Defining parameters
Level: | \( N \) | \(=\) | \( 195 = 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 195.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(56\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(195, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 32 | 8 | 24 |
Cusp forms | 24 | 8 | 16 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(195, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
195.2.b.a | $2$ | $1.557$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q-q^{3}+2q^{4}+iq^{5}+3iq^{7}+q^{9}+\cdots\) |
195.2.b.b | $2$ | $1.557$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q+iq^{2}+q^{3}+q^{4}+iq^{5}+iq^{6}-2iq^{7}+\cdots\) |
195.2.b.c | $4$ | $1.557$ | \(\Q(i, \sqrt{17})\) | None | \(0\) | \(4\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+q^{3}+(-3+\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(195, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(195, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)