Defining parameters
Level: | \( N \) | \(=\) | \( 179 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 179.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(30\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(179))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 16 | 16 | 0 |
Cusp forms | 15 | 15 | 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.
\(179\) | Dim |
---|---|
\(+\) | \(3\) |
\(-\) | \(12\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(179))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 179 | |||||||
179.2.a.a | $1$ | $1.429$ | \(\Q\) | None | \(2\) | \(0\) | \(3\) | \(-4\) | $-$ | \(q+2q^{2}+2q^{4}+3q^{5}-4q^{7}-3q^{9}+\cdots\) | |
179.2.a.b | $3$ | $1.429$ | \(\Q(\zeta_{14})^+\) | None | \(-1\) | \(-2\) | \(-4\) | \(-4\) | $+$ | \(q-\beta _{1}q^{2}+(-1+\beta _{1})q^{3}+\beta _{2}q^{4}+(-2+\cdots)q^{5}+\cdots\) | |
179.2.a.c | $11$ | $1.429$ | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) | None | \(-3\) | \(0\) | \(3\) | \(8\) | $-$ | \(q-\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\) |