Defining parameters
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 19 \) |
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: | \(28\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{19}(10, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 58 | 18 | 40 |
Cusp forms | 50 | 18 | 32 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{19}^{\mathrm{new}}(10, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
10.19.c.a | $8$ | $20.539$ | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) | None | \(2048\) | \(37026\) | \(-3132450\) | \(-43579766\) | \(q+(2^{8}-2^{8}\beta _{1})q^{2}+(4628+4628\beta _{1}+\cdots)q^{3}+\cdots\) |
10.19.c.b | $10$ | $20.539$ | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) | None | \(-2560\) | \(3230\) | \(-1436130\) | \(-71828530\) | \(q+(-2^{8}-2^{8}\beta _{1})q^{2}+(323-323\beta _{1}+\cdots)q^{3}+\cdots\) |
Decomposition of \(S_{19}^{\mathrm{old}}(10, [\chi])\) into lower level spaces
\( S_{19}^{\mathrm{old}}(10, [\chi]) \cong \) \(S_{19}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)