Defining parameters
Level: | \( N \) | \(=\) | \( 668 = 2^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 668.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(168\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(668))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 87 | 14 | 73 |
Cusp forms | 82 | 14 | 68 |
Eisenstein series | 5 | 0 | 5 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(167\) | Fricke | Dim |
---|---|---|---|
\(-\) | \(+\) | $-$ | \(7\) |
\(-\) | \(-\) | $+$ | \(7\) |
Plus space | \(+\) | \(7\) | |
Minus space | \(-\) | \(7\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(668))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 167 | |||||||
668.2.a.a | $2$ | $5.334$ | \(\Q(\sqrt{13}) \) | None | \(0\) | \(1\) | \(-6\) | \(3\) | $-$ | $+$ | \(q+\beta q^{3}-3q^{5}+(1+\beta )q^{7}+\beta q^{9}+(4+\cdots)q^{13}+\cdots\) | |
668.2.a.b | $5$ | $5.334$ | 5.5.826865.1 | None | \(0\) | \(3\) | \(10\) | \(9\) | $-$ | $+$ | \(q+(1-\beta _{2})q^{3}+2q^{5}+(2-\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots\) | |
668.2.a.c | $7$ | $5.334$ | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) | None | \(0\) | \(-4\) | \(-2\) | \(-12\) | $-$ | $-$ | \(q+(-1-\beta _{3})q^{3}+(\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(668))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(668)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(334))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(167))\)\(^{\oplus 3}\)