Defining parameters
Level: | \( N \) | \(=\) | \( 125 = 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 125.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(25\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(125))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 17 | 8 | 9 |
Cusp forms | 8 | 8 | 0 |
Eisenstein series | 9 | 0 | 9 |
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 |
---|---|
\(+\) | \(2\) |
\(-\) | \(6\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(125))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 5 | |||||||
125.2.a.a | $2$ | $0.998$ | \(\Q(\sqrt{5}) \) | None | \(-1\) | \(-3\) | \(0\) | \(-6\) | $+$ | \(q-\beta q^{2}+(-2+\beta )q^{3}+(-1+\beta )q^{4}+\cdots\) | |
125.2.a.b | $2$ | $0.998$ | \(\Q(\sqrt{5}) \) | None | \(1\) | \(3\) | \(0\) | \(6\) | $-$ | \(q+\beta q^{2}+(2-\beta )q^{3}+(-1+\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\) | |
125.2.a.c | $4$ | $0.998$ | 4.4.4400.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | $-$ | \(q-\beta _{3}q^{2}-\beta _{1}q^{3}+(1-2\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\) |