Defining parameters
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.z (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 144 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(576\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1728, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1248 | 104 | 1144 |
Cusp forms | 1056 | 88 | 968 |
Eisenstein series | 192 | 16 | 176 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1728, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1728.2.z.a | $88$ | $13.798$ | None | \(0\) | \(0\) | \(6\) | \(4\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1728, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1728, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 2}\)