Defining parameters
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 76 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(380, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 64 | 40 | 24 |
Cusp forms | 56 | 40 | 16 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(380, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
380.2.f.a | $20$ | $3.034$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(0\) | \(0\) | \(-20\) | \(0\) | \(q-\beta _{12}q^{2}+\beta _{10}q^{3}+\beta _{16}q^{4}-q^{5}+\cdots\) |
380.2.f.b | $20$ | $3.034$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(0\) | \(0\) | \(20\) | \(0\) | \(q-\beta _{15}q^{2}+\beta _{9}q^{3}-\beta _{19}q^{4}+q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(380, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(380, [\chi]) \cong \)