Defining parameters
Level: | \( N \) | \(=\) | \( 140 = 2^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 140.g (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 28 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(48\) | ||
Trace bound: | \(6\) | ||
Distinguishing \(T_p\): | \(3\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(140, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 28 | 16 | 12 |
Cusp forms | 20 | 16 | 4 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(140, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
140.2.g.a | $4$ | $1.118$ | \(\Q(\zeta_{12})\) | None | \(-2\) | \(0\) | \(0\) | \(0\) | \(q+(\beta_{2}-\beta_1)q^{2}+(\beta_{3}-\beta_{2}+\beta_1)q^{3}+\cdots\) |
140.2.g.b | $4$ | $1.118$ | \(\Q(\zeta_{12})\) | None | \(-2\) | \(0\) | \(0\) | \(0\) | \(q+(\beta_{2}-\beta_1)q^{2}+(-\beta_{3}+\beta_{2}-\beta_1)q^{3}+\cdots\) |
140.2.g.c | $8$ | $1.118$ | 8.0.342102016.5 | None | \(2\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{7}q^{2}+(-\beta _{4}+\beta _{6})q^{3}+(-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(140, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(140, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)