Defining parameters
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.l (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(432\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(720, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 312 | 16 | 296 |
Cusp forms | 264 | 16 | 248 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(720, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
720.3.l.a | $4$ | $19.619$ | \(\Q(\sqrt{-2}, \sqrt{-5})\) | None | \(0\) | \(0\) | \(0\) | \(-16\) | \(q+\beta _{2}q^{5}+(-4-\beta _{3})q^{7}+(-7\beta _{1}+2\beta _{2}+\cdots)q^{11}+\cdots\) |
720.3.l.b | $4$ | $19.619$ | \(\Q(\sqrt{-2}, \sqrt{-5})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{5}-\beta _{3}q^{7}+(-\beta _{1}+2\beta _{2})q^{11}+\cdots\) |
720.3.l.c | $4$ | $19.619$ | \(\Q(\sqrt{-2}, \sqrt{-5})\) | None | \(0\) | \(0\) | \(0\) | \(16\) | \(q-\beta _{2}q^{5}+(4-\beta _{3})q^{7}+(-\beta _{1}+6\beta _{2}+\cdots)q^{11}+\cdots\) |
720.3.l.d | $4$ | $19.619$ | \(\Q(\sqrt{-2}, \sqrt{-5})\) | None | \(0\) | \(0\) | \(0\) | \(32\) | \(q-\beta _{2}q^{5}+(8+\beta _{3})q^{7}+(\beta _{1}-6\beta _{2})q^{11}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(720, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(720, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)