Defining parameters
Level: | \( N \) | \(=\) | \( 268 = 2^{2} \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 268.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(68\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(268))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 37 | 5 | 32 |
Cusp forms | 32 | 5 | 27 |
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.
\(2\) | \(67\) | Fricke | Dim |
---|---|---|---|
\(-\) | \(+\) | $-$ | \(3\) |
\(-\) | \(-\) | $+$ | \(2\) |
Plus space | \(+\) | \(2\) | |
Minus space | \(-\) | \(3\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(268))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 67 | |||||||
268.2.a.a | $1$ | $2.140$ | \(\Q\) | None | \(0\) | \(2\) | \(2\) | \(2\) | $-$ | $+$ | \(q+2q^{3}+2q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots\) | |
268.2.a.b | $2$ | $2.140$ | \(\Q(\sqrt{5}) \) | None | \(0\) | \(-3\) | \(0\) | \(-5\) | $-$ | $-$ | \(q+(-1-\beta )q^{3}+(-1+2\beta )q^{5}+(-2+\cdots)q^{7}+\cdots\) | |
268.2.a.c | $2$ | $2.140$ | \(\Q(\sqrt{21}) \) | None | \(0\) | \(1\) | \(-2\) | \(1\) | $-$ | $+$ | \(q+\beta q^{3}-q^{5}+(1-\beta )q^{7}+(2+\beta )q^{9}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(268))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(268)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(67))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(134))\)\(^{\oplus 2}\)