Defining parameters
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
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: | \(60\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(45, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 58 | 24 | 34 |
Cusp forms | 50 | 22 | 28 |
Eisenstein series | 8 | 2 | 6 |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(45, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
45.10.b.a | $2$ | $23.177$ | \(\Q(\sqrt{-5}) \) | \(\Q(\sqrt{-15}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+19\beta q^{2}-1293q^{4}-5^{4}\beta q^{5}-14839\beta q^{8}+\cdots\) |
45.10.b.b | $4$ | $23.177$ | 4.0.49740556.1 | None | \(0\) | \(0\) | \(-1140\) | \(0\) | \(q+\beta _{1}q^{2}+(-342-\beta _{3})q^{4}+(-285+\cdots)q^{5}+\cdots\) |
45.10.b.c | $8$ | $23.177$ | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) | None | \(0\) | \(0\) | \(690\) | \(0\) | \(q+\beta _{3}q^{2}+(-149-\beta _{1})q^{4}+(86+2\beta _{1}+\cdots)q^{5}+\cdots\) |
45.10.b.d | $8$ | $23.177$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(-18+\beta _{2})q^{4}+(24\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{10}^{\mathrm{old}}(45, [\chi])\) into lower level spaces
\( S_{10}^{\mathrm{old}}(45, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)