Defining parameters
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.g (of order \(21\) and degree \(12\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 49 \) |
Character field: | \(\Q(\zeta_{21})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(140\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(98, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1536 | 504 | 1032 |
Cusp forms | 1488 | 504 | 984 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(98, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
98.10.g.a | $252$ | $50.474$ | None | \(-336\) | \(-568\) | \(1085\) | \(6796\) | ||
98.10.g.b | $252$ | $50.474$ | None | \(336\) | \(730\) | \(733\) | \(-5012\) |
Decomposition of \(S_{10}^{\mathrm{old}}(98, [\chi])\) into lower level spaces
\( S_{10}^{\mathrm{old}}(98, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)