Defining parameters
| Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 15 \) |
| Character orbit: | \([\chi]\) | \(=\) | 75.d (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 15 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(150\) | ||
| Trace bound: | \(4\) | ||
| Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{15}(75, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 146 | 86 | 60 |
| Cusp forms | 134 | 82 | 52 |
| Eisenstein series | 12 | 4 | 8 |
Trace form
Decomposition of \(S_{15}^{\mathrm{new}}(75, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
| 75.15.d.a | $2$ | $93.247$ | \(\Q(\sqrt{-1}) \) | \(\Q(\sqrt{-3}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+3^{7}iq^{3}-2^{14}q^{4}-72061iq^{7}+\cdots\) |
| 75.15.d.b | $8$ | $93.247$ | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(-3\beta _{1}+11\beta _{2}+\beta _{5})q^{3}+\cdots\) |
| 75.15.d.c | $36$ | $93.247$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
| 75.15.d.d | $36$ | $93.247$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
Decomposition of \(S_{15}^{\mathrm{old}}(75, [\chi])\) into lower level spaces
\( S_{15}^{\mathrm{old}}(75, [\chi]) \simeq \) \(S_{15}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)