Defining parameters
Level: | \( N \) | \(=\) | \( 90 = 2 \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 90.g (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(90\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(90, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 160 | 20 | 140 |
Cusp forms | 128 | 20 | 108 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(90, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
90.5.g.a | $2$ | $9.303$ | \(\Q(\sqrt{-1}) \) | None | \(-4\) | \(0\) | \(30\) | \(-38\) | \(q+(-2 i-2)q^{2}+8 i q^{4}+(20 i+15)q^{5}+\cdots\) |
90.5.g.b | $2$ | $9.303$ | \(\Q(\sqrt{-1}) \) | None | \(4\) | \(0\) | \(30\) | \(58\) | \(q+(2 i+2)q^{2}+8 i q^{4}+(-20 i+15)q^{5}+\cdots\) |
90.5.g.c | $4$ | $9.303$ | \(\Q(i, \sqrt{6})\) | None | \(-8\) | \(0\) | \(-36\) | \(68\) | \(q+(-2+2\beta _{2})q^{2}-8\beta _{2}q^{4}+(-9-11\beta _{1}+\cdots)q^{5}+\cdots\) |
90.5.g.d | $4$ | $9.303$ | \(\Q(i, \sqrt{26})\) | None | \(-8\) | \(0\) | \(-24\) | \(-100\) | \(q+(-2-2\beta _{2})q^{2}+8\beta _{2}q^{4}+(-6-2\beta _{1}+\cdots)q^{5}+\cdots\) |
90.5.g.e | $4$ | $9.303$ | \(\Q(i, \sqrt{6})\) | None | \(8\) | \(0\) | \(-84\) | \(-28\) | \(q+(2-2\beta _{2})q^{2}-8\beta _{2}q^{4}+(-21+\beta _{1}+\cdots)q^{5}+\cdots\) |
90.5.g.f | $4$ | $9.303$ | \(\Q(i, \sqrt{26})\) | None | \(8\) | \(0\) | \(24\) | \(-100\) | \(q+(2+2\beta _{2})q^{2}+8\beta _{2}q^{4}+(6-2\beta _{1}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{5}^{\mathrm{old}}(90, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(90, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)