Newspace parameters
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(61.6569959560\) |
Analytic rank: | \(0\) |
Dimension: | \(23\) |
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.
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 | −5.41975 | 4.17361 | 21.3737 | −5.00000 | −22.6199 | −25.0607 | −72.4822 | −9.58100 | 27.0988 | ||||||||||||||||||
1.2 | −4.98043 | −7.40260 | 16.8047 | −5.00000 | 36.8681 | 8.03646 | −43.8509 | 27.7985 | 24.9021 | ||||||||||||||||||
1.3 | −4.38057 | 7.64668 | 11.1894 | −5.00000 | −33.4968 | 9.94553 | −13.9715 | 31.4717 | 21.9029 | ||||||||||||||||||
1.4 | −4.30610 | 2.30247 | 10.5425 | −5.00000 | −9.91467 | 14.9972 | −10.9483 | −21.6986 | 21.5305 | ||||||||||||||||||
1.5 | −3.61172 | −0.308289 | 5.04454 | −5.00000 | 1.11345 | −23.5260 | 10.6743 | −26.9050 | 18.0586 | ||||||||||||||||||
1.6 | −2.96023 | −4.00535 | 0.762942 | −5.00000 | 11.8567 | 6.39895 | 21.4233 | −10.9572 | 14.8011 | ||||||||||||||||||
1.7 | −2.48215 | 3.78622 | −1.83894 | −5.00000 | −9.39797 | 1.80512 | 24.4217 | −12.6645 | 12.4107 | ||||||||||||||||||
1.8 | −1.58489 | −6.85881 | −5.48811 | −5.00000 | 10.8705 | 9.66724 | 21.3772 | 20.0432 | 7.92447 | ||||||||||||||||||
1.9 | −1.45938 | 5.64597 | −5.87020 | −5.00000 | −8.23963 | −17.6407 | 20.2419 | 4.87695 | 7.29692 | ||||||||||||||||||
1.10 | −0.449859 | −1.82696 | −7.79763 | −5.00000 | 0.821874 | 22.2872 | 7.10670 | −23.6622 | 2.24929 | ||||||||||||||||||
1.11 | −0.128788 | 9.96634 | −7.98341 | −5.00000 | −1.28354 | −35.2392 | 2.05847 | 72.3280 | 0.643939 | ||||||||||||||||||
1.12 | 0.666010 | −10.2430 | −7.55643 | −5.00000 | −6.82192 | 4.34789 | −10.3607 | 77.9184 | −3.33005 | ||||||||||||||||||
1.13 | 0.814185 | 3.88289 | −7.33710 | −5.00000 | 3.16139 | 17.3543 | −12.4872 | −11.9232 | −4.07093 | ||||||||||||||||||
1.14 | 1.51379 | 1.98888 | −5.70843 | −5.00000 | 3.01075 | −28.4418 | −20.7517 | −23.0444 | −7.56896 | ||||||||||||||||||
1.15 | 2.28558 | 0.0269626 | −2.77614 | −5.00000 | 0.0616250 | −20.0645 | −24.6297 | −26.9993 | −11.4279 | ||||||||||||||||||
1.16 | 2.38912 | −1.09640 | −2.29208 | −5.00000 | −2.61943 | −1.10283 | −24.5891 | −25.7979 | −11.9456 | ||||||||||||||||||
1.17 | 2.47265 | 8.18859 | −1.88602 | −5.00000 | 20.2475 | 19.1708 | −24.4446 | 40.0529 | −12.3632 | ||||||||||||||||||
1.18 | 3.33800 | −7.01943 | 3.14227 | −5.00000 | −23.4309 | 0.402575 | −16.2151 | 22.2724 | −16.6900 | ||||||||||||||||||
1.19 | 4.05796 | −1.73694 | 8.46702 | −5.00000 | −7.04845 | −13.5343 | 1.89515 | −23.9830 | −20.2898 | ||||||||||||||||||
1.20 | 4.39002 | −6.92776 | 11.2723 | −5.00000 | −30.4130 | −34.5356 | 14.3653 | 20.9939 | −21.9501 | ||||||||||||||||||
See all 23 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(5\) | \(1\) |
\(11\) | \(1\) |
\(19\) | \(1\) |
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 | 1045.4.a.g | ✓ | 23 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
1045.4.a.g | ✓ | 23 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{23} - 6 T_{2}^{22} - 120 T_{2}^{21} + 746 T_{2}^{20} + 5933 T_{2}^{19} - 38973 T_{2}^{18} - 155165 T_{2}^{17} + 1114970 T_{2}^{16} + 2267759 T_{2}^{15} - 19087352 T_{2}^{14} - 17244282 T_{2}^{13} + \cdots + 174456832 \)
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1045))\).