Defining parameters
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.o (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 180 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(360\) | ||
Trace bound: | \(8\) | ||
Distinguishing \(T_p\): | \(7\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(900, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 384 | 224 | 160 |
Cusp forms | 336 | 208 | 128 |
Eisenstein series | 48 | 16 | 32 |
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.o.a | $16$ | $7.187$ | 16.0.\(\cdots\).3 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{5}q^{2}+(-\beta _{5}-\beta _{14}-\beta _{15})q^{3}+\cdots\) |
900.2.o.b | $48$ | $7.187$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
900.2.o.c | $48$ | $7.187$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
900.2.o.d | $96$ | $7.187$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(900, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)