Defining parameters
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(90\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(108, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 78 | 32 | 46 |
Cusp forms | 66 | 32 | 34 |
Eisenstein series | 12 | 0 | 12 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(108, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
108.5.d.a | $16$ | $11.164$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{4}+(-\beta _{1}-\beta _{7}+\cdots)q^{5}+\cdots\) |
108.5.d.b | $16$ | $11.164$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{7}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{7}+\beta _{9}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{5}^{\mathrm{old}}(108, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)