Defining parameters
Level: | \( N \) | \(=\) | \( 667 = 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 667.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(667))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 62 | 51 | 11 |
Cusp forms | 59 | 51 | 8 |
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.
\(23\) | \(29\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(12\) |
\(+\) | \(-\) | $-$ | \(13\) |
\(-\) | \(+\) | $-$ | \(16\) |
\(-\) | \(-\) | $+$ | \(10\) |
Plus space | \(+\) | \(22\) | |
Minus space | \(-\) | \(29\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(667))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 23 | 29 | |||||||
667.2.a.a | $10$ | $5.326$ | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) | None | \(-3\) | \(-9\) | \(-10\) | \(1\) | $-$ | $-$ | \(q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(1+\beta _{2})q^{4}+\cdots\) | |
667.2.a.b | $12$ | $5.326$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(-3\) | \(-3\) | \(-16\) | \(-7\) | $+$ | $+$ | \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(1-\beta _{4}-\beta _{6}+\beta _{8}+\cdots)q^{4}+\cdots\) | |
667.2.a.c | $13$ | $5.326$ | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) | None | \(4\) | \(3\) | \(16\) | \(1\) | $+$ | $-$ | \(q+\beta _{1}q^{2}-\beta _{12}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\) | |
667.2.a.d | $16$ | $5.326$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(3\) | \(5\) | \(16\) | \(1\) | $-$ | $+$ | \(q+\beta _{1}q^{2}+\beta _{11}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(667))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(667)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 2}\)