Defining parameters
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.c (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(7\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(10, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 16 | 4 | 12 |
Cusp forms | 8 | 4 | 4 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(10, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
10.5.c.a | $2$ | $1.034$ | \(\Q(\sqrt{-1}) \) | None | \(-4\) | \(18\) | \(-30\) | \(58\) | \(q+(-2 i-2)q^{2}+(-9 i+9)q^{3}+\cdots\) |
10.5.c.b | $2$ | $1.034$ | \(\Q(\sqrt{-1}) \) | None | \(4\) | \(2\) | \(-30\) | \(-38\) | \(q+(2 i+2)q^{2}+(-i+1)q^{3}+8 i q^{4}+\cdots\) |
Decomposition of \(S_{5}^{\mathrm{old}}(10, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(10, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)