Newspace parameters
Level: | \( N \) | \(=\) | \( 275 = 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 275.i (of order \(5\), degree \(4\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(2.19588605559\) |
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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
56.1 | −0.847393 | − | 2.60801i | 0.282837 | − | 0.205493i | −4.46560 | + | 3.24445i | 1.18952 | + | 1.89342i | −0.775602 | − | 0.563508i | 4.12997 | 7.80866 | + | 5.67332i | −0.889282 | + | 2.73693i | 3.93007 | − | 4.70675i | ||
56.2 | −0.749343 | − | 2.30624i | 1.41740 | − | 1.02980i | −3.13919 | + | 2.28076i | −2.10136 | + | 0.764385i | −3.43709 | − | 2.49719i | −4.46925 | 3.68870 | + | 2.68000i | 0.0214834 | − | 0.0661192i | 3.33749 | + | 4.27346i | ||
56.3 | −0.614887 | − | 1.89243i | −1.67850 | + | 1.21950i | −1.58516 | + | 1.15169i | 2.23365 | − | 0.103885i | 3.33991 | + | 2.42659i | −3.97514 | −0.0654098 | − | 0.0475230i | 0.403133 | − | 1.24071i | −1.57004 | − | 4.16315i | ||
56.4 | −0.593152 | − | 1.82553i | −1.65284 | + | 1.20086i | −1.36271 | + | 0.990068i | 0.437546 | − | 2.19284i | 3.17259 | + | 2.30502i | 3.96949 | −0.490086 | − | 0.356068i | 0.362767 | − | 1.11648i | −4.26264 | + | 0.501933i | ||
56.5 | −0.383688 | − | 1.18087i | 1.38363 | − | 1.00527i | 0.370797 | − | 0.269400i | 0.160480 | − | 2.23030i | −1.71797 | − | 1.24818i | −0.528113 | −2.46941 | − | 1.79413i | −0.0231746 | + | 0.0713241i | −2.69527 | + | 0.666234i | ||
56.6 | −0.253584 | − | 0.780452i | 2.37547 | − | 1.72588i | 1.07323 | − | 0.779750i | 0.790188 | + | 2.09179i | −1.94935 | − | 1.41628i | −1.59619 | −2.20850 | − | 1.60457i | 1.73714 | − | 5.34636i | 1.43217 | − | 1.14715i | ||
56.7 | −0.0516459 | − | 0.158950i | −0.303083 | + | 0.220202i | 1.59544 | − | 1.15915i | 1.93201 | + | 1.12576i | 0.0506541 | + | 0.0368023i | 0.678243 | −0.537066 | − | 0.390201i | −0.883681 | + | 2.71969i | 0.0791593 | − | 0.365233i | ||
56.8 | −0.00137816 | − | 0.00424154i | −2.06095 | + | 1.49737i | 1.61802 | − | 1.17556i | −2.22854 | − | 0.183378i | 0.00919146 | + | 0.00667799i | 4.51694 | −0.0144322 | − | 0.0104856i | 1.07835 | − | 3.31882i | 0.00229348 | + | 0.00970516i | ||
56.9 | 0.126287 | + | 0.388670i | 0.876499 | − | 0.636814i | 1.48292 | − | 1.07740i | −1.49442 | − | 1.66334i | 0.358200 | + | 0.260248i | 0.810085 | 1.26727 | + | 0.920727i | −0.564333 | + | 1.73684i | 0.457765 | − | 0.790895i | ||
56.10 | 0.317055 | + | 0.975794i | −0.474307 | + | 0.344604i | 0.766384 | − | 0.556811i | −1.56781 | + | 1.59435i | −0.486644 | − | 0.353567i | −5.27769 | 2.44644 | + | 1.77744i | −0.820836 | + | 2.52627i | −2.05284 | − | 1.02437i | ||
56.11 | 0.532896 | + | 1.64009i | −0.485785 | + | 0.352943i | −0.787872 | + | 0.572422i | 2.09251 | − | 0.788291i | −0.837731 | − | 0.608647i | −0.652091 | 1.43161 | + | 1.04012i | −0.815633 | + | 2.51026i | 2.40796 | + | 3.01182i | ||
