Newspace parameters
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.h (of order \(5\), degree \(4\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
191.1 | −0.809017 | − | 0.587785i | −1.01321 | − | 3.11835i | 0.309017 | + | 0.951057i | −2.01188 | − | 0.975874i | −1.01321 | + | 3.11835i | −3.17274 | 0.309017 | − | 0.951057i | −6.27043 | + | 4.55573i | 1.05404 | + | 1.97205i | ||
191.2 | −0.809017 | − | 0.587785i | −0.853804 | − | 2.62774i | 0.309017 | + | 0.951057i | −0.950820 | + | 2.02384i | −0.853804 | + | 2.62774i | 1.85248 | 0.309017 | − | 0.951057i | −3.74897 | + | 2.72379i | 1.95881 | − | 1.07845i | ||
191.3 | −0.809017 | − | 0.587785i | −0.410709 | − | 1.26403i | 0.309017 | + | 0.951057i | 0.971992 | − | 2.01376i | −0.410709 | + | 1.26403i | −2.95140 | 0.309017 | − | 0.951057i | 0.997953 | − | 0.725055i | −1.97002 | + | 1.05784i | ||
191.4 | −0.809017 | − | 0.587785i | −0.199467 | − | 0.613896i | 0.309017 | + | 0.951057i | 1.52772 | + | 1.63281i | −0.199467 | + | 0.613896i | 4.95147 | 0.309017 | − | 0.951057i | 2.08997 | − | 1.51845i | −0.276209 | − | 2.21894i | ||
191.5 | −0.809017 | − | 0.587785i | −0.0472563 | − | 0.145440i | 0.309017 | + | 0.951057i | 1.99007 | + | 1.01962i | −0.0472563 | + | 0.145440i | −0.777730 | 0.309017 | − | 0.951057i | 2.40813 | − | 1.74961i | −1.01068 | − | 1.99462i | ||
191.6 | −0.809017 | − | 0.587785i | −0.0202803 | − | 0.0624164i | 0.309017 | + | 0.951057i | −0.536379 | − | 2.17078i | −0.0202803 | + | 0.0624164i | 2.69704 | 0.309017 | − | 0.951057i | 2.42357 | − | 1.76082i | −0.842014 | + | 2.07148i | ||
191.7 | −0.809017 | − | 0.587785i | 0.272680 | + | 0.839224i | 0.309017 | + | 0.951057i | 0.404965 | + | 2.19909i | 0.272680 | − | 0.839224i | −4.83673 | 0.309017 | − | 0.951057i | 1.79711 | − | 1.30568i | 0.964970 | − | 2.01713i | ||
191.8 | −0.809017 | − | 0.587785i | 0.416614 | + | 1.28220i | 0.309017 | + | 0.951057i | −1.66523 | + | 1.49231i | 0.416614 | − | 1.28220i | 0.369301 | 0.309017 | − | 0.951057i | 0.956568 | − | 0.694988i | 2.22436 | − | 0.228508i | ||
191.9 | −0.809017 | − | 0.587785i | 0.558576 | + | 1.71912i | 0.309017 | + | 0.951057i | −1.95557 | − | 1.08432i | 0.558576 | − | 1.71912i | 1.04781 | 0.309017 | − | 0.951057i | −0.216318 | + | 0.157164i | 0.944740 | + | 2.02669i | ||
191.10 | −0.809017 | − | 0.587785i | 0.869807 | + | 2.67699i | 0.309017 | + | 0.951057i | 2.22514 | − | 0.220827i | 0.869807 | − | 2.67699i | 0.0565513 | 0.309017 | − | 0.951057i | −3.98267 | + | 2.89358i | −1.92997 | − | 1.12925i | ||
381.1 | 0.309017 | + | 0.951057i | −2.17406 | + | 1.57955i | −0.809017 | + | 0.587785i | 1.08520 | + | 1.95508i | −2.17406 | − | 1.57955i | −3.41021 | −0.809017 | − | 0.587785i | 1.30452 | − | 4.01490i | −1.52404 | + | 1.63624i | ||
