Defining parameters
Level: | \( N \) | = | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | = | \( 2 \) |
Character orbit: | \([\chi]\) | = | 403.be (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | = | \( 403 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newforms: | \( 3 \) | ||
Sturm bound: | \(74\) | ||
Trace bound: | \(6\) | ||
Distinguishing \(T_p\): | \(2\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(403, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 160 | 160 | 0 |
Cusp forms | 144 | 144 | 0 |
Eisenstein series | 16 | 16 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(403, [\chi])\) into irreducible Hecke orbits
Label | Dim. | \(A\) | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||
403.2.be.a | \(4\) | \(3.218\) | \(\Q(\zeta_{12})\) | None | \(-2\) | \(6\) | \(-2\) | \(-10\) | \(q+(-1+\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+\cdots\) |
403.2.be.b | \(4\) | \(3.218\) | \(\Q(\zeta_{12})\) | None | \(-2\) | \(6\) | \(-2\) | \(8\) | \(q+(-\zeta_{12}-\zeta_{12}^{2})q^{2}+(1-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\) |
403.2.be.c | \(136\) | \(3.218\) | None | \(-4\) | \(-24\) | \(2\) | \(-2\) |