Defining parameters
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.k (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(576\) | ||
Trace bound: | \(25\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1512, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 312 | 32 | 280 |
Cusp forms | 264 | 32 | 232 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1512, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1512.2.k.a | $16$ | $12.073$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-2\) | \(q-\beta _{9}q^{5}-\beta _{1}q^{7}-\beta _{10}q^{11}-\beta _{5}q^{13}+\cdots\) |
1512.2.k.b | $16$ | $12.073$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-2\) | \(q+\beta _{1}q^{5}-\beta _{12}q^{7}+\beta _{10}q^{11}+(\beta _{4}+\cdots)q^{13}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1512, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1512, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)