Defining parameters
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(36\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(45, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 34 | 14 | 20 |
Cusp forms | 26 | 12 | 14 |
Eisenstein series | 8 | 2 | 6 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(45, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
45.6.b.a | $2$ | $7.217$ | \(\Q(\sqrt{-5}) \) | \(\Q(\sqrt{-15}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta q^{2}-93q^{4}+5\beta q^{5}-61\beta q^{8}+\cdots\) |
45.6.b.b | $2$ | $7.217$ | \(\Q(\sqrt{-11}) \) | None | \(0\) | \(0\) | \(90\) | \(0\) | \(q-\beta q^{2}-12q^{4}+(45-5\beta )q^{5}-9\beta q^{7}+\cdots\) |
45.6.b.c | $4$ | $7.217$ | \(\Q(i, \sqrt{89})\) | None | \(0\) | \(0\) | \(-120\) | \(0\) | \(q+\beta _{1}q^{2}+(-11+\beta _{3})q^{4}+(-30-5\beta _{1}+\cdots)q^{5}+\cdots\) |
45.6.b.d | $4$ | $7.217$ | \(\Q(\sqrt{-5}, \sqrt{-14})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{2}+12q^{4}+(5\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots\) |
Decomposition of \(S_{6}^{\mathrm{old}}(45, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(45, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)