Defining parameters
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.j (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(182\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1521, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 66 | 16 | 50 |
Cusp forms | 10 | 6 | 4 |
Eisenstein series | 56 | 10 | 46 |
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 | 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.j.a | $2$ | $0.759$ | \(\Q(\sqrt{-1}) \) | $D_{4}$ | \(\Q(\sqrt{-39}) \) | None | \(-2\) | \(0\) | \(2\) | \(0\) | \(q+(-1-i)q^{2}+iq^{4}+(1+i)q^{5}-q^{8}+\cdots\) |
1521.1.j.b | $2$ | $0.759$ | \(\Q(\sqrt{-1}) \) | $D_{4}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(2\) | \(q-iq^{4}+(1-i)q^{7}-q^{16}+(1+i)q^{19}+\cdots\) |
1521.1.j.c | $2$ | $0.759$ | \(\Q(\sqrt{-1}) \) | $D_{4}$ | \(\Q(\sqrt{-39}) \) | None | \(2\) | \(0\) | \(-2\) | \(0\) | \(q+(1+i)q^{2}+iq^{4}+(-1-i)q^{5}+q^{8}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1521, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1521, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)