Defining parameters
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.u (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 45 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(540\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(900, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 756 | 72 | 684 |
Cusp forms | 684 | 72 | 612 |
Eisenstein series | 72 | 0 | 72 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(900, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
900.3.u.a | $8$ | $24.523$ | 8.0.303595776.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\beta _{1}-\beta _{5}-\beta _{7})q^{3}+(-3\beta _{1}-3\beta _{4}+\cdots)q^{7}+\cdots\) |
900.3.u.b | $8$ | $24.523$ | 8.0.12960000.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+3\beta _{1}q^{3}+(4\beta _{1}+\beta _{6})q^{7}-9\beta _{2}q^{9}+\cdots\) |
900.3.u.c | $24$ | $24.523$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
900.3.u.d | $32$ | $24.523$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{3}^{\mathrm{old}}(900, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)