Defining parameters
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.br (of order \(30\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 385 \) |
Character field: | \(\Q(\zeta_{30})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(770, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1216 | 384 | 832 |
Cusp forms | 1088 | 384 | 704 |
Eisenstein series | 128 | 0 | 128 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(770, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
770.2.br.a | $192$ | $6.148$ | None | \(-24\) | \(0\) | \(6\) | \(6\) | ||
770.2.br.b | $192$ | $6.148$ | None | \(24\) | \(0\) | \(6\) | \(-6\) |
Decomposition of \(S_{2}^{\mathrm{old}}(770, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(770, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)