Defining parameters
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.m (of order \(15\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 99 \) |
Character field: | \(\Q(\zeta_{15})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(99, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 112 | 112 | 0 |
Cusp forms | 80 | 80 | 0 |
Eisenstein series | 32 | 32 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(99, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
99.2.m.a | $8$ | $0.791$ | \(\Q(\zeta_{15})\) | None | \(-4\) | \(3\) | \(6\) | \(-1\) | \(q+(1-2\zeta_{15}^{2}+\zeta_{15}^{3}-\zeta_{15}^{4}+\zeta_{15}^{5}+\cdots)q^{2}+\cdots\) |
99.2.m.b | $72$ | $0.791$ | None | \(-1\) | \(-12\) | \(-8\) | \(-2\) |