Defining parameters
| Level: | \( N \) | \(=\) | \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1872.d (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 12 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(1344\) | ||
| Trace bound: | \(13\) | ||
| Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1872, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1032 | 72 | 960 |
| Cusp forms | 984 | 72 | 912 |
| Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(1872, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
| 1872.4.d.a | $12$ | $110.452$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{6}q^{5}-\beta _{1}q^{7}-\beta _{7}q^{11}-13q^{13}+\cdots\) |
| 1872.4.d.b | $12$ | $110.452$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{7}q^{5}-\beta _{1}q^{7}-\beta _{11}q^{11}+13q^{13}+\cdots\) |
| 1872.4.d.c | $24$ | $110.452$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
| 1872.4.d.d | $24$ | $110.452$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
Decomposition of \(S_{4}^{\mathrm{old}}(1872, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1872, [\chi]) \cong \)