Defining parameters
Level: | \( N \) | \(=\) | \( 806 = 2 \cdot 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 806.bk (of order \(15\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 31 \) |
Character field: | \(\Q(\zeta_{15})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(224\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(806, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 928 | 256 | 672 |
Cusp forms | 864 | 256 | 608 |
Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(806, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
806.2.bk.a | $48$ | $6.436$ | None | \(-12\) | \(-3\) | \(9\) | \(-7\) | ||
806.2.bk.b | $56$ | $6.436$ | None | \(14\) | \(-1\) | \(1\) | \(4\) | ||
806.2.bk.c | $72$ | $6.436$ | None | \(18\) | \(-1\) | \(5\) | \(17\) | ||
806.2.bk.d | $80$ | $6.436$ | None | \(-20\) | \(-3\) | \(-11\) | \(10\) |
Decomposition of \(S_{2}^{\mathrm{old}}(806, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(806, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(403, [\chi])\)\(^{\oplus 2}\)