Defining parameters
Level: | \( N \) | \(=\) | \( 266 = 2 \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 266.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(80\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(266))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 44 | 9 | 35 |
Cusp forms | 37 | 9 | 28 |
Eisenstein series | 7 | 0 | 7 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(7\) | \(19\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(-\) | \(-\) | \(2\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(2\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(3\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(2\) |
Plus space | \(+\) | \(0\) | ||
Minus space | \(-\) | \(9\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(266))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 7 | 19 | |||||||
266.2.a.a | $2$ | $2.124$ | \(\Q(\sqrt{29}) \) | None | \(-2\) | \(1\) | \(-1\) | \(-2\) | $+$ | $+$ | $-$ | \(q-q^{2}+(1-\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots\) | |
266.2.a.b | $2$ | $2.124$ | \(\Q(\sqrt{5}) \) | None | \(-2\) | \(3\) | \(1\) | \(2\) | $+$ | $-$ | $+$ | \(q-q^{2}+(1+\beta )q^{3}+q^{4}+(2-3\beta )q^{5}+\cdots\) | |
266.2.a.c | $2$ | $2.124$ | \(\Q(\sqrt{13}) \) | None | \(2\) | \(1\) | \(1\) | \(2\) | $-$ | $-$ | $-$ | \(q+q^{2}+\beta q^{3}+q^{4}+(1-\beta )q^{5}+\beta q^{6}+\cdots\) | |
266.2.a.d | $3$ | $2.124$ | 3.3.469.1 | None | \(3\) | \(-1\) | \(5\) | \(-3\) | $-$ | $+$ | $+$ | \(q+q^{2}+\beta _{2}q^{3}+q^{4}+(2-\beta _{1})q^{5}+\beta _{2}q^{6}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(266))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(266)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 2}\)