Defining parameters
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
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: | \(22\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{15}(10, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 46 | 14 | 32 |
Cusp forms | 38 | 14 | 24 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{15}^{\mathrm{new}}(10, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
10.15.c.a | $6$ | $12.433$ | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) | None | \(-384\) | \(2912\) | \(82500\) | \(943128\) | \(q+(-2^{6}+2^{6}\beta _{1})q^{2}+(485+485\beta _{1}+\cdots)q^{3}+\cdots\) |
10.15.c.b | $8$ | $12.433$ | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) | None | \(512\) | \(1404\) | \(-100860\) | \(1333276\) | \(q+(2^{6}-2^{6}\beta _{1})q^{2}+(175+176\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\) |
Decomposition of \(S_{15}^{\mathrm{old}}(10, [\chi])\) into lower level spaces
\( S_{15}^{\mathrm{old}}(10, [\chi]) \cong \) \(S_{15}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)