Defining parameters
Level: | \( N \) | \(=\) | \( 261 = 3^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 261.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(60\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(2\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(261))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 34 | 11 | 23 |
Cusp forms | 27 | 11 | 16 |
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.
\(3\) | \(29\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(2\) |
\(+\) | \(-\) | $-$ | \(2\) |
\(-\) | \(+\) | $-$ | \(5\) |
\(-\) | \(-\) | $+$ | \(2\) |
Plus space | \(+\) | \(4\) | |
Minus space | \(-\) | \(7\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(261))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | 29 | |||||||
261.2.a.a | $2$ | $2.084$ | \(\Q(\sqrt{5}) \) | None | \(-1\) | \(0\) | \(-4\) | \(0\) | $+$ | $+$ | \(q-\beta q^{2}+(-1+\beta )q^{4}-2q^{5}+(-1+\cdots)q^{7}+\cdots\) | |
261.2.a.b | $2$ | $2.084$ | \(\Q(\sqrt{5}) \) | None | \(-1\) | \(0\) | \(-2\) | \(-4\) | $-$ | $-$ | \(q-\beta q^{2}+(-1+\beta )q^{4}+(-2+2\beta )q^{5}+\cdots\) | |
261.2.a.c | $2$ | $2.084$ | \(\Q(\sqrt{5}) \) | None | \(1\) | \(0\) | \(4\) | \(0\) | $+$ | $-$ | \(q+\beta q^{2}+(-1+\beta )q^{4}+2q^{5}+(-1+\cdots)q^{7}+\cdots\) | |
261.2.a.d | $2$ | $2.084$ | \(\Q(\sqrt{2}) \) | None | \(2\) | \(0\) | \(2\) | \(0\) | $-$ | $+$ | \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}-2\beta q^{7}+\cdots\) | |
261.2.a.e | $3$ | $2.084$ | 3.3.229.1 | None | \(-2\) | \(0\) | \(0\) | \(4\) | $-$ | $+$ | \(q+(-1-\beta _{2})q^{2}+(2+\beta _{1})q^{4}+2\beta _{1}q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(261))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(261)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 2}\)