Defining parameters
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(13\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_0(5))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 13 | 9 | 4 |
Cusp forms | 11 | 9 | 2 |
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.
\(5\) | Dim |
---|---|
\(+\) | \(4\) |
\(-\) | \(5\) |
Trace form
Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_0(5))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 5 | |||||||
5.26.a.a | $4$ | $19.800$ | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) | None | \(600\) | \(-798600\) | \(-976562500\) | \(-48938107000\) | $+$ | \(q+(150-\beta _{1})q^{2}+(-199650+17\beta _{1}+\cdots)q^{3}+\cdots\) | |
5.26.a.b | $5$ | $19.800$ | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) | None | \(-4602\) | \(626204\) | \(1220703125\) | \(55481235808\) | $-$ | \(q+(-920-\beta _{1})q^{2}+(125251-5^{2}\beta _{1}+\cdots)q^{3}+\cdots\) |
Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_0(5))\) into lower level spaces
\( S_{26}^{\mathrm{old}}(\Gamma_0(5)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)