Defining parameters
Level: | \( N \) | \(=\) | \( 207 = 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 207.i (of order \(11\) and degree \(10\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 23 \) |
Character field: | \(\Q(\zeta_{11})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(207, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 760 | 310 | 450 |
Cusp forms | 680 | 290 | 390 |
Eisenstein series | 80 | 20 | 60 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(207, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
207.4.i.a | $50$ | $12.213$ | None | \(11\) | \(0\) | \(19\) | \(-19\) | ||
207.4.i.b | $60$ | $12.213$ | None | \(-4\) | \(0\) | \(6\) | \(-4\) | ||
207.4.i.c | $60$ | $12.213$ | None | \(0\) | \(0\) | \(-22\) | \(24\) | ||
207.4.i.d | $120$ | $12.213$ | None | \(0\) | \(0\) | \(0\) | \(-20\) |
Decomposition of \(S_{4}^{\mathrm{old}}(207, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(207, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)