Defining parameters
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 37 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(12\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{37}(3, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 13 | 13 | 0 |
Cusp forms | 11 | 11 | 0 |
Eisenstein series | 2 | 2 | 0 |
Trace form
Decomposition of \(S_{37}^{\mathrm{new}}(3, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
3.37.b.a | $1$ | $24.627$ | \(\Q\) | \(\Q(\sqrt{-3}) \) | \(0\) | \(387420489\) | \(0\) | \(27\!\cdots\!98\) | \(q+3^{18}q^{3}+2^{36}q^{4}+2757049053441698q^{7}+\cdots\) |
3.37.b.b | $10$ | $24.627$ | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) | None | \(0\) | \(-552156750\) | \(0\) | \(-12\!\cdots\!00\) | \(q+\beta _{1}q^{2}+(-55215675-69\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\) |