Defining parameters
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(448\) | ||
Trace bound: | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(384, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 400 | 96 | 304 |
Cusp forms | 368 | 96 | 272 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(384, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
384.7.e.a | $24$ | $88.341$ | None | \(0\) | \(-20\) | \(0\) | \(-408\) | ||
384.7.e.b | $24$ | $88.341$ | None | \(0\) | \(-20\) | \(0\) | \(408\) | ||
384.7.e.c | $24$ | $88.341$ | None | \(0\) | \(20\) | \(0\) | \(-408\) | ||
384.7.e.d | $24$ | $88.341$ | None | \(0\) | \(20\) | \(0\) | \(408\) |
Decomposition of \(S_{7}^{\mathrm{old}}(384, [\chi])\) into lower level spaces
\( S_{7}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)