Defining parameters
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(672\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1764, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 384 | 12 | 372 |
Cusp forms | 288 | 12 | 276 |
Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1764, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1764.2.f.a | $4$ | $14.086$ | \(\Q(\sqrt{-2}, \sqrt{-3})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{5}-\beta _{3}q^{11}+\beta _{1}q^{13}+2\beta _{2}q^{17}+\cdots\) |
1764.2.f.b | $8$ | $14.086$ | \(\Q(\zeta_{16})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{16}^{5}q^{5}-\zeta_{16}q^{11}+(2\zeta_{16}^{2}+\zeta_{16}^{4}+\cdots)q^{13}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1764, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1764, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 2}\)