Defining parameters
Level: | \( N \) | \(=\) | \( 195 = 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 195.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(56\) | ||
Trace bound: | \(1\) | ||
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 | 12 | 20 |
Cusp forms | 24 | 12 | 12 |
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.c.a | $2$ | $1.557$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q+iq^{3}+2q^{4}+(-1+2i)q^{5}+iq^{7}+\cdots\) |
195.2.c.b | $10$ | $1.557$ | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-1-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(195, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(195, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)