Defining parameters
Level: | \( N \) | \(=\) | \( 195 = 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 195.j (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 195 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(84\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(195, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 120 | 120 | 0 |
Cusp forms | 104 | 104 | 0 |
Eisenstein series | 16 | 16 | 0 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(195, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
195.3.j.a | $2$ | $5.313$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(-6\) | \(0\) | \(0\) | \(q+iq^{2}-3q^{3}+3q^{4}+5iq^{5}-3iq^{6}+\cdots\) |
195.3.j.b | $2$ | $5.313$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-iq^{2}-3iq^{3}+3q^{4}-5iq^{5}-3q^{6}+\cdots\) |
195.3.j.c | $4$ | $5.313$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(8\) | \(0\) | \(0\) | \(q+(2\zeta_{8}+2\zeta_{8}^{3})q^{2}+(2+2\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\cdots\) |
195.3.j.d | $96$ | $5.313$ | None | \(0\) | \(-6\) | \(0\) | \(0\) |