Defining parameters
Level: | \( N \) | \(=\) | \( 23 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 23.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(16\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(23))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 15 | 13 | 2 |
Cusp forms | 13 | 13 | 0 |
Eisenstein series | 2 | 0 | 2 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(23\) | Dim |
---|---|
\(+\) | \(8\) |
\(-\) | \(5\) |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(23))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 23 | |||||||
23.8.a.a | $5$ | $7.185$ | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) | None | \(-16\) | \(-68\) | \(-56\) | \(-1156\) | $-$ | \(q+(-3+\beta _{1})q^{2}+(-14+\beta _{2})q^{3}+(51+\cdots)q^{4}+\cdots\) | |
23.8.a.b | $8$ | $7.185$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(40\) | \(444\) | \(1446\) | $+$ | \(q+\beta _{1}q^{2}+(5-\beta _{1}+\beta _{2})q^{3}+(80+2\beta _{1}+\cdots)q^{4}+\cdots\) |