Defining parameters
| Level: | \( N \) | \(=\) | \( 3025 = 5^{2} \cdot 11^{2} \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3025.bl (of order \(20\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 55 \) |
| Character field: | \(\Q(\zeta_{20})\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(330\) | ||
| Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3025, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 328 | 88 | 240 |
| Cusp forms | 40 | 24 | 16 |
| Eisenstein series | 288 | 64 | 224 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 24 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3025, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 3025.1.bl.a | $8$ | $1.510$ | \(\Q(\zeta_{20})\) | $D_{4}$ | \(\Q(\sqrt{-55}) \) | None | \(-2\) | \(0\) | \(0\) | \(2\) | \(q+(\zeta_{20}-\zeta_{20}^{6})q^{2}-\zeta_{20}^{7}q^{4}+(\zeta_{20}^{2}+\cdots)q^{7}+\cdots\) |
| 3025.1.bl.b | $8$ | $1.510$ | \(\Q(\zeta_{20})\) | $D_{4}$ | \(\Q(\sqrt{-11}) \) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q+(-\zeta_{20}^{3}-\zeta_{20}^{8})q^{3}+\zeta_{20}^{7}q^{4}+\cdots\) |
| 3025.1.bl.c | $8$ | $1.510$ | \(\Q(\zeta_{20})\) | $D_{4}$ | \(\Q(\sqrt{-55}) \) | None | \(2\) | \(0\) | \(0\) | \(-2\) | \(q+(-\zeta_{20}+\zeta_{20}^{6})q^{2}-\zeta_{20}^{7}q^{4}+(-\zeta_{20}^{2}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3025, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3025, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)