381.2 | 0.309017 | + | 0.951057i | −1.69612 | + | 1.23231i | −0.809017 | + | 0.587785i | −2.05239 | − | 0.887532i | −1.69612 | − | 1.23231i | −0.189957 | −0.809017 | − | 0.587785i | 0.431206 | − | 1.32712i | 0.209871 | − | 2.22620i | ||
381.3 | 0.309017 | + | 0.951057i | −1.03616 | + | 0.752812i | −0.809017 | + | 0.587785i | −0.232130 | − | 2.22399i | −1.03616 | − | 0.752812i | −0.203240 | −0.809017 | − | 0.587785i | −0.420156 | + | 1.29311i | 2.04340 | − | 0.908018i | ||
381.4 | 0.309017 | + | 0.951057i | −0.346529 | + | 0.251768i | −0.809017 | + | 0.587785i | −1.41712 | + | 1.72968i | −0.346529 | − | 0.251768i | 1.40627 | −0.809017 | − | 0.587785i | −0.870356 | + | 2.67868i | −2.08293 | − | 0.813259i | ||
381.5 | 0.309017 | + | 0.951057i | −0.0867222 | + | 0.0630074i | −0.809017 | + | 0.587785i | 2.07960 | − | 0.821736i | −0.0867222 | − | 0.0630074i | −1.31483 | −0.809017 | − | 0.587785i | −0.923500 | + | 2.84224i | 1.42415 | + | 1.72389i | ||
381.6 | 0.309017 | + | 0.951057i | 0.786708 | − | 0.571577i | −0.809017 | + | 0.587785i | −2.18231 | − | 0.487343i | 0.786708 | + | 0.571577i | 4.32575 | −0.809017 | − | 0.587785i | −0.634842 | + | 1.95384i | −0.210881 | − | 2.22610i | ||
381.7 | 0.309017 | + | 0.951057i | 1.41542 | − | 1.02837i | −0.809017 | + | 0.587785i | −1.29625 | + | 1.82202i | 1.41542 | + | 1.02837i | −2.41426 | −0.809017 | − | 0.587785i | 0.0188385 | − | 0.0579789i | −2.13340 | − | 0.669769i | ||
381.8 | 0.309017 | + | 0.951057i | 1.59293 | − | 1.15733i | −0.809017 | + | 0.587785i | 2.11352 | + | 0.730086i | 1.59293 | + | 1.15733i | −1.09272 | −0.809017 | − | 0.587785i | 0.270952 | − | 0.833904i | −0.0412386 | + | 2.23569i | ||
381.9 | 0.309017 | + | 0.951057i | 2.18620 | − | 1.58837i | −0.809017 | + | 0.587785i | 1.58887 | + | 1.57337i | 2.18620 | + | 1.58837i | 2.75740 | −0.809017 | − | 0.587785i | 1.32952 | − | 4.09183i | −1.00537 | + | 1.99731i | ||
381.10 | 0.309017 | + | 0.951057i | 2.28538 | − | 1.66043i | −0.809017 | + | 0.587785i | 0.312990 | − | 2.21405i | 2.28538 | + | 1.66043i | −5.10025 | −0.809017 | − | 0.587785i | 1.53890 | − | 4.73626i | 2.20241 | − | 0.386510i | ||
See all 40 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
25.d | even | 5 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 950.2.h.b | ✓ | 40 |
25.d | even | 5 | 1 | inner | 950.2.h.b | ✓ | 40 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
950.2.h.b | ✓ | 40 | 1.a | even | 1 | 1 | trivial |
950.2.h.b | ✓ | 40 | 25.d | even | 5 | 1 | inner |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{40} - 5 T_{3}^{39} + 29 T_{3}^{38} - 113 T_{3}^{37} + 465 T_{3}^{36} - 1360 T_{3}^{35} + 4448 T_{3}^{34} - 11690 T_{3}^{33} + 37078 T_{3}^{32} - 95871 T_{3}^{31} + 271335 T_{3}^{30} - 628317 T_{3}^{29} + 1605041 T_{3}^{28} + \cdots + 16 \)
acting on \(S_{2}^{\mathrm{new}}(950, [\chi])\).