Defining parameters
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.v (of order \(10\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 300 \) |
Character field: | \(\Q(\zeta_{10})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(360\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(900, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 752 | 240 | 512 |
Cusp forms | 688 | 240 | 448 |
Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(900, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
900.2.v.a | $16$ | $7.187$ | \(\Q(\zeta_{40})\) | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{40}^{6}q^{2}+2\zeta_{40}^{7}q^{4}-\zeta_{40}^{8}q^{5}+\cdots\) |
900.2.v.b | $224$ | $7.187$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(900, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)