Defining parameters
Level: | \( N \) | \(=\) | \( 1005 = 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1005.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(272\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1005, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 140 | 68 | 72 |
Cusp forms | 132 | 68 | 64 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1005, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1005.2.c.a | $2$ | $8.025$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(4\) | \(0\) | \(q+iq^{2}+iq^{3}+q^{4}+(2+i)q^{5}-q^{6}+\cdots\) |
1005.2.c.b | $4$ | $8.025$ | \(\Q(i, \sqrt{6})\) | None | \(0\) | \(0\) | \(-4\) | \(0\) | \(q+(-\beta _{1}-\beta _{3})q^{2}+\beta _{2}q^{3}-4q^{4}+(-1+\cdots)q^{5}+\cdots\) |
1005.2.c.c | $28$ | $8.025$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
1005.2.c.d | $34$ | $8.025$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1005, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1005, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(335, [\chi])\)\(^{\oplus 2}\)