Defining parameters
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(15\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(50))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 13 | 2 | 11 |
Cusp forms | 2 | 2 | 0 |
Eisenstein series | 11 | 0 | 11 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(5\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(-\) | \(-\) | \(1\) |
\(-\) | \(+\) | \(-\) | \(1\) |
Plus space | \(+\) | \(0\) | |
Minus space | \(-\) | \(2\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(50))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 5 | |||||||
50.2.a.a | $1$ | $0.399$ | \(\Q\) | None | \(-1\) | \(1\) | \(0\) | \(2\) | $+$ | $-$ | \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\) | |
50.2.a.b | $1$ | $0.399$ | \(\Q\) | None | \(1\) | \(-1\) | \(0\) | \(-2\) | $-$ | $+$ | \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\) |