Newspace parameters
Level: | \( N \) | \(=\) | \( 550 = 2 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 550.j (of order \(5\), degree \(4\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(4.39177211117\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(15\) 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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
81.1 | 0.309017 | − | 0.951057i | −0.950235 | − | 2.92452i | −0.809017 | − | 0.587785i | 2.07322 | − | 0.837701i | −3.07503 | −0.250676 | − | 0.771502i | −0.809017 | + | 0.587785i | −5.22284 | + | 3.79461i | −0.156039 | − | 2.23062i | ||
81.2 | 0.309017 | − | 0.951057i | −0.798378 | − | 2.45716i | −0.809017 | − | 0.587785i | −0.351676 | + | 2.20824i | −2.58361 | 0.962145 | + | 2.96118i | −0.809017 | + | 0.587785i | −2.97315 | + | 2.16012i | 1.99149 | + | 1.01685i | ||
81.3 | 0.309017 | − | 0.951057i | −0.632955 | − | 1.94804i | −0.809017 | − | 0.587785i | −0.818463 | − | 2.08089i | −2.04829 | −1.46197 | − | 4.49947i | −0.809017 | + | 0.587785i | −0.967161 | + | 0.702684i | −2.23197 | + | 0.135373i | ||
81.4 | 0.309017 | − | 0.951057i | −0.600130 | − | 1.84701i | −0.809017 | − | 0.587785i | −2.13045 | − | 0.679120i | −1.94206 | 0.275504 | + | 0.847915i | −0.809017 | + | 0.587785i | −0.624244 | + | 0.453540i | −1.30423 | + | 1.81631i | ||
81.5 | 0.309017 | − | 0.951057i | −0.293907 | − | 0.904554i | −0.809017 | − | 0.587785i | −0.536306 | + | 2.17080i | −0.951104 | −0.974143 | − | 2.99810i | −0.809017 | + | 0.587785i | 1.69521 | − | 1.23165i | 1.89883 | + | 1.18087i | ||
81.6 | 0.309017 | − | 0.951057i | −0.224929 | − | 0.692259i | −0.809017 | − | 0.587785i | 1.90463 | − | 1.17148i | −0.727884 | 1.27708 | + | 3.93044i | −0.809017 | + | 0.587785i | 1.99842 | − | 1.45194i | −0.525580 | − | 2.17342i | ||
81.7 | 0.309017 | − | 0.951057i | −0.0525279 | − | 0.161664i | −0.809017 | − | 0.587785i | −0.0858628 | − | 2.23442i | −0.169984 | 0.376127 | + | 1.15760i | −0.809017 | + | 0.587785i | 2.40367 | − | 1.74637i | −2.15159 | − | 0.608813i | ||
81.8 | 0.309017 | − | 0.951057i | 0.0548441 | + | 0.168793i | −0.809017 | − | 0.587785i | −2.22390 | + | 0.232910i | 0.177479 | 0.806547 | + | 2.48230i | −0.809017 | + | 0.587785i | 2.40157 | − | 1.74484i | −0.465714 | + | 2.18703i | ||
81.9 | 0.309017 | − | 0.951057i | 0.166113 | + | 0.511243i | −0.809017 | − | 0.587785i | −1.05185 | + | 1.97322i | 0.537553 | −0.668877 | − | 2.05859i | −0.809017 | + | 0.587785i | 2.19328 | − | 1.59351i | 1.55160 | + | 1.61013i | ||
81.10 | 0.309017 | − | 0.951057i | 0.423436 | + | 1.30320i | −0.809017 | − | 0.587785i | 2.09937 | + | 0.769843i | 1.37027 | 0.201752 | + | 0.620927i | −0.809017 | + | 0.587785i | 0.908011 | − | 0.659709i | 1.38090 | − | 1.75872i | ||
81.11 | 0.309017 | − | 0.951057i | 0.487764 | + | 1.50118i | −0.809017 | − | 0.587785i | 1.30223 | + | 1.81775i | 1.57844 | 0.881273 | + | 2.71228i | −0.809017 | + | 0.587785i | 0.411412 | − | 0.298908i | 2.13119 | − | 0.676779i | ||
