e9 0 −1.81744e11 −4.83200e11 5.74883e12
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.24
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(7\) \(1\)

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 49.26.a.h 24
7.b odd 2 1 inner 49.26.a.h 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
49.26.a.h 24 1.a even 1 1 trivial
49.26.a.h 24 7.b odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{26}^{\mathrm{new}}(\Gamma_0(49))\):

\( T_{2}^{12} + 8145 T_{2}^{11} - 251500698 T_{2}^{10} - 1913354786520 T_{2}^{9} + \cdots + 45\!\cdots\!24 \) Copy content Toggle raw display
\( T_{3}^{24} - 12704039736176 T_{3}^{22} + \cdots + 42\!\cdots\!56 \) Copy content Toggle raw display