Defining parameters
| Level: | \( N \) | \(=\) | \( 1520 = 2^{4} \cdot 5 \cdot 19 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1520.m (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 95 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(240\) | ||
| Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1520, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 38 | 7 | 31 |
| Cusp forms | 26 | 5 | 21 |
| Eisenstein series | 12 | 2 | 10 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 5 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1520, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 1520.1.m.a | $1$ | $0.759$ | \(\Q\) | $D_{2}$ | \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-95}) \) | \(\Q(\sqrt{5}) \) | \(0\) | \(0\) | \(1\) | \(0\) | \(q+q^{5}-q^{9}+2q^{11}-q^{19}+q^{25}+\cdots\) |
| 1520.1.m.b | $2$ | $0.759$ | \(\Q(\sqrt{2}) \) | $D_{4}$ | \(\Q(\sqrt{-95}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q-\beta q^{3}-q^{5}+q^{9}-\beta q^{13}+\beta q^{15}+\cdots\) |
| 1520.1.m.c | $2$ | $0.759$ | \(\Q(\sqrt{-3}) \) | $D_{6}$ | \(\Q(\sqrt{-19}) \) | None | \(0\) | \(0\) | \(-1\) | \(0\) | \(q-\zeta_{6}q^{5}+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{9}-q^{11}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1520, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1520, [\chi]) \cong \)