Defining parameters
Level: | \( N \) | \(=\) | \( 104 = 2^{3} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 104.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(28\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(104, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 16 | 12 | 4 |
Cusp forms | 12 | 12 | 0 |
Eisenstein series | 4 | 0 | 4 |
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.b.a | $2$ | $0.830$ | \(\Q(\sqrt{-1}) \) | None | \(-2\) | \(0\) | \(0\) | \(6\) | \(q+(i-1)q^{2}-i q^{3}-2 i q^{4}+3 i q^{5}+\cdots\) |
104.2.b.b | $4$ | $0.830$ | \(\Q(\zeta_{12})\) | None | \(2\) | \(0\) | \(0\) | \(-12\) | \(q+(-\beta_{2}+\beta_1)q^{2}+2\beta_{2} q^{3}+(\beta_{3}+\beta_1)q^{4}+\cdots\) |
104.2.b.c | $6$ | $0.830$ | 6.0.399424.1 | None | \(-2\) | \(0\) | \(0\) | \(2\) | \(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{5})q^{3}+(\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\) |