Defining parameters
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.c (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 17 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(51\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(289, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 68 | 60 | 8 |
Cusp forms | 32 | 32 | 0 |
Eisenstein series | 36 | 28 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(289, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
289.2.c.a | $4$ | $2.308$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{8}^{2}q^{2}+q^{4}+\zeta_{8}q^{5}+2\zeta_{8}^{3}q^{7}+\cdots\) |
289.2.c.b | $8$ | $2.308$ | 8.0.1871773696.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{5}q^{2}+\beta _{1}q^{3}+(-2-\beta _{4})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\) |
289.2.c.c | $8$ | $2.308$ | \(\Q(\zeta_{16})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\zeta_{16}^{2}-\zeta_{16}^{3})q^{2}+(-\zeta_{16}+\zeta_{16}^{7})q^{3}+\cdots\) |
289.2.c.d | $12$ | $2.308$ | 12.0.\(\cdots\).1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\beta _{4}-\beta _{9})q^{2}+(-\beta _{8}-\beta _{10})q^{3}+\cdots\) |