Defining parameters
Level: | \( N \) | \(=\) | \( 115 = 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 115.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 23 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(36\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(115, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 26 | 16 | 10 |
Cusp forms | 22 | 16 | 6 |
Eisenstein series | 4 | 0 | 4 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(115, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
115.3.d.a | $6$ | $3.134$ | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) | None | \(-6\) | \(2\) | \(0\) | \(0\) | \(q-q^{2}+\beta _{4}q^{3}-3q^{4}-\beta _{3}q^{5}-\beta _{4}q^{6}+\cdots\) |
115.3.d.b | $10$ | $3.134$ | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) | None | \(2\) | \(-2\) | \(0\) | \(0\) | \(q+\beta _{4}q^{2}-\beta _{7}q^{3}+(3+\beta _{6})q^{4}+\beta _{5}q^{5}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(115, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(115, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)