Defining parameters
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.h (of order \(5\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 25 \) |
Character field: | \(\Q(\zeta_{5})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(225, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 376 | 156 | 220 |
Cusp forms | 344 | 148 | 196 |
Eisenstein series | 32 | 8 | 24 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(225, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
225.4.h.a | $28$ | $13.275$ | None | \(0\) | \(0\) | \(15\) | \(-54\) | ||
225.4.h.b | $28$ | $13.275$ | None | \(1\) | \(0\) | \(20\) | \(-16\) | ||
225.4.h.c | $28$ | $13.275$ | None | \(4\) | \(0\) | \(-15\) | \(58\) | ||
225.4.h.d | $64$ | $13.275$ | None | \(0\) | \(0\) | \(0\) | \(20\) |
Decomposition of \(S_{4}^{\mathrm{old}}(225, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(225, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)