Defining parameters
Level: | \( N \) | \(=\) | \( 90 = 2 \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 90.i (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 45 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(36\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(90, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 44 | 12 | 32 |
Cusp forms | 28 | 12 | 16 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(90, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
90.2.i.a | $4$ | $0.719$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\) |
90.2.i.b | $8$ | $0.719$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(-4\) | \(0\) | \(q+\zeta_{24}^{2}q^{2}+(\zeta_{24}^{2}+\zeta_{24}^{3}-\zeta_{24}^{5}+\cdots)q^{3}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(90, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(90, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)