Defining parameters
Level: | \( N \) | \(=\) | \( 95 = 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 95.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 95 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(90\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(95, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 82 | 82 | 0 |
Cusp forms | 78 | 78 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(95, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
95.9.d.a | $1$ | $38.701$ | \(\Q\) | \(\Q(\sqrt{-95}) \) | \(-13\) | \(142\) | \(625\) | \(0\) | \(q-13q^{2}+142q^{3}-87q^{4}+5^{4}q^{5}+\cdots\) |
95.9.d.b | $1$ | $38.701$ | \(\Q\) | \(\Q(\sqrt{-95}) \) | \(13\) | \(-142\) | \(625\) | \(0\) | \(q+13q^{2}-142q^{3}-87q^{4}+5^{4}q^{5}+\cdots\) |
95.9.d.c | $2$ | $38.701$ | \(\Q(\sqrt{-19}) \) | \(\Q(\sqrt{-19}) \) | \(0\) | \(0\) | \(-289\) | \(0\) | \(q-2^{8}q^{4}+(-191+93\beta )q^{5}+(-365+\cdots)q^{7}+\cdots\) |
95.9.d.d | $2$ | $38.701$ | \(\Q(\sqrt{95}) \) | \(\Q(\sqrt{-95}) \) | \(0\) | \(0\) | \(1250\) | \(0\) | \(q+3\beta q^{2}-8\beta q^{3}+599q^{4}+5^{4}q^{5}+\cdots\) |
95.9.d.e | $4$ | $38.701$ | \(\Q(\sqrt{2}, \sqrt{95})\) | \(\Q(\sqrt{-95}) \) | \(0\) | \(0\) | \(-2500\) | \(0\) | \(q+(\beta _{1}+2\beta _{2})q^{2}+(-5\beta _{1}+13\beta _{2})q^{3}+\cdots\) |
95.9.d.f | $68$ | $38.701$ | None | \(0\) | \(0\) | \(8\) | \(0\) |