Defining parameters
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.bf (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 180 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(360\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(900, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 768 | 448 | 320 |
Cusp forms | 672 | 416 | 256 |
Eisenstein series | 96 | 32 | 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.bf.a | $8$ | $7.187$ | 8.0.12960000.1 | \(\Q(\sqrt{-5}) \) | \(-4\) | \(-2\) | \(0\) | \(-6\) | \(q+(-1+\beta _{4}+\beta _{7})q^{2}+(\beta _{1}+\beta _{3})q^{3}+\cdots\) |
900.2.bf.b | $8$ | $7.187$ | 8.0.12960000.1 | \(\Q(\sqrt{-5}) \) | \(4\) | \(2\) | \(0\) | \(6\) | \(q+(1-\beta _{4}+\beta _{7})q^{2}+(\beta _{1}+\beta _{2})q^{3}+2\beta _{1}q^{4}+\cdots\) |
900.2.bf.c | $16$ | $7.187$ | 16.0.\(\cdots\).1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\beta _{1}-\beta _{3}+\beta _{13})q^{2}+(-\beta _{9}-2\beta _{15})q^{3}+\cdots\) |
900.2.bf.d | $64$ | $7.187$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
900.2.bf.e | $128$ | $7.187$ | None | \(2\) | \(0\) | \(0\) | \(0\) | ||
900.2.bf.f | $192$ | $7.187$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(900, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)