Defining parameters
Level: | \( N \) | \(=\) | \( 104 = 2^{3} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 104.s (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 104 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(28\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(104, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 32 | 32 | 0 |
Cusp forms | 24 | 24 | 0 |
Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(104, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
104.2.s.a | $4$ | $0.830$ | \(\Q(\zeta_{12})\) | None | \(-4\) | \(-6\) | \(-8\) | \(-12\) | \(q+(-1+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\) |
104.2.s.b | $4$ | $0.830$ | \(\Q(\zeta_{12})\) | None | \(-2\) | \(6\) | \(8\) | \(-12\) | \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(1+\zeta_{12}+\cdots)q^{3}+\cdots\) |
104.2.s.c | $16$ | $0.830$ | 16.0.\(\cdots\).2 | None | \(3\) | \(0\) | \(0\) | \(18\) | \(q+(\beta _{1}-\beta _{14})q^{2}+(\beta _{3}-\beta _{11})q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots\) |