Defining parameters
Level: | \( N \) | \(=\) | \( 616 = 2^{3} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 616.bi (of order \(10\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 616 \) |
Character field: | \(\Q(\zeta_{10})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(192\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\), \(29\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(616, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 400 | 400 | 0 |
Cusp forms | 368 | 368 | 0 |
Eisenstein series | 32 | 32 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(616, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
616.2.bi.a | $8$ | $4.919$ | 8.0.37515625.1 | \(\Q(\sqrt{-7}) \) | \(-1\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\) |
616.2.bi.b | $8$ | $4.919$ | 8.0.37515625.1 | \(\Q(\sqrt{-7}) \) | \(1\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\) |
616.2.bi.c | $352$ | $4.919$ | None | \(-10\) | \(0\) | \(0\) | \(-10\) |