Defining parameters
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(360\) | ||
Trace bound: | \(19\) | ||
Distinguishing \(T_p\): | \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(900, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 216 | 8 | 208 |
Cusp forms | 144 | 8 | 136 |
Eisenstein series | 72 | 0 | 72 |
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.d.a | $2$ | $7.187$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{7}-6q^{11}+5iq^{13}-6iq^{17}+\cdots\) |
900.2.d.b | $2$ | $7.187$ | \(\Q(\sqrt{-1}) \) | \(\Q(\sqrt{-3}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+2iq^{7}+iq^{13}-8q^{19}-4q^{31}+\cdots\) |
900.2.d.c | $2$ | $7.187$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{7}-iq^{13}+3iq^{17}+4q^{19}+\cdots\) |
900.2.d.d | $2$ | $7.187$ | \(\Q(\sqrt{-1}) \) | \(\Q(\sqrt{-3}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{7}-7iq^{13}+7q^{19}+11q^{31}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(900, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 3}\)