Defining parameters
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.c (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(12\) | ||
Trace bound: | \(6\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(25, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 26 | 14 | 12 |
Cusp forms | 14 | 10 | 4 |
Eisenstein series | 12 | 4 | 8 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(25, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
25.5.c.a | $2$ | $2.584$ | \(\Q(\sqrt{-1}) \) | None | \(2\) | \(12\) | \(0\) | \(52\) | \(q+(1+i)q^{2}+(6-6i)q^{3}-14iq^{4}+\cdots\) |
25.5.c.b | $4$ | $2.584$ | \(\Q(i, \sqrt{6})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+3\beta _{1}q^{2}+7\beta _{3}q^{3}+11\beta _{2}q^{4}-63q^{6}+\cdots\) |
25.5.c.c | $4$ | $2.584$ | \(\Q(i, \sqrt{21})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{3}q^{2}+\beta _{2}q^{3}-26\beta _{1}q^{4}+42q^{6}+\cdots\) |
Decomposition of \(S_{5}^{\mathrm{old}}(25, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(25, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)