Defining parameters
Level: | \( N \) | \(=\) | \( 152 = 2^{3} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 152.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 19 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(60\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(152, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 44 | 10 | 34 |
Cusp forms | 36 | 10 | 26 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(152, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
152.3.e.a | $2$ | $4.142$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(14\) | \(22\) | \(q+\beta q^{3}+7q^{5}+11q^{7}-23q^{9}+3q^{11}+\cdots\) |
152.3.e.b | $8$ | $4.142$ | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) | None | \(0\) | \(0\) | \(-14\) | \(-6\) | \(q+\beta _{1}q^{3}+(-2-\beta _{4})q^{5}+(-1+\beta _{3}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(152, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(152, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)