Defining parameters
Level: | \( N \) | \(=\) | \( 270 = 2 \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 270.k (of order \(9\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 27 \) |
Character field: | \(\Q(\zeta_{9})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(108\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(270, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 348 | 72 | 276 |
Cusp forms | 300 | 72 | 228 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(270, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
270.2.k.a | $6$ | $2.156$ | \(\Q(\zeta_{18})\) | None | \(0\) | \(0\) | \(0\) | \(6\) | \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(\zeta_{18}-2\zeta_{18}^{4}+\cdots)q^{3}+\cdots\) |
270.2.k.b | $12$ | $2.156$ | 12.0.\(\cdots\).1 | None | \(0\) | \(3\) | \(0\) | \(-12\) | \(q-\beta _{7}q^{2}+(1-\beta _{5}-\beta _{7}-\beta _{11})q^{3}+\cdots\) |
270.2.k.c | $12$ | $2.156$ | 12.0.\(\cdots\).1 | None | \(0\) | \(3\) | \(0\) | \(6\) | \(q+(-\beta _{7}-\beta _{10})q^{2}+(-\beta _{1}+\beta _{4}-\beta _{7}+\cdots)q^{3}+\cdots\) |
270.2.k.d | $18$ | $2.156$ | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) | None | \(0\) | \(-3\) | \(0\) | \(-3\) | \(q+\beta _{2}q^{2}-\beta _{7}q^{3}+\beta _{3}q^{4}+(\beta _{3}-\beta _{8}+\cdots)q^{5}+\cdots\) |
270.2.k.e | $24$ | $2.156$ | None | \(0\) | \(-3\) | \(0\) | \(3\) |
Decomposition of \(S_{2}^{\mathrm{old}}(270, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(270, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)