Newspace parameters
Level: | |||
Weight: | |||
Character orbit: | 4.b (of order , degree , minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Coefficient field: | |
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | multiple of |
Twist minimal: | yes |
Sato-Tate group: |
-expansion
Coefficients of the -expansion are expressed in terms of a basis for the coefficient ring described below. We also show the integral -expansion of the trace form.
Basis of coefficient ring in terms of a root of
:
Character values
We give the values of on generators for .
Embeddings
For each embedding of the coefficient field, the values are shown below.
For more information on an embedded modular form you can click on its label.
Label | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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3.1 |
|
−3.68465e6 | − | 2.00389e6i | − | 5.36316e10i | 9.56104e12 | + | 1.47672e13i | 7.16734e14 | −1.07472e17 | + | 1.97613e17i | 1.83098e18i | −5.63715e18 | − | 7.35713e19i | −1.89157e21 | −2.64091e21 | − | 1.43626e21i | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
3.2 | −3.68465e6 | + | 2.00389e6i | 5.36316e10i | 9.56104e12 | − | 1.47672e13i | 7.16734e14 | −1.07472e17 | − | 1.97613e17i | − | 1.83098e18i | −5.63715e18 | + | 7.35713e19i | −1.89157e21 | −2.64091e21 | + | 1.43626e21i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
3.3 | −3.36765e6 | − | 2.50023e6i | 3.81573e10i | 5.08992e12 | + | 1.68398e13i | −2.81252e15 | 9.54019e16 | − | 1.28500e17i | 3.86238e18i | 2.49622e19 | − | 6.94364e19i | −4.71210e20 | 9.47159e21 | + | 7.03195e21i | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
3.4 | −3.36765e6 | + | 2.50023e6i | − | 3.81573e10i | 5.08992e12 | − | 1.68398e13i | −2.81252e15 | 9.54019e16 | + | 1.28500e17i | − | 3.86238e18i | 2.49622e19 | + | 6.94364e19i | −4.71210e20 | 9.47159e21 | − | 7.03195e21i | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
3.5 | −2.67504e6 | − | 3.23054e6i | 1.97789e10i | −3.28055e12 | + | 1.72836e13i | 4.32114e15 | 6.38964e16 | − | 5.29092e16i | − | 4.05908e18i | 6.46109e19 | − | 3.56363e19i | 5.93567e20 | −1.15592e22 | − | 1.39596e22i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
3.6 | −2.67504e6 | + | 3.23054e6i | − | 1.97789e10i | −3.28055e12 | − | 1.72836e13i | 4.32114e15 | 6.38964e16 | + | 5.29092e16i | 4.05908e18i | 6.46109e19 | + | 3.56363e19i | 5.93567e20 | −1.15592e22 | + | 1.39596e22i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
3.7 | −1.53066e6 | − | 3.90503e6i | − | 1.95946e10i | −1.29064e13 | + | 1.19545e13i | −3.24586e15 | −7.65175e16 | + | 2.99926e16i | − | 5.50179e18i | 6.64381e19 | + | 3.21014e19i | 6.00823e20 | 4.96831e21 | + | 1.26752e22i | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
3.8 | −1.53066e6 | + | 3.90503e6i | 1.95946e10i | −1.29064e13 | − | 1.19545e13i | −3.24586e15 | −7.65175e16 | − | 2.99926e16i | 5.50179e18i | 6.64381e19 | − | 3.21014e19i | 6.00823e20 | 4.96831e21 | − | 1.26752e22i | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
3.9 | −174802. | − | 4.19066e6i | − | 2.16788e10i | −1.75311e13 | + | 1.46508e12i | 1.03983e15 | −9.08484e16 | + | 3.78950e15i | 7.00373e18i | 9.20411e18 | + | 7.32107e19i | 5.14802e20 | −1.81765e20 | − | 4.35758e21i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
