Defining parameters
| Level: | \( N \) | \(=\) | \( 3775 = 5^{2} \cdot 151 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3775.c (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 755 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(380\) | ||
| Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3775, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 42 | 16 | 26 |
| Cusp forms | 36 | 14 | 22 |
| Eisenstein series | 6 | 2 | 4 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 6 | 0 | 0 | 8 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3775, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 3775.1.c.a | $4$ | $1.884$ | \(\Q(i, \sqrt{5})\) | $A_{5}$ | None | None | \(0\) | \(-4\) | \(0\) | \(2\) | \(q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+\beta _{1}q^{6}-\beta _{2}q^{7}+\cdots\) |
| 3775.1.c.b | $4$ | $1.884$ | \(\Q(i, \sqrt{5})\) | $A_{5}$ | None | None | \(0\) | \(4\) | \(0\) | \(-2\) | \(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}-\beta _{1}q^{6}+\beta _{2}q^{7}+\cdots\) |
| 3775.1.c.c | $6$ | $1.884$ | 6.0.153664.1 | $D_{7}$ | \(\Q(\sqrt{-151}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{8}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3775, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3775, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(755, [\chi])\)\(^{\oplus 2}\)