Defining parameters
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.by (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 91 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(74\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(2\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(273, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 168 | 72 | 96 |
Cusp forms | 136 | 72 | 64 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(273, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
273.2.by.a | $4$ | $2.180$ | \(\Q(\zeta_{12})\) | None | \(2\) | \(0\) | \(-2\) | \(-2\) | \(q+(1-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\) |
273.2.by.b | $4$ | $2.180$ | \(\Q(\zeta_{12})\) | None | \(2\) | \(0\) | \(2\) | \(0\) | \(q+(1-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\) |
273.2.by.c | $32$ | $2.180$ | None | \(-2\) | \(0\) | \(-2\) | \(-2\) | ||
273.2.by.d | $32$ | $2.180$ | None | \(-2\) | \(0\) | \(2\) | \(2\) |
Decomposition of \(S_{2}^{\mathrm{old}}(273, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(273, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)