3.10 | −174802. | + | 4.19066e6i | 2.16788e10i | −1.75311e13 | − | 1.46508e12i | 1.03983e15 | −9.08484e16 | − | 3.78950e15i | − | 7.00373e18i | 9.20411e18 | − | 7.32107e19i | 5.14802e20 | −1.81765e20 | + | 4.35758e21i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
3.11 | 692907. | − | 4.13667e6i | 4.93751e10i | −1.66319e13 | − | 5.73266e12i | 3.31017e14 | 2.04249e17 | + | 3.42123e16i | − | 3.30487e17i | −3.52385e19 | + | 6.48287e19i | −1.45313e21 | 2.29364e20 | − | 1.36931e21i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
3.12 | 692907. | + | 4.13667e6i | − | 4.93751e10i | −1.66319e13 | + | 5.73266e12i | 3.31017e14 | 2.04249e17 | − | 3.42123e16i | 3.30487e17i | −3.52385e19 | − | 6.48287e19i | −1.45313e21 | 2.29364e20 | + | 1.36931e21i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
3.13 | 2.45341e6 | − | 3.40190e6i | − | 4.81236e10i | −5.55370e12 | − | 1.66926e13i | 2.94946e15 | −1.63712e17 | − | 1.18067e17i | − | 5.91201e18i | −7.04120e19 | − | 2.20606e19i | −1.33111e21 | 7.23624e21 | − | 1.00338e22i | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
3.14 | 2.45341e6 | + | 3.40190e6i | 4.81236e10i | −5.55370e12 | + | 1.66926e13i | 2.94946e15 | −1.63712e17 | + | 1.18067e17i | 5.91201e18i | −7.04120e19 | + | 2.20606e19i | −1.33111e21 | 7.23624e21 | + | 1.00338e22i | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
3.15 | 2.63672e6 | − | 3.26188e6i | 5.11393e9i | −3.68760e12 | − | 1.72014e13i | −1.83599e15 | 1.66811e16 | + | 1.34840e16i | − | 1.24564e18i | −6.58320e19 | − | 3.33266e19i | 9.58619e20 | −4.84100e21 | + | 5.98879e21i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
3.16 | 2.63672e6 | + | 3.26188e6i | − | 5.11393e9i | −3.68760e12 | + | 1.72014e13i | −1.83599e15 | 1.66811e16 | − | 1.34840e16i | 1.24564e18i | −6.58320e19 | + | 3.33266e19i | 9.58619e20 | −4.84100e21 | − | 5.98879e21i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
3.17 | 3.98169e6 | − | 1.31845e6i | 2.39886e10i | 1.41156e13 | − | 1.04993e13i | 1.91424e15 | 3.16279e16 | + | 9.55154e16i | 2.07168e18i | 4.23609e19 | − | 6.04158e19i | 4.09316e20 | 7.62190e21 | − | 2.52383e21i | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
3.18 | 3.98169e6 | + | 1.31845e6i | − | 2.39886e10i | 1.41156e13 | + | 1.04993e13i | 1.91424e15 | 3.16279e16 | − | 9.55154e16i | − | 2.07168e18i | 4.23609e19 | + | 6.04158e19i | 4.09316e20 | 7.62190e21 | + | 2.52383e21i | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
3.19 | 4.06802e6 | − | 1.02149e6i | − | 4.78233e10i | 1.55053e13 | − | 8.31084e12i | −4.02131e15 | −4.88508e16 | − | 1.94546e17i | 5.21410e18i | 5.45865e19 | − | 4.96471e19i | −1.30230e21 | −1.63587e22 | + | 4.10771e21i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
3.20 | 4.06802e6 | + | 1.02149e6i | 4.78233e10i | 1.55053e13 | + | 8.31084e12i | −4.02131e15 | −4.88508e16 | + | 1.94546e17i | − | 5.21410e18i | 5.45865e19 | + | 4.96471e19i | −1.30230e21 | −1.63587e22 | − | 4.10771e21i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
4.b | odd | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 4.45.b.b | ✓ | 20 |
4.b | odd | 2 | 1 | inner | 4.45.b.b | ✓ | 20 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
4.45.b.b | ✓ | 20 | 1.a | even | 1 | 1 | trivial |
4.45.b.b | ✓ | 20 | 4.b | odd | 2 | 1 | inner |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
acting on .