Defining parameters
Level: | \( N \) | \(=\) | \( 238 = 2 \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 238.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 17 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(72\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(238, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 40 | 8 | 32 |
Cusp forms | 32 | 8 | 24 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(238, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
238.2.b.a | $2$ | $1.900$ | \(\Q(\sqrt{-1}) \) | None | \(-2\) | \(0\) | \(0\) | \(0\) | \(q-q^{2}+q^{4}+iq^{7}-q^{8}+3q^{9}+2q^{13}+\cdots\) |
238.2.b.b | $6$ | $1.900$ | 6.0.350464.1 | None | \(6\) | \(0\) | \(0\) | \(0\) | \(q+q^{2}+(\beta _{1}+\beta _{4})q^{3}+q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(238, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(238, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 2}\)