Defining parameters
Level: | \( N \) | \(=\) | \( 1870 = 2 \cdot 5 \cdot 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1870.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(648\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(3\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1870, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 332 | 80 | 252 |
Cusp forms | 316 | 80 | 236 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1870, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1870.2.b.a | $2$ | $14.932$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q-iq^{2}+2iq^{3}-q^{4}+(1-2i)q^{5}+\cdots\) |
1870.2.b.b | $2$ | $14.932$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q-iq^{2}+2iq^{3}-q^{4}+(1-2i)q^{5}+\cdots\) |
1870.2.b.c | $10$ | $14.932$ | 10.0.\(\cdots\).1 | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q-\beta _{3}q^{2}+\beta _{9}q^{3}-q^{4}+(\beta _{1}+\beta _{7})q^{5}+\cdots\) |
1870.2.b.d | $14$ | $14.932$ | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) | None | \(0\) | \(0\) | \(-6\) | \(0\) | \(q-\beta _{8}q^{2}-\beta _{1}q^{3}-q^{4}+(\beta _{4}+\beta _{7}+\beta _{11}+\cdots)q^{5}+\cdots\) |
1870.2.b.e | $26$ | $14.932$ | None | \(0\) | \(0\) | \(-4\) | \(0\) | ||
1870.2.b.f | $26$ | $14.932$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1870, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1870, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(935, [\chi])\)\(^{\oplus 2}\)