Defining parameters
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 24 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(60\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{24}(25, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 60 | 36 | 24 |
Cusp forms | 54 | 34 | 20 |
Eisenstein series | 6 | 2 | 4 |
Trace form
Decomposition of \(S_{24}^{\mathrm{new}}(25, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
25.24.b.a | $4$ | $83.801$ | \(\mathbb{Q}[x]/(x^{4} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(54\beta _{1}+\beta _{2})q^{2}+(-16974\beta _{1}+48\beta _{2}+\cdots)q^{3}+\cdots\) |
25.24.b.b | $6$ | $83.801$ | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\beta _{1}-\beta _{2})q^{2}+(-2^{6}\beta _{1}-179\beta _{2}+\cdots)q^{3}+\cdots\) |
25.24.b.c | $8$ | $83.801$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{2}+(-35\beta _{1}+39\beta _{2}-\beta _{3})q^{3}+\cdots\) |
25.24.b.d | $16$ | $83.801$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(-9\beta _{1}+\beta _{9})q^{3}+(-4381999+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{24}^{\mathrm{old}}(25, [\chi])\) into lower level spaces
\( S_{24}^{\mathrm{old}}(25, [\chi]) \cong \) \(S_{24}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)