Newspace parameters
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.et (of order \(12\), degree \(4\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 273) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
136.1 | −1.93326 | + | 1.93326i | 0 | − | 5.47495i | 0.212233 | − | 0.792066i | 0 | 2.21517 | − | 1.44673i | 6.71797 | + | 6.71797i | 0 | 1.12096 | + | 1.94157i | |||||||
136.2 | −1.57115 | + | 1.57115i | 0 | − | 2.93701i | −0.922649 | + | 3.44337i | 0 | −2.64488 | + | 0.0678683i | 1.47218 | + | 1.47218i | 0 | −3.96043 | − | 6.85967i | |||||||
136.3 | −1.09526 | + | 1.09526i | 0 | − | 0.399185i | −0.128983 | + | 0.481371i | 0 | 2.51963 | + | 0.807124i | −1.75331 | − | 1.75331i | 0 | −0.385956 | − | 0.668496i | |||||||
136.4 | −1.07562 | + | 1.07562i | 0 | − | 0.313900i | 0.962166 | − | 3.59085i | 0 | −2.21486 | − | 1.44721i | −1.81360 | − | 1.81360i | 0 | 2.82746 | + | 4.89730i | |||||||
136.5 | 0.184060 | − | 0.184060i | 0 | 1.93224i | −0.900201 | + | 3.35960i | 0 | 0.939961 | − | 2.47315i | 0.723769 | + | 0.723769i | 0 | 0.452676 | + | 0.784058i | ||||||||
136.6 | 0.326747 | − | 0.326747i | 0 | 1.78647i | 0.562238 | − | 2.09830i | 0 | 2.25993 | − | 1.37576i | 1.23722 | + | 1.23722i | 0 | −0.501904 | − | 0.869322i | ||||||||
136.7 | 0.783932 | − | 0.783932i | 0 | 0.770902i | 0.994915 | − | 3.71307i | 0 | 0.0389254 | + | 2.64546i | 2.17220 | + | 2.17220i | 0 | −2.13085 | − | 3.69074i | ||||||||
136.8 | 1.03264 | − | 1.03264i | 0 | − | 0.132693i | −0.456824 | + | 1.70489i | 0 | −2.58707 | + | 0.554121i | 1.92826 | + | 1.92826i | 0 | 1.28880 | + | 2.23227i | |||||||
136.9 | 1.59737 | − | 1.59737i | 0 | − | 3.10321i | −0.609466 | + | 2.27456i | 0 | 1.40839 | + | 2.23974i | −1.76223 | − | 1.76223i | 0 | 2.65977 | + | 4.60686i | |||||||
136.10 | 1.75053 | − | 1.75053i | 0 | − | 4.12868i | 0.286571 | − | 1.06950i | 0 | 1.02891 | − | 2.43749i | −3.72630 | − | 3.72630i | 0 | −1.37053 | − | 2.37383i | |||||||
145.1 | −1.85908 | + | 1.85908i | 0 | − | 4.91234i | −0.502992 | + | 0.134776i | 0 | −1.89546 | + | 1.84587i | 5.41427 | + | 5.41427i | 0 | 0.684542 | − | 1.18566i | |||||||
145.2 | −1.55234 | + | 1.55234i | 0 | − | 2.81950i | 0.926472 | − | 0.248247i | 0 | 0.619609 | − | 2.57218i | 1.27214 | + | 1.27214i | 0 | −1.05283 | + | 1.82356i | |||||||
145.3 | −0.884731 | + | 0.884731i | 0 | 0.434503i | −3.68041 | + | 0.986163i | 0 | −2.53212 | − | 0.767050i | −2.15388 | − | 2.15388i | 0 | 2.38368 | − | 4.12866i | ||||||||
145.4 | −0.837153 | + | 0.837153i | 0 | 0.598351i | 1.58368 | − | 0.424345i | 0 | 2.46703 | + | 0.955901i | −2.17522 | − | 2.17522i | 0 | −0.970539 | + | 1.68102i | ||||||||
145.5 | −0.465913 | + | 0.465913i | 0 | 1.56585i | 3.81958 | − | 1.02345i | 0 | −2.61148 | + | 0.424440i | −1.66138 | − | 1.66138i | 0 | −1.30275 | + | 2.25643i | ||||||||
145.6 | 0.240784 | − | 0.240784i | 0 | 1.88405i | −2.06336 | + | 0.552877i | 0 | 1.35855 | − | 2.27032i | 0.935214 | + | 0.935214i | 0 | −0.363700 | + | 0.629948i | ||||||||
145.7 | 0.507981 | − | 0.507981i | 0 | 1.48391i | −1.10096 | + | 0.295002i | 0 | 0.718657 | + | 2.54628i | 1.76976 | + | 1.76976i | 0 | −0.409414 | + | 0.709125i | ||||||||
145.8 | 1.22934 | − | 1.22934i | 0 | − | 1.02253i | 1.95691 | − | 0.524353i | 0 | −1.82011 | − | 1.92021i | 1.20163 | + | 1.20163i | 0 | 1.76110 | − | 3.05031i | |||||||
145.9 | 1.65256 | − | 1.65256i | 0 | − | 3.46192i | −2.69306 | + | 0.721604i | 0 | −2.54381 | − | 0.727358i | −2.41591 | − | 2.41591i | 0 | −3.25795 | + | 5.64294i | |||||||
145.10 | 1.96855 | − | 1.96855i | 0 | − | 5.75037i | 1.75415 | − | 0.470023i | 0 | 2.27503 | + | 1.35065i | −7.38279 | − | 7.38279i | 0 | 2.52787 | − | 4.37840i | |||||||
See all 40 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
91.ba | even | 12 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 819.2.et.d | 40 | |
3.b | odd | 2 | 1 | 273.2.bt.b | ✓ | 40 | |
7.d | odd | 6 | 1 | 819.2.gh.d | 40 | ||
13.f | odd | 12 | 1 | 819.2.gh.d | 40 | ||
21.g | even | 6 | 1 | 273.2.cg.b | yes | 40 | |
39.k | even | 12 | 1 | 273.2.cg.b | yes | 40 | |
91.ba | even | 12 | 1 | inner | 819.2.et.d | 40 | |
273.bs | odd | 12 | 1 | 273.2.bt.b | ✓ | 40 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
273.2.bt.b | ✓ | 40 | 3.b | odd | 2 | 1 | |
273.2.bt.b | ✓ | 40 | 273.bs | odd | 12 | 1 | |
273.2.cg.b | yes | 40 | 21.g | even | 6 | 1 | |
273.2.cg.b | yes | 40 | 39.k | even | 12 | 1 | |
819.2.et.d | 40 | 1.a | even | 1 | 1 | trivial | |
819.2.et.d | 40 | 91.ba | even | 12 | 1 | inner | |
819.2.gh.d | 40 | 7.d | odd | 6 | 1 | ||
819.2.gh.d | 40 | 13.f | odd | 12 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{40} + 168 T_{2}^{36} + 2 T_{2}^{35} - 8 T_{2}^{33} + 10786 T_{2}^{32} + 308 T_{2}^{31} + 2 T_{2}^{30} - 1192 T_{2}^{29} + 335772 T_{2}^{28} + 18394 T_{2}^{27} + 312 T_{2}^{26} - 78396 T_{2}^{25} + 5319379 T_{2}^{24} + \cdots + 59049 \)
acting on \(S_{2}^{\mathrm{new}}(819, [\chi])\).