Defining parameters
Level: | \( N \) | \(=\) | \( 261 = 3^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 261.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 29 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(60\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(261, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 34 | 14 | 20 |
Cusp forms | 26 | 12 | 14 |
Eisenstein series | 8 | 2 | 6 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(261, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
261.2.c.a | $2$ | $2.084$ | \(\Q(\sqrt{-5}) \) | None | \(0\) | \(0\) | \(6\) | \(4\) | \(q+\beta q^{2}-3q^{4}+3q^{5}+2q^{7}-\beta q^{8}+\cdots\) |
261.2.c.b | $4$ | $2.084$ | \(\Q(i, \sqrt{5})\) | None | \(0\) | \(0\) | \(-4\) | \(-8\) | \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+2\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots\) |
261.2.c.c | $6$ | $2.084$ | 6.0.\(\cdots\).1 | \(\Q(\sqrt{-87}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(261, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(261, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 2}\)