Defining parameters
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(40\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(177))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 22 | 9 | 13 |
Cusp forms | 19 | 9 | 10 |
Eisenstein series | 3 | 0 | 3 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(59\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(2\) |
\(+\) | \(-\) | $-$ | \(3\) |
\(-\) | \(+\) | $-$ | \(2\) |
\(-\) | \(-\) | $+$ | \(2\) |
Plus space | \(+\) | \(4\) | |
Minus space | \(-\) | \(5\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(177))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | 59 | |||||||
177.2.a.a | $2$ | $1.413$ | \(\Q(\sqrt{5}) \) | None | \(-3\) | \(2\) | \(-6\) | \(-7\) | $-$ | $-$ | \(q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}-3q^{5}+\cdots\) | |
177.2.a.b | $2$ | $1.413$ | \(\Q(\sqrt{5}) \) | None | \(-1\) | \(-2\) | \(0\) | \(-7\) | $+$ | $+$ | \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots\) | |
177.2.a.c | $2$ | $1.413$ | \(\Q(\sqrt{5}) \) | None | \(1\) | \(2\) | \(2\) | \(1\) | $-$ | $+$ | \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\) | |
177.2.a.d | $3$ | $1.413$ | 3.3.229.1 | None | \(0\) | \(-3\) | \(-2\) | \(9\) | $+$ | $-$ | \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(177))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(177)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 2}\)