Defining parameters
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(17\) | ||
Distinguishing \(T_p\): | \(5\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(768, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 280 | 32 | 248 |
Cusp forms | 232 | 32 | 200 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(768, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
768.3.b.a | $4$ | $20.926$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{12}q^{3}+(-2\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+\cdots\) |
768.3.b.b | $4$ | $20.926$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{12}q^{3}+3\zeta_{12}^{3}q^{5}-2\zeta_{12}^{2}q^{7}+\cdots\) |
768.3.b.c | $4$ | $20.926$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{12}q^{3}+\zeta_{12}^{3}q^{5}+2\zeta_{12}^{2}q^{7}+\cdots\) |
768.3.b.d | $4$ | $20.926$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{12}q^{3}+(-2\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+\cdots\) |
768.3.b.e | $8$ | $20.926$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{24}^{2}q^{3}+(-\zeta_{24}-\zeta_{24}^{3}+\zeta_{24}^{4}+\cdots)q^{5}+\cdots\) |
768.3.b.f | $8$ | $20.926$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{24}^{2}q^{3}+(-\zeta_{24}-\zeta_{24}^{3}+\zeta_{24}^{4}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(768, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(768, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)