Newspace parameters
Level: | \( N \) | \(=\) | \( 945 = 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 945.k (of order \(3\), degree \(2\), not minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(7.54586299101\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 315) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
361.1 | −1.28004 | + | 2.21710i | 0 | −2.27701 | − | 3.94390i | 1.00000 | 0 | −1.62783 | − | 2.08571i | 6.53853 | 0 | −1.28004 | + | 2.21710i | ||||||||||
361.2 | −0.859635 | + | 1.48893i | 0 | −0.477944 | − | 0.827824i | 1.00000 | 0 | 0.594106 | − | 2.57818i | −1.79511 | 0 | −0.859635 | + | 1.48893i | ||||||||||
361.3 | −0.805191 | + | 1.39463i | 0 | −0.296664 | − | 0.513837i | 1.00000 | 0 | 2.48389 | − | 0.911196i | −2.26528 | 0 | −0.805191 | + | 1.39463i | ||||||||||
361.4 | −0.517769 | + | 0.896802i | 0 | 0.463831 | + | 0.803378i | 1.00000 | 0 | −1.07729 | + | 2.41649i | −3.03170 | 0 | −0.517769 | + | 0.896802i | ||||||||||
361.5 | −0.304907 | + | 0.528114i | 0 | 0.814064 | + | 1.41000i | 1.00000 | 0 | 1.83653 | + | 1.90451i | −2.21248 | 0 | −0.304907 | + | 0.528114i | ||||||||||
361.6 | −0.154039 | + | 0.266804i | 0 | 0.952544 | + | 1.64985i | 1.00000 | 0 | 2.20433 | − | 1.46319i | −1.20307 | 0 | −0.154039 | + | 0.266804i | ||||||||||
361.7 | 0.148731 | − | 0.257610i | 0 | 0.955758 | + | 1.65542i | 1.00000 | 0 | −2.64436 | − | 0.0857253i | 1.16353 | 0 | 0.148731 | − | 0.257610i | ||||||||||
361.8 | 0.259245 | − | 0.449026i | 0 | 0.865584 | + | 1.49923i | 1.00000 | 0 | −1.91816 | − | 1.82226i | 1.93458 | 0 | 0.259245 | − | 0.449026i | ||||||||||
361.9 | 0.599034 | − | 1.03756i | 0 | 0.282317 | + | 0.488988i | 1.00000 | 0 | 2.04342 | + | 1.68061i | 3.07261 | 0 | 0.599034 | − | 1.03756i | ||||||||||
361.10 | 1.08176 | − | 1.87367i | 0 | −1.34041 | − | 2.32167i | 1.00000 | 0 | 2.14928 | − | 1.54292i | −1.47299 | 0 | 1.08176 | − | 1.87367i | ||||||||||
361.11 | 1.16277 | − | 2.01398i | 0 | −1.70408 | − | 2.95156i | 1.00000 | 0 | 0.459529 | + | 2.60554i | −3.27475 | 0 | 1.16277 | − | 2.01398i | ||||||||||
361.12 | 1.17004 | − | 2.02657i | 0 | −1.73798 | − | 3.01027i | 1.00000 | 0 | −1.00344 | − | 2.44808i | −3.45385 | 0 | 1.17004 | − | 2.02657i | ||||||||||
856.1 | −1.28004 | − | 2.21710i | 0 | −2.27701 | + | 3.94390i | 1.00000 | 0 | −1.62783 | + | 2.08571i | 6.53853 | 0 | −1.28004 | − | 2.21710i | ||||||||||
856.2 | −0.859635 | − | 1.48893i | 0 | −0.477944 | + | 0.827824i | 1.00000 | 0 | 0.594106 | + | 2.57818i | −1.79511 | 0 | −0.859635 | − | 1.48893i | ||||||||||
856.3 | −0.805191 | − | 1.39463i | 0 | −0.296664 | + | 0.513837i | 1.00000 | 0 | 2.48389 | + | 0.911196i | −2.26528 | 0 | −0.805191 | − | 1.39463i | ||||||||||
856.4 | −0.517769 | − | 0.896802i | 0 | 0.463831 | − | 0.803378i | 1.00000 | 0 | −1.07729 | − | 2.41649i | −3.03170 | 0 | −0.517769 | − | 0.896802i | ||||||||||
856.5 | −0.304907 | − | 0.528114i | 0 | 0.814064 | − | 1.41000i | 1.00000 | 0 | 1.83653 | − | 1.90451i | −2.21248 | 0 | −0.304907 | − | 0.528114i | ||||||||||
856.6 | −0.154039 | − | 0.266804i | 0 | 0.952544 | − | 1.64985i | 1.00000 | 0 | 2.20433 | + | 1.46319i | −1.20307 | 0 | −0.154039 | − | 0.266804i | ||||||||||
856.7 | 0.148731 | + | 0.257610i | 0 | 0.955758 | − | 1.65542i | 1.00000 | 0 | −2.64436 | + | 0.0857253i | 1.16353 | 0 | 0.148731 | + | 0.257610i | ||||||||||
856.8 | 0.259245 | + | 0.449026i | 0 | 0.865584 | − | 1.49923i | 1.00000 | 0 | −1.91816 | + | 1.82226i | 1.93458 | 0 | 0.259245 | + | 0.449026i | ||||||||||
See all 24 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
63.g | even | 3 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 945.2.k.b | 24 | |
3.b | odd | 2 | 1 | 315.2.k.b | ✓ | 24 | |
7.c | even | 3 | 1 | 945.2.l.b | 24 | ||
9.c | even | 3 | 1 | 945.2.l.b | 24 | ||
9.d | odd | 6 | 1 | 315.2.l.b | yes | 24 | |
21.h | odd | 6 | 1 | 315.2.l.b | yes | 24 | |
63.g | even | 3 | 1 | inner | 945.2.k.b | 24 | |
63.n | odd | 6 | 1 | 315.2.k.b | ✓ | 24 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
315.2.k.b | ✓ | 24 | 3.b | odd | 2 | 1 | |
315.2.k.b | ✓ | 24 | 63.n | odd | 6 | 1 | |
315.2.l.b | yes | 24 | 9.d | odd | 6 | 1 | |
315.2.l.b | yes | 24 | 21.h | odd | 6 | 1 | |
945.2.k.b | 24 | 1.a | even | 1 | 1 | trivial | |
945.2.k.b | 24 | 63.g | even | 3 | 1 | inner | |
945.2.l.b | 24 | 7.c | even | 3 | 1 | ||
945.2.l.b | 24 | 9.c | even | 3 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{24} - T_{2}^{23} + 16 T_{2}^{22} - 9 T_{2}^{21} + 157 T_{2}^{20} - 62 T_{2}^{19} + 930 T_{2}^{18} - 70 T_{2}^{17} + 3854 T_{2}^{16} + 284 T_{2}^{15} + 10997 T_{2}^{14} + 2832 T_{2}^{13} + 21841 T_{2}^{12} + 5217 T_{2}^{11} + 26201 T_{2}^{10} + \cdots + 9 \)
acting on \(S_{2}^{\mathrm{new}}(945, [\chi])\).