Defining parameters
Level: | \( N \) | \(=\) | \( 385 = 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 385.n (of order \(5\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 11 \) |
Character field: | \(\Q(\zeta_{5})\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(385, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 208 | 96 | 112 |
Cusp forms | 176 | 96 | 80 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(385, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
385.2.n.a | $4$ | $3.074$ | \(\Q(\zeta_{10})\) | None | \(1\) | \(-3\) | \(-1\) | \(-1\) | \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\cdots)q^{3}+\cdots\) |
385.2.n.b | $4$ | $3.074$ | \(\Q(\zeta_{10})\) | None | \(5\) | \(3\) | \(1\) | \(1\) | \(q+(1+\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(\zeta_{10}+\cdots)q^{3}+\cdots\) |
385.2.n.c | $8$ | $3.074$ | 8.0.13140625.1 | None | \(2\) | \(4\) | \(-2\) | \(-2\) | \(q+(-\beta _{3}+\beta _{5}+\beta _{6})q^{2}+(1-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\) |
385.2.n.d | $16$ | $3.074$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(-4\) | \(4\) | \(4\) | \(4\) | \(q+(-1-\beta _{4}+\beta _{7}-\beta _{8}-\beta _{9}-\beta _{10}+\cdots)q^{2}+\cdots\) |
385.2.n.e | $28$ | $3.074$ | None | \(3\) | \(0\) | \(7\) | \(-7\) | ||
385.2.n.f | $36$ | $3.074$ | None | \(1\) | \(0\) | \(-9\) | \(9\) |
Decomposition of \(S_{2}^{\mathrm{old}}(385, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(385, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)