Defining parameters
Level: | \( N \) | \(=\) | \( 1519 = 7^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1519.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 31 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(149\) | ||
Trace bound: | \(10\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1519, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 18 | 12 | 6 |
Cusp forms | 10 | 7 | 3 |
Eisenstein series | 8 | 5 | 3 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 7 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1519, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1519.1.c.a | $1$ | $0.758$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-31}) \) | None | \(-1\) | \(0\) | \(1\) | \(0\) | \(q-q^{2}+q^{5}+q^{8}+q^{9}-q^{10}-q^{16}+\cdots\) |
1519.1.c.b | $3$ | $0.758$ | \(\Q(\zeta_{18})^+\) | $D_{9}$ | \(\Q(\sqrt{-31}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\beta _{1}-\beta _{2})q^{2}+(1-\beta _{1})q^{4}-\beta _{1}q^{5}+\cdots\) |
1519.1.c.c | $3$ | $0.758$ | \(\Q(\zeta_{18})^+\) | $D_{9}$ | \(\Q(\sqrt{-31}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\beta _{1}-\beta _{2})q^{2}+(1-\beta _{1})q^{4}+\beta _{1}q^{5}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1519, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1519, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 3}\)