Defining parameters
Level: | \( N \) | \(=\) | \( 539 = 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 539.bc (of order \(105\) and degree \(48\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 539 \) |
Character field: | \(\Q(\zeta_{105})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(112\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(539, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2784 | 2784 | 0 |
Cusp forms | 2592 | 2592 | 0 |
Eisenstein series | 192 | 192 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(539, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
539.2.bc.a | $2592$ | $4.304$ | None | \(-39\) | \(-39\) | \(-41\) | \(-35\) |