Defining parameters
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(160\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(177))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 142 | 68 | 74 |
Cusp forms | 138 | 68 | 70 |
Eisenstein series | 4 | 0 | 4 |
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 |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(17\) |
\(+\) | \(-\) | $-$ | \(16\) |
\(-\) | \(+\) | $-$ | \(17\) |
\(-\) | \(-\) | $+$ | \(18\) |
Plus space | \(+\) | \(35\) | |
Minus space | \(-\) | \(33\) |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(177))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | 59 | |||||||
177.8.a.a | $16$ | $55.292$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(-6\) | \(-432\) | \(-68\) | \(-2343\) | $+$ | $-$ | \(q-\beta _{1}q^{2}-3^{3}q^{3}+(61+\beta _{2})q^{4}+(-5+\cdots)q^{5}+\cdots\) | |
177.8.a.b | $17$ | $55.292$ | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) | None | \(-32\) | \(459\) | \(-1072\) | \(-2407\) | $-$ | $+$ | \(q+(-2+\beta _{1})q^{2}+3^{3}q^{3}+(69-3\beta _{1}+\cdots)q^{4}+\cdots\) | |
177.8.a.c | $17$ | $55.292$ | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) | None | \(2\) | \(-459\) | \(-318\) | \(3145\) | $+$ | $+$ | \(q+\beta _{1}q^{2}-3^{3}q^{3}+(68+\beta _{1}+\beta _{2})q^{4}+\cdots\) | |
177.8.a.d | $18$ | $55.292$ | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) | None | \(24\) | \(486\) | \(678\) | \(3081\) | $-$ | $-$ | \(q+(1+\beta _{1})q^{2}+3^{3}q^{3}+(75+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(177))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_0(177)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 2}\)