Defining parameters
Level: | \( N \) | \(=\) | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 240.bg (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(144\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(240, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 216 | 24 | 192 |
Cusp forms | 168 | 24 | 144 |
Eisenstein series | 48 | 0 | 48 |
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.bg.a | $4$ | $6.540$ | \(\Q(i, \sqrt{6})\) | None | \(0\) | \(0\) | \(-4\) | \(-4\) | \(q+\beta _{1}q^{3}+(-1-\beta _{1}-3\beta _{2}+2\beta _{3})q^{5}+\cdots\) |
240.3.bg.b | $4$ | $6.540$ | \(\Q(i, \sqrt{6})\) | None | \(0\) | \(0\) | \(0\) | \(16\) | \(q+\beta _{1}q^{3}+(2\beta _{1}+\beta _{2}-2\beta _{3})q^{5}+(4+\cdots)q^{7}+\cdots\) |
240.3.bg.c | $4$ | $6.540$ | \(\Q(i, \sqrt{6})\) | None | \(0\) | \(0\) | \(4\) | \(12\) | \(q+\beta _{1}q^{3}+(1-\beta _{1}+3\beta _{2}+2\beta _{3})q^{5}+\cdots\) |
240.3.bg.d | $4$ | $6.540$ | \(\Q(i, \sqrt{6})\) | None | \(0\) | \(0\) | \(12\) | \(-20\) | \(q+\beta _{1}q^{3}+(3-\beta _{1}+\beta _{2}-2\beta _{3})q^{5}+\cdots\) |
240.3.bg.e | $8$ | $6.540$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(0\) | \(-12\) | \(-4\) | \(q+\beta _{4}q^{3}+(-1+\beta _{4}-\beta _{5})q^{5}+(-1+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(240, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(240, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)