Defining parameters
Level: | \( N \) | \(=\) | \( 1001 = 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1001.i (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(224\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1001, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 232 | 160 | 72 |
Cusp forms | 216 | 160 | 56 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1001, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1001.2.i.a | $8$ | $7.993$ | 8.0.447703281.1 | None | \(-2\) | \(-1\) | \(1\) | \(-16\) | \(q-\beta _{3}q^{2}+(-\beta _{5}+\beta _{6})q^{3}+(-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\) |
1001.2.i.b | $22$ | $7.993$ | None | \(2\) | \(-1\) | \(0\) | \(15\) | ||
1001.2.i.c | $30$ | $7.993$ | None | \(6\) | \(2\) | \(3\) | \(1\) | ||
1001.2.i.d | $50$ | $7.993$ | None | \(-6\) | \(2\) | \(1\) | \(1\) | ||
1001.2.i.e | $50$ | $7.993$ | None | \(0\) | \(-2\) | \(3\) | \(-1\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1001, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1001, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)