Defining parameters
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(576\) | ||
Trace bound: | \(17\) | ||
Distinguishing \(T_p\): | \(7\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(960, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 408 | 32 | 376 |
Cusp forms | 360 | 32 | 328 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(960, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
960.3.e.a | $4$ | $26.158$ | \(\Q(\sqrt{-3}, \sqrt{5})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{3}+\beta _{1}q^{5}+(2\beta _{2}+2\beta _{3})q^{7}+\cdots\) |
960.3.e.b | $4$ | $26.158$ | \(\Q(\sqrt{-3}, \sqrt{5})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{3}-\beta _{1}q^{5}+(2\beta _{2}+2\beta _{3})q^{7}+\cdots\) |
960.3.e.c | $8$ | $26.158$ | 8.0.85100625.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{3}+\beta _{1}q^{5}+(2\beta _{2}+\beta _{5})q^{7}-3q^{9}+\cdots\) |
960.3.e.d | $8$ | $26.158$ | 8.0.12960000.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{3}+\beta _{1}q^{5}+(-4\beta _{2}-\beta _{3}+\beta _{5}+\cdots)q^{7}+\cdots\) |
960.3.e.e | $8$ | $26.158$ | 8.0.12960000.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{3}-\beta _{1}q^{5}+(\beta _{3}-\beta _{5})q^{7}-3q^{9}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(960, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)