Defining parameters
| Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 525.e (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 35 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(240\) | ||
| Trace bound: | \(1\) | ||
| Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(525, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 172 | 48 | 124 |
| Cusp forms | 148 | 48 | 100 |
| Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(525, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
| 525.3.e.a | $4$ | $14.305$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}+3q^{4}+\zeta_{12}^{2}q^{6}+\cdots\) |
| 525.3.e.b | $20$ | $14.305$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{4}q^{2}-\beta _{10}q^{3}+(-1+\beta _{1})q^{4}+\cdots\) |
| 525.3.e.c | $24$ | $14.305$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
Decomposition of \(S_{3}^{\mathrm{old}}(525, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)