Defining parameters
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.q (of order \(21\) and degree \(12\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 49 \) |
Character field: | \(\Q(\zeta_{21})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(56\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(245, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 360 | 216 | 144 |
Cusp forms | 312 | 216 | 96 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(245, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
245.2.q.a | $96$ | $1.956$ | None | \(-1\) | \(1\) | \(-8\) | \(0\) | ||
245.2.q.b | $120$ | $1.956$ | None | \(1\) | \(1\) | \(10\) | \(-2\) |
Decomposition of \(S_{2}^{\mathrm{old}}(245, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(245, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)