Defining parameters
Level: | \( N \) | \(=\) | \( 95 = 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 95.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 95 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(50\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(95, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 42 | 42 | 0 |
Cusp forms | 38 | 38 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(95, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
95.5.d.a | $2$ | $9.820$ | \(\Q(\sqrt{-19}) \) | \(\Q(\sqrt{-19}) \) | \(0\) | \(0\) | \(31\) | \(0\) | \(q-2^{4}q^{4}+(14+3\beta )q^{5}+(5-10\beta )q^{7}+\cdots\) |
95.5.d.b | $2$ | $9.820$ | \(\Q(\sqrt{19}) \) | \(\Q(\sqrt{-95}) \) | \(0\) | \(0\) | \(50\) | \(0\) | \(q+\beta q^{2}-4\beta q^{3}+3q^{4}+5^{2}q^{5}-76q^{6}+\cdots\) |
95.5.d.c | $2$ | $9.820$ | \(\Q(\sqrt{5}) \) | \(\Q(\sqrt{-95}) \) | \(0\) | \(0\) | \(50\) | \(0\) | \(q-3\beta q^{2}-2\beta q^{3}+29q^{4}+5^{2}q^{5}+\cdots\) |
95.5.d.d | $4$ | $9.820$ | \(\Q(\sqrt{10}, \sqrt{38})\) | \(\Q(\sqrt{-95}) \) | \(0\) | \(0\) | \(-100\) | \(0\) | \(q+(\beta _{1}+\beta _{2})q^{2}+(4\beta _{1}-3\beta _{2})q^{3}+(2^{4}+\cdots)q^{4}+\cdots\) |
95.5.d.e | $28$ | $9.820$ | None | \(0\) | \(0\) | \(-42\) | \(0\) |