Defining parameters
Level: | \( N \) | \(=\) | \( 90 = 2 \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 90.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(72\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(90, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 62 | 8 | 54 |
Cusp forms | 46 | 8 | 38 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(90, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
90.4.c.a | $2$ | $5.310$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-4\) | \(0\) | \(q+2 i q^{2}-4 q^{4}+(11 i-2)q^{5}+2 i q^{7}+\cdots\) |
90.4.c.b | $2$ | $5.310$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(10\) | \(0\) | \(q+\beta q^{2}-4 q^{4}+(-5\beta+5)q^{5}-13\beta q^{7}+\cdots\) |
90.4.c.c | $4$ | $5.310$ | \(\Q(i, \sqrt{31})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{2}-4q^{4}-\beta _{1}q^{5}-\beta _{3}q^{7}+4\beta _{2}q^{8}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(90, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(90, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)