Defining parameters
Level: | \( N \) | \(=\) | \( 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 53.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(9\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(53))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 5 | 5 | 0 |
Cusp forms | 4 | 4 | 0 |
Eisenstein series | 1 | 1 | 0 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(53\) | Dim |
---|---|
\(+\) | \(1\) |
\(-\) | \(3\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(53))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 53 | |||||||
53.2.a.a | $1$ | $0.423$ | \(\Q\) | None | \(-1\) | \(-3\) | \(0\) | \(-4\) | $+$ | \(q-q^{2}-3q^{3}-q^{4}+3q^{6}-4q^{7}+3q^{8}+\cdots\) | |
53.2.a.b | $3$ | $0.423$ | 3.3.148.1 | None | \(-1\) | \(3\) | \(-2\) | \(4\) | $-$ | \(q-\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\) |