Defining parameters
Level: | \( N \) | \(=\) | \( 78 = 2 \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 78.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 39 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(42\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(78, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 32 | 8 | 24 |
Cusp forms | 24 | 8 | 16 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(78, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
78.3.d.a | $4$ | $2.125$ | \(\Q(\sqrt{2}, \sqrt{-5})\) | None | \(0\) | \(-8\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(-2-\beta _{3})q^{3}+2q^{4}+3\beta _{1}q^{5}+\cdots\) |
78.3.d.b | $4$ | $2.125$ | \(\Q(\sqrt{2}, \sqrt{-5})\) | None | \(0\) | \(8\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(2+\beta _{3})q^{3}+2q^{4}-\beta _{1}q^{5}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(78, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(78, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)