Defining parameters
Level: | \( N \) | \(=\) | \( 90 = 2 \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 90.j (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 45 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(54\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(90, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 80 | 24 | 56 |
Cusp forms | 64 | 24 | 40 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(90, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
90.3.j.a | $8$ | $2.452$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(-12\) | \(0\) | \(q-\zeta_{24}^{4}q^{2}+3\zeta_{24}q^{3}+(-2+2\zeta_{24}^{2}+\cdots)q^{4}+\cdots\) |
90.3.j.b | $16$ | $2.452$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(30\) | \(0\) | \(q-\beta _{7}q^{2}+\beta _{13}q^{3}+2\beta _{6}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(90, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(90, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)