Defining parameters
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.f (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 35 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(56\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\), \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(245, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 72 | 48 | 24 |
Cusp forms | 40 | 32 | 8 |
Eisenstein series | 32 | 16 | 16 |
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.f.a | $4$ | $1.956$ | \(\Q(\zeta_{12})\) | None | \(2\) | \(-2\) | \(8\) | \(0\) | \(q+(1-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}+\cdots)q^{3}+\cdots\) |
245.2.f.b | $4$ | $1.956$ | \(\Q(\zeta_{12})\) | None | \(2\) | \(2\) | \(-8\) | \(0\) | \(q+(1-\zeta_{12}+\zeta_{12}^{2})q^{2}+(1-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\) |
245.2.f.c | $24$ | $1.956$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(245, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(245, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)