Defining parameters
Level: | \( N \) | \(=\) | \( 26 = 2 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 26.f (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(10\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(26, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 36 | 12 | 24 |
Cusp forms | 20 | 12 | 8 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(26, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
26.3.f.a | $4$ | $0.708$ | \(\Q(\zeta_{12})\) | None | \(2\) | \(0\) | \(0\) | \(-22\) | \(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\) |
26.3.f.b | $8$ | $0.708$ | 8.0.\(\cdots\).1 | None | \(-4\) | \(0\) | \(6\) | \(-2\) | \(q+(-\beta _{3}-\beta _{4})q^{2}+(-\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(26, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(26, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)