Defining parameters
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.e (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(45, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 40 | 24 | 16 |
Cusp forms | 32 | 24 | 8 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(45, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
45.4.e.a | $4$ | $2.655$ | \(\Q(\sqrt{-3}, \sqrt{-11})\) | None | \(1\) | \(-6\) | \(-10\) | \(-9\) | \(q+\beta _{3}q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{3})q^{3}+\cdots\) |
45.4.e.b | $6$ | $2.655$ | 6.0.15759792.1 | None | \(1\) | \(9\) | \(-15\) | \(43\) | \(q+(-\beta _{1}+\beta _{5})q^{2}+(1+\beta _{2}-\beta _{5})q^{3}+\cdots\) |
45.4.e.c | $14$ | $2.655$ | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) | None | \(2\) | \(-5\) | \(35\) | \(-22\) | \(q+(-\beta _{1}+\beta _{2})q^{2}+(\beta _{7}-\beta _{10})q^{3}+(-5+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(45, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(45, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)