81.12 | 0.309017 | − | 0.951057i | 0.615443 | + | 1.89414i | −0.809017 | − | 0.587785i | 2.20137 | − | 0.392380i | 1.99161 | −1.33176 | − | 4.09873i | −0.809017 | + | 0.587785i | −0.781936 | + | 0.568109i | 0.307086 | − | 2.21488i | ||
81.13 | 0.309017 | − | 0.951057i | 0.753141 | + | 2.31793i | −0.809017 | − | 0.587785i | −2.23552 | + | 0.0494187i | 2.43722 | −1.11298 | − | 3.42540i | −0.809017 | + | 0.587785i | −2.37853 | + | 1.72810i | −0.643814 | + | 2.14138i | ||
81.14 | 0.309017 | − | 0.951057i | 0.867391 | + | 2.66956i | −0.809017 | − | 0.587785i | −1.93587 | + | 1.11912i | 2.80694 | 1.24292 | + | 3.82531i | −0.809017 | + | 0.587785i | −3.94711 | + | 2.86774i | 0.466129 | + | 2.18694i | ||
81.15 | 0.309017 | − | 0.951057i | 0.993948 | + | 3.05906i | −0.809017 | − | 0.587785i | 0.671040 | − | 2.13300i | 3.21648 | 0.704109 | + | 2.16703i | −0.809017 | + | 0.587785i | −5.94284 | + | 4.31773i | −1.82124 | − | 1.29733i | ||
141.1 | −0.809017 | + | 0.587785i | −2.66369 | − | 1.93528i | 0.309017 | − | 0.951057i | −1.49078 | + | 1.66661i | 3.29250 | −0.773637 | − | 0.562080i | 0.309017 | + | 0.951057i | 2.42287 | + | 7.45683i | 0.226460 | − | 2.22457i | ||
141.2 | −0.809017 | + | 0.587785i | −2.18364 | − | 1.58651i | 0.309017 | − | 0.951057i | 2.19604 | + | 0.421183i | 2.69912 | 2.81132 | + | 2.04255i | 0.309017 | + | 0.951057i | 1.32422 | + | 4.07554i | −2.02420 | + | 0.950058i | ||
141.3 | −0.809017 | + | 0.587785i | −2.11723 | − | 1.53826i | 0.309017 | − | 0.951057i | 0.345051 | − | 2.20928i | 2.61704 | −3.91599 | − | 2.84513i | 0.309017 | + | 0.951057i | 1.18938 | + | 3.66054i | 1.01943 | + | 1.99017i | ||
141.4 | −0.809017 | + | 0.587785i | −1.41706 | − | 1.02955i | 0.309017 | − | 0.951057i | 1.10889 | + | 1.94174i | 1.75158 | −1.01444 | − | 0.737034i | 0.309017 | + | 0.951057i | 0.0210224 | + | 0.0647003i | −2.03844 | − | 0.919110i | ||
141.5 | −0.809017 | + | 0.587785i | −1.27001 | − | 0.922720i | 0.309017 | − | 0.951057i | −2.22425 | + | 0.229544i | 1.56982 | 0.831135 | + | 0.603855i | 0.309017 | + | 0.951057i | −0.165525 | − | 0.509434i | 1.66454 | − | 1.49309i | ||
See all 60 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
275.j | even | 5 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 550.2.j.c | yes | 60 |
11.c | even | 5 | 1 | 550.2.g.c | ✓ | 60 | |
25.d | even | 5 | 1 | 550.2.g.c | ✓ | 60 | |
275.j | even | 5 | 1 | inner | 550.2.j.c | yes | 60 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
550.2.g.c | ✓ | 60 | 11.c | even | 5 | 1 | |
550.2.g.c | ✓ | 60 | 25.d | even | 5 | 1 | |
550.2.j.c | yes | 60 | 1.a | even | 1 | 1 | trivial |
550.2.j.c | yes | 60 | 275.j | even | 5 | 1 | inner |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{60} - T_{3}^{59} + 29 T_{3}^{58} - 18 T_{3}^{57} + 537 T_{3}^{56} - 296 T_{3}^{55} + 8385 T_{3}^{54} - 4022 T_{3}^{53} + 113560 T_{3}^{52} - 48860 T_{3}^{51} + 1254655 T_{3}^{50} - 472271 T_{3}^{49} + 11873047 T_{3}^{48} + \cdots + 2253001 \)
acting on \(S_{2}^{\mathrm{new}}(550, [\chi])\).