Defining parameters
Level: | \( N \) | \(=\) | \( 1340 = 2^{2} \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1340.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(408\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1340, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 210 | 34 | 176 |
Cusp forms | 198 | 34 | 164 |
Eisenstein series | 12 | 0 | 12 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1340, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1340.2.d.a | $2$ | $10.700$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-4\) | \(0\) | \(q+iq^{3}+(-2+i)q^{5}+3iq^{7}+2q^{9}+\cdots\) |
1340.2.d.b | $8$ | $10.700$ | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) | None | \(0\) | \(0\) | \(16\) | \(0\) | \(q+\beta _{6}q^{3}+(2-\beta _{5})q^{5}+(-\beta _{1}-\beta _{5}+\cdots)q^{7}+\cdots\) |
1340.2.d.c | $24$ | $10.700$ | None | \(0\) | \(0\) | \(-10\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1340, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1340, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(335, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(670, [\chi])\)\(^{\oplus 2}\)