Defining parameters
Level: | \( N \) | \(=\) | \( 90 = 2 \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 90.l (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 45 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
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 | 88 | 24 | 64 |
Cusp forms | 56 | 24 | 32 |
Eisenstein series | 32 | 0 | 32 |
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.l.a | $8$ | $0.719$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(4\) | \(12\) | \(-8\) | \(q+\zeta_{24}^{7}q^{2}+(1+\zeta_{24}^{2}-\zeta_{24}^{4}+\zeta_{24}^{5}+\cdots)q^{3}+\cdots\) |
90.2.l.b | $16$ | $0.719$ | 16.0.\(\cdots\).9 | None | \(0\) | \(0\) | \(-12\) | \(8\) | \(q-\beta _{11}q^{2}+(-\beta _{3}-\beta _{4}-\beta _{5}+\beta _{8}+\cdots)q^{3}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(90, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(90, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)