Defining parameters
Level: | \( N \) | \(=\) | \( 130 = 2 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 130.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 65 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(42\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(130, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 24 | 8 | 16 |
Cusp forms | 16 | 8 | 8 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(130, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
130.2.c.a | $4$ | $1.038$ | \(\Q(\sqrt{-3}, \sqrt{-11})\) | None | \(-4\) | \(0\) | \(3\) | \(2\) | \(q-q^{2}-\beta _{2}q^{3}+q^{4}+(1-\beta _{3})q^{5}+\beta _{2}q^{6}+\cdots\) |
130.2.c.b | $4$ | $1.038$ | \(\Q(\sqrt{-3}, \sqrt{-11})\) | None | \(4\) | \(0\) | \(-3\) | \(-2\) | \(q+q^{2}-\beta _{2}q^{3}+q^{4}+(-1+\beta _{3})q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(130, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(130, [\chi]) \cong \)