Defining parameters
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(64\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(224, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 40 | 6 | 34 |
Cusp forms | 24 | 6 | 18 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(224, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
224.2.b.a | $2$ | $1.789$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(-2\) | \(q+\beta q^{3}+\beta q^{5}-q^{7}+q^{9}+2\beta q^{11}+\cdots\) |
224.2.b.b | $4$ | $1.789$ | 4.0.2312.1 | None | \(0\) | \(0\) | \(0\) | \(4\) | \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+q^{7}+(-2+\beta _{3})q^{9}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(224, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(224, [\chi]) \cong \)