Defining parameters
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(51\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\), \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(289))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 34 | 30 | 4 |
Cusp forms | 17 | 15 | 2 |
Eisenstein series | 17 | 15 | 2 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(17\) | Dim |
---|---|
\(+\) | \(6\) |
\(-\) | \(9\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(289))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 17 | |||||||
289.2.a.a | $1$ | $2.308$ | \(\Q\) | None | \(-1\) | \(0\) | \(2\) | \(-4\) | $+$ | \(q-q^{2}-q^{4}+2q^{5}-4q^{7}+3q^{8}-3q^{9}+\cdots\) | |
289.2.a.b | $2$ | $2.308$ | \(\Q(\sqrt{13}) \) | None | \(-1\) | \(-1\) | \(-1\) | \(-3\) | $+$ | \(q-\beta q^{2}+(-1+\beta )q^{3}+(1+\beta )q^{4}-\beta q^{5}+\cdots\) | |
289.2.a.c | $2$ | $2.308$ | \(\Q(\sqrt{13}) \) | None | \(-1\) | \(1\) | \(1\) | \(3\) | $-$ | \(q-\beta q^{2}+(1-\beta )q^{3}+(1+\beta )q^{4}+\beta q^{5}+\cdots\) | |
289.2.a.d | $3$ | $2.308$ | \(\Q(\zeta_{18})^+\) | None | \(0\) | \(-3\) | \(-6\) | \(0\) | $+$ | \(q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+\beta _{2}q^{4}+(-2+\cdots)q^{5}+\cdots\) | |
289.2.a.e | $3$ | $2.308$ | \(\Q(\zeta_{18})^+\) | None | \(0\) | \(3\) | \(6\) | \(0\) | $-$ | \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{3}+\beta _{2}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\) | |
289.2.a.f | $4$ | $2.308$ | \(\Q(\zeta_{16})^+\) | None | \(4\) | \(0\) | \(0\) | \(0\) | $-$ | \(q+(1+\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(1+2\beta _{2}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(289))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(289)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 2}\)