Defining parameters
Level: | \( N \) | \(=\) | \( 402 = 2 \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 402.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 201 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(136\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(402, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 72 | 24 | 48 |
Cusp forms | 64 | 24 | 40 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(402, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
402.2.d.a | $12$ | $3.210$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(-12\) | \(1\) | \(0\) | \(0\) | \(q-q^{2}+\beta _{8}q^{3}+q^{4}-\beta _{7}q^{5}-\beta _{8}q^{6}+\cdots\) |
402.2.d.b | $12$ | $3.210$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(12\) | \(-1\) | \(0\) | \(0\) | \(q+q^{2}-\beta _{8}q^{3}+q^{4}+\beta _{7}q^{5}-\beta _{8}q^{6}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(402, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(402, [\chi]) \cong \)