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: | \(44\) |
Relative dimension: | \(11\) 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 | −1.00220 | − | 3.08444i | 0.309017 | + | 0.951057i | −2.22762 | + | 0.194172i | 1.00220 | − | 3.08444i | −1.89338 | −0.309017 | + | 0.951057i | −6.08232 | + | 4.41906i | −1.91632 | − | 1.15227i | ||
191.2 | 0.809017 | + | 0.587785i | −0.806394 | − | 2.48183i | 0.309017 | + | 0.951057i | 1.11301 | − | 1.93938i | 0.806394 | − | 2.48183i | −1.68962 | −0.309017 | + | 0.951057i | −3.08213 | + | 2.23930i | 2.04039 | − | 0.914782i | ||
191.3 | 0.809017 | + | 0.587785i | −0.734690 | − | 2.26114i | 0.309017 | + | 0.951057i | −0.796273 | − | 2.08949i | 0.734690 | − | 2.26114i | 3.12738 | −0.309017 | + | 0.951057i | −2.14595 | + | 1.55912i | 0.583970 | − | 2.15847i | ||
191.4 | 0.809017 | + | 0.587785i | −0.320919 | − | 0.987687i | 0.309017 | + | 0.951057i | −0.846301 | + | 2.06973i | 0.320919 | − | 0.987687i | −2.76904 | −0.309017 | + | 0.951057i | 1.55451 | − | 1.12942i | −1.90123 | + | 1.17700i | ||
191.5 | 0.809017 | + | 0.587785i | −0.183900 | − | 0.565985i | 0.309017 | + | 0.951057i | 2.14212 | + | 0.641332i | 0.183900 | − | 0.565985i | 2.23803 | −0.309017 | + | 0.951057i | 2.14053 | − | 1.55519i | 1.35605 | + | 1.77796i | ||
191.6 | 0.809017 | + | 0.587785i | −0.00648263 | − | 0.0199515i | 0.309017 | + | 0.951057i | 2.20515 | + | 0.370553i | 0.00648263 | − | 0.0199515i | −4.68808 | −0.309017 | + | 0.951057i | 2.42669 | − | 1.76310i | 1.56620 | + | 1.59594i | ||
191.7 | 0.809017 | + | 0.587785i | 0.0375929 | + | 0.115699i | 0.309017 | + | 0.951057i | −2.23367 | + | 0.103463i | −0.0375929 | + | 0.115699i | 1.64271 | −0.309017 | + | 0.951057i | 2.41508 | − | 1.75466i | −1.86789 | − | 1.22922i | ||
191.8 | 0.809017 | + | 0.587785i | 0.154308 | + | 0.474912i | 0.309017 | + | 0.951057i | −1.19349 | − | 1.89092i | −0.154308 | + | 0.474912i | −2.61594 | −0.309017 | + | 0.951057i | 2.22532 | − | 1.61679i | 0.145902 | − | 2.23130i | ||
191.9 | 0.809017 | + | 0.587785i | 0.578674 | + | 1.78097i | 0.309017 | + | 0.951057i | −1.13510 | + | 1.92654i | −0.578674 | + | 1.78097i | −2.72132 | −0.309017 | + | 0.951057i | −0.409956 | + | 0.297850i | −2.05071 | + | 0.891406i | ||
191.10 | 0.809017 | + | 0.587785i | 0.611239 | + | 1.88120i | 0.309017 | + | 0.951057i | 2.16649 | − | 0.553476i | −0.611239 | + | 1.88120i | 2.35142 | −0.309017 | + | 0.951057i | −0.738252 | + | 0.536372i | 2.07805 | + | 0.825657i | ||
191.11 | 0.809017 | + | 0.587785i | 0.863749 | + | 2.65835i | 0.309017 | + | 0.951057i | −1.38530 | + | 1.75527i | −0.863749 | + | 2.65835i | 3.39982 | −0.309017 | + | 0.951057i | −3.89370 | + | 2.82894i | −2.15245 | + | 0.605783i | ||
