Defining parameters
Level: | \( N \) | \(=\) | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 240.j (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 20 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(144\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(240, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 108 | 12 | 96 |
Cusp forms | 84 | 12 | 72 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(240, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
240.3.j.a | $4$ | $6.540$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(-20\) | \(0\) | \(q+\zeta_{12}q^{3}-5q^{5}-4\zeta_{12}q^{7}+3q^{9}+\cdots\) |
240.3.j.b | $4$ | $6.540$ | \(\Q(\sqrt{3}, \sqrt{-7})\) | None | \(0\) | \(0\) | \(-8\) | \(0\) | \(q+\beta _{1}q^{3}+(-2+\beta _{2})q^{5}+2\beta _{1}q^{7}+\cdots\) |
240.3.j.c | $4$ | $6.540$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(16\) | \(0\) | \(q-\zeta_{12}^{2}q^{3}+(4-\zeta_{12}^{3})q^{5}-2\zeta_{12}^{2}q^{7}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(240, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(240, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)