Defining parameters
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(72\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(144, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 60 | 4 | 56 |
Cusp forms | 36 | 4 | 32 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(144, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
144.3.e.a | $2$ | $3.924$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(-24\) | \(q+5\beta q^{5}-12q^{7}+4\beta q^{11}-8q^{13}+\cdots\) |
144.3.e.b | $2$ | $3.924$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(8\) | \(q+\beta q^{5}+4q^{7}+4\beta q^{11}+8q^{13}+3\beta q^{17}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(144, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(144, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)