Defining parameters
Level: | \( N \) | \(=\) | \( 138 = 2 \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 138.e (of order \(11\) and degree \(10\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 23 \) |
Character field: | \(\Q(\zeta_{11})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(48\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(138, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 280 | 40 | 240 |
Cusp forms | 200 | 40 | 160 |
Eisenstein series | 80 | 0 | 80 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(138, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
138.2.e.a | $10$ | $1.102$ | \(\Q(\zeta_{22})\) | None | \(-1\) | \(-1\) | \(8\) | \(8\) | \(q-\zeta_{22}q^{2}+\zeta_{22}^{8}q^{3}+\zeta_{22}^{2}q^{4}+(1+\cdots)q^{5}+\cdots\) |
138.2.e.b | $10$ | $1.102$ | \(\Q(\zeta_{22})\) | None | \(-1\) | \(1\) | \(-2\) | \(0\) | \(q-\zeta_{22}q^{2}-\zeta_{22}^{8}q^{3}+\zeta_{22}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots\) |
138.2.e.c | $10$ | $1.102$ | \(\Q(\zeta_{22})\) | None | \(1\) | \(-1\) | \(0\) | \(-2\) | \(q+\zeta_{22}q^{2}+\zeta_{22}^{8}q^{3}+\zeta_{22}^{2}q^{4}+(1+\cdots)q^{5}+\cdots\) |
138.2.e.d | $10$ | $1.102$ | \(\Q(\zeta_{22})\) | None | \(1\) | \(1\) | \(2\) | \(2\) | \(q+\zeta_{22}q^{2}-\zeta_{22}^{8}q^{3}+\zeta_{22}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(138, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(138, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)