381.1 | −0.309017 | − | 0.951057i | −2.30507 | + | 1.67473i | −0.809017 | + | 0.587785i | −0.482704 | − | 2.18335i | 2.30507 | + | 1.67473i | −2.79249 | 0.809017 | + | 0.587785i | 1.58157 | − | 4.86758i | −1.92732 | + | 1.13377i | ||
381.2 | −0.309017 | − | 0.951057i | −2.00675 | + | 1.45799i | −0.809017 | + | 0.587785i | −2.21649 | + | 0.295244i | 2.00675 | + | 1.45799i | 2.78117 | 0.809017 | + | 0.587785i | 0.974256 | − | 2.99845i | 0.965727 | + | 2.01677i | ||
381.3 | −0.309017 | − | 0.951057i | −1.70816 | + | 1.24105i | −0.809017 | + | 0.587785i | 2.12953 | − | 0.681987i | 1.70816 | + | 1.24105i | −1.90564 | 0.809017 | + | 0.587785i | 0.450556 | − | 1.38667i | −1.30667 | − | 1.81456i | ||
381.4 | −0.309017 | − | 0.951057i | −1.20914 | + | 0.878491i | −0.809017 | + | 0.587785i | 0.176849 | − | 2.22906i | 1.20914 | + | 0.878491i | 2.76699 | 0.809017 | + | 0.587785i | −0.236780 | + | 0.728734i | −2.17461 | + | 0.520625i | ||
381.5 | −0.309017 | − | 0.951057i | −0.628367 | + | 0.456535i | −0.809017 | + | 0.587785i | −0.766450 | + | 2.10061i | 0.628367 | + | 0.456535i | −4.62972 | 0.809017 | + | 0.587785i | −0.740631 | + | 2.27943i | 2.23464 | + | 0.0798131i | ||
381.6 | −0.309017 | − | 0.951057i | −0.591887 | + | 0.430031i | −0.809017 | + | 0.587785i | 1.69555 | + | 1.45777i | 0.591887 | + | 0.430031i | 1.38478 | 0.809017 | + | 0.587785i | −0.761648 | + | 2.34411i | 0.862467 | − | 2.06304i | ||
381.7 | −0.309017 | − | 0.951057i | 0.616737 | − | 0.448085i | −0.809017 | + | 0.587785i | −1.35137 | + | 1.78152i | −0.616737 | − | 0.448085i | −0.0296482 | 0.809017 | + | 0.587785i | −0.747467 | + | 2.30047i | 2.11192 | + | 0.734710i | ||
381.8 | −0.309017 | − | 0.951057i | 0.823288 | − | 0.598153i | −0.809017 | + | 0.587785i | −1.34910 | − | 1.78323i | −0.823288 | − | 0.598153i | 3.63885 | 0.809017 | + | 0.587785i | −0.607036 | + | 1.86826i | −1.27906 | + | 1.83412i | ||
381.9 | −0.309017 | − | 0.951057i | 2.31854 | − | 1.68452i | −0.809017 | + | 0.587785i | 1.05411 | − | 1.97202i | −2.31854 | − | 1.68452i | −0.662081 | 0.809017 | + | 0.587785i | 1.61098 | − | 4.95809i | −2.20124 | − | 0.393129i | ||
See all 44 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.d | ✓ | 44 |
25.d | even | 5 | 1 | inner | 950.2.h.d | ✓ | 44 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
950.2.h.d | ✓ | 44 | 1.a | even | 1 | 1 | trivial |
950.2.h.d | ✓ | 44 | 25.d | even | 5 | 1 | inner |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{44} + T_{3}^{43} + 17 T_{3}^{42} + 7 T_{3}^{41} + 247 T_{3}^{40} + 398 T_{3}^{39} + 3568 T_{3}^{38} + 5780 T_{3}^{37} + 38850 T_{3}^{36} + 69157 T_{3}^{35} + 362221 T_{3}^{34} + 729119 T_{3}^{33} + 3190375 T_{3}^{32} + \cdots + 1936 \)
acting on \(S_{2}^{\mathrm{new}}(950, [\chi])\).