Defining parameters
Level: | \( N \) | \(=\) | \( 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 79.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 \(M_{2}(\Gamma_0(79))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 7 | 7 | 0 |
Cusp forms | 6 | 6 | 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.
\(79\) | Dim |
---|---|
\(+\) | \(1\) |
\(-\) | \(5\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(79))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 79 | |||||||
79.2.a.a | $1$ | $0.631$ | \(\Q\) | None | \(-1\) | \(-1\) | \(-3\) | \(-1\) | $+$ | \(q-q^{2}-q^{3}-q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\) | |
79.2.a.b | $5$ | $0.631$ | 5.5.81589.1 | None | \(0\) | \(1\) | \(7\) | \(-5\) | $-$ | \(q+\beta _{1}q^{2}+(1-\beta _{2}-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots\) |