Defining parameters
Level: | \( N \) | \(=\) | \( 120 = 2^{3} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 120.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 24 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(48\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(23\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(120, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 28 | 16 | 12 |
Cusp forms | 20 | 16 | 4 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(120, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
120.2.b.a | $8$ | $0.958$ | 8.0.1649659456.5 | None | \(-1\) | \(0\) | \(8\) | \(0\) | \(q-\beta _{1}q^{2}-\beta _{6}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots\) |
120.2.b.b | $8$ | $0.958$ | 8.0.1649659456.5 | None | \(1\) | \(0\) | \(-8\) | \(0\) | \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(120, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(120, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)