Defining parameters
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.bd (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(182\) | ||
Trace bound: | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1521, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 128 | 36 | 92 |
Cusp forms | 16 | 16 | 0 |
Eisenstein series | 112 | 20 | 92 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 16 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1521, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1521.1.bd.a | $4$ | $0.759$ | \(\Q(\zeta_{12})\) | $D_{4}$ | \(\Q(\sqrt{-39}) \) | None | \(-2\) | \(0\) | \(-4\) | \(0\) | \(q+(-\zeta_{12}^{2}-\zeta_{12}^{5})q^{2}-\zeta_{12}q^{4}+(-1+\cdots)q^{5}+\cdots\) |
1521.1.bd.b | $4$ | $0.759$ | \(\Q(\zeta_{12})\) | $D_{4}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(-2\) | \(q+\zeta_{12}q^{4}+(\zeta_{12}+\zeta_{12}^{4})q^{7}+\zeta_{12}^{2}q^{16}+\cdots\) |
1521.1.bd.c | $4$ | $0.759$ | \(\Q(\zeta_{12})\) | $D_{4}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(2\) | \(q+\zeta_{12}q^{4}+(-\zeta_{12}-\zeta_{12}^{4})q^{7}+\zeta_{12}^{2}q^{16}+\cdots\) |
1521.1.bd.d | $4$ | $0.759$ | \(\Q(\zeta_{12})\) | $D_{4}$ | \(\Q(\sqrt{-39}) \) | None | \(2\) | \(0\) | \(4\) | \(0\) | \(q+(\zeta_{12}^{2}+\zeta_{12}^{5})q^{2}-\zeta_{12}q^{4}+(1+\zeta_{12}^{3}+\cdots)q^{5}+\cdots\) |