Defining parameters
Level: | \( N \) | \(=\) | \( 2448 = 2^{4} \cdot 3^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2448.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 12 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(864\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(2448, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 456 | 32 | 424 |
Cusp forms | 408 | 32 | 376 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(2448, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
2448.2.e.a | $8$ | $19.547$ | 8.0.18939904.2 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{4}q^{5}+(\beta _{6}+\beta _{7})q^{7}-\beta _{1}q^{11}+(-1+\cdots)q^{13}+\cdots\) |
2448.2.e.b | $24$ | $19.547$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(2448, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(2448, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(204, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(612, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(816, [\chi])\)\(^{\oplus 2}\)