Defining parameters
Level: | \( N \) | \(=\) | \( 120 = 2^{3} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 120.m (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 120 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(120, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 76 | 76 | 0 |
Cusp forms | 68 | 68 | 0 |
Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(120, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
120.4.m.a | $4$ | $7.080$ | \(\Q(\sqrt{3}, \sqrt{-5})\) | \(\Q(\sqrt{-15}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{3}q^{2}+(-\beta _{1}+2\beta _{3})q^{3}+(6+\beta _{2}+\cdots)q^{4}+\cdots\) |
120.4.m.b | $64$ | $7.080$ | None | \(0\) | \(0\) | \(0\) | \(0\) |