56.12 | 0.549271 | + | 1.69048i | 2.64305 | − | 1.92029i | −0.937997 | + | 0.681495i | −2.13719 | − | 0.657589i | 4.69797 | + | 3.41327i | −0.0570090 | 1.20875 | + | 0.878209i | 2.37116 | − | 7.29768i | −0.0622530 | − | 3.97407i | ||
56.13 | 0.643133 | + | 1.97936i | −2.55218 | + | 1.85427i | −1.88621 | + | 1.37041i | −0.839175 | − | 2.07263i | −5.31166 | − | 3.85915i | −2.50218 | −0.558133 | − | 0.405507i | 2.14827 | − | 6.61170i | 3.56277 | − | 2.99400i | ||
56.14 | 0.783991 | + | 2.41288i | −1.82681 | + | 1.32725i | −3.58930 | + | 2.60778i | −0.0917842 | + | 2.23418i | −4.63470 | − | 3.36730i | 2.83405 | −5.00118 | − | 3.63357i | 0.648573 | − | 1.99610i | −5.46277 | + | 1.53012i | ||
56.15 | 0.851456 | + | 2.62051i | 1.55557 | − | 1.13018i | −4.52407 | + | 3.28693i | 2.00634 | − | 0.987214i | 4.28616 | + | 3.11408i | 2.11888 | −8.00720 | − | 5.81757i | 0.215417 | − | 0.662985i | 4.29532 | + | 4.41707i | ||
111.1 | −2.10502 | + | 1.52938i | 0.913514 | − | 2.81151i | 1.47404 | − | 4.53664i | 1.95157 | + | 1.09151i | 2.37691 | + | 7.31538i | 3.15600 | 2.22729 | + | 6.85489i | −4.64302 | − | 3.37335i | −5.77741 | + | 0.687058i | ||
111.2 | −1.96894 | + | 1.43052i | −1.01785 | + | 3.13261i | 1.21231 | − | 3.73111i | 1.19246 | + | 1.89157i | −2.47718 | − | 7.62397i | −0.337264 | 1.44632 | + | 4.45132i | −6.35016 | − | 4.61366i | −5.05382 | − | 2.01855i | ||
111.3 | −1.88069 | + | 1.36640i | −0.178254 | + | 0.548608i | 1.05190 | − | 3.23742i | 1.77953 | − | 1.35399i | −0.414378 | − | 1.27533i | −4.13856 | 1.00860 | + | 3.10414i | 2.15785 | + | 1.56777i | −1.49665 | + | 4.97797i | ||
111.4 | −1.48661 | + | 1.08008i | 0.310838 | − | 0.956660i | 0.425384 | − | 1.30920i | −2.11835 | + | 0.715970i | 0.571178 | + | 1.75791i | 2.93566 | −0.354003 | − | 1.08951i | 1.60847 | + | 1.16862i | 2.37584 | − | 3.35235i | ||
111.5 | −1.00729 | + | 0.731839i | −0.570382 | + | 1.75545i | −0.138989 | + | 0.427764i | −0.988997 | − | 2.00546i | −0.710170 | − | 2.18568i | −1.68501 | −0.942554 | − | 2.90088i | −0.329235 | − | 0.239203i | 2.46388 | + | 1.29630i | ||
See all 60 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 | 275.2.i.b | ✓ | 60 |
25.d | even | 5 | 1 | inner | 275.2.i.b | ✓ | 60 |
25.d | even | 5 | 1 | 6875.2.a.h | 30 | ||
25.e | even | 10 | 1 | 6875.2.a.g | 30 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
275.2.i.b | ✓ | 60 | 1.a | even | 1 | 1 | trivial |
275.2.i.b | ✓ | 60 | 25.d | even | 5 | 1 | inner |
6875.2.a.g | 30 | 25.e | even | 10 | 1 | ||
6875.2.a.h | 30 | 25.d | even | 5 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{60} + T_{2}^{59} + 25 T_{2}^{58} + 28 T_{2}^{57} + 381 T_{2}^{56} + 454 T_{2}^{55} + 4589 T_{2}^{54} + 5781 T_{2}^{53} + 48247 T_{2}^{52} + 62508 T_{2}^{51} + 428533 T_{2}^{50} + 563785 T_{2}^{49} + 3299463 T_{2}^{48} + \cdots + 256 \)
acting on \(S_{2}^{\mathrm{new}}(275, [\chi])\).