Defining parameters
Level: | \( N \) | \(=\) | \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1260.t (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 63 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(576\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1260, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 600 | 64 | 536 |
Cusp forms | 552 | 64 | 488 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1260, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1260.2.t.a | $2$ | $10.061$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(-2\) | \(-1\) | \(q+(1-2\zeta_{6})q^{3}-q^{5}+(1-3\zeta_{6})q^{7}+\cdots\) |
1260.2.t.b | $2$ | $10.061$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(-2\) | \(4\) | \(q+(1-2\zeta_{6})q^{3}-q^{5}+(1+2\zeta_{6})q^{7}+\cdots\) |
1260.2.t.c | $2$ | $10.061$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(2\) | \(-4\) | \(q+(1-2\zeta_{6})q^{3}+q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\) |
1260.2.t.d | $26$ | $10.061$ | None | \(0\) | \(-1\) | \(26\) | \(3\) | ||
1260.2.t.e | $32$ | $10.061$ | None | \(0\) | \(1\) | \(-32\) | \(-4\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1260, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1260, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)