Defining parameters
Level: | \( N \) | \(=\) | \( 26 = 2 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 26.c (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(14\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(26, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 26 | 6 | 20 |
Cusp forms | 18 | 6 | 12 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(26, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
26.4.c.a | $2$ | $1.534$ | \(\Q(\sqrt{-3}) \) | None | \(2\) | \(3\) | \(4\) | \(5\) | \(q+(2-2\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\) |
26.4.c.b | $4$ | $1.534$ | \(\Q(\sqrt{-3}, \sqrt{217})\) | None | \(-4\) | \(3\) | \(-14\) | \(45\) | \(q-2\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-4+4\beta _{2}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(26, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(26, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)