Defining parameters
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.f (of order \(5\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 11 \) |
Character field: | \(\Q(\zeta_{5})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(99, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 64 | 24 | 40 |
Cusp forms | 32 | 16 | 16 |
Eisenstein series | 32 | 8 | 24 |
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.f.a | $4$ | $0.791$ | \(\Q(\zeta_{10})\) | None | \(1\) | \(0\) | \(3\) | \(1\) | \(q+(-1+2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\) |
99.2.f.b | $4$ | $0.791$ | \(\Q(\zeta_{10})\) | None | \(3\) | \(0\) | \(1\) | \(-3\) | \(q+(1-\zeta_{10}^{3})q^{2}+(1-\zeta_{10})q^{4}+(1-2\zeta_{10}+\cdots)q^{5}+\cdots\) |
99.2.f.c | $8$ | $0.791$ | 8.0.484000000.9 | None | \(0\) | \(0\) | \(0\) | \(-6\) | \(q+\beta _{1}q^{2}+(1+2\beta _{2}+\beta _{3})q^{4}+(\beta _{4}+\beta _{7})q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(99, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(99, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)