Defining parameters
Level: | \( N \) | \(=\) | \( 670 = 2 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 670.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(204\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(670, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 106 | 34 | 72 |
Cusp forms | 98 | 34 | 64 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(670, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
670.2.c.a | $10$ | $5.350$ | 10.0.\(\cdots\).1 | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q+\beta _{3}q^{2}-\beta _{8}q^{3}-q^{4}+(\beta _{1}-\beta _{7})q^{5}+\cdots\) |
670.2.c.b | $24$ | $5.350$ | None | \(0\) | \(0\) | \(-2\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(670, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(670, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(335, [\chi])\)\(^{\oplus 2}\)