Defining parameters
Level: | \( N \) | \(=\) | \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1890.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(864\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(11\), \(17\), \(41\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1890, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 456 | 40 | 416 |
Cusp forms | 408 | 40 | 368 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1890, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1890.2.b.a | $8$ | $15.092$ | 8.0.303595776.1 | None | \(0\) | \(0\) | \(-8\) | \(0\) | \(q-\beta _{4}q^{2}-q^{4}-q^{5}+(\beta _{1}-\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots\) |
1890.2.b.b | $8$ | $15.092$ | 8.0.303595776.1 | None | \(0\) | \(0\) | \(8\) | \(0\) | \(q-\beta _{4}q^{2}-q^{4}+q^{5}+(-\beta _{1}+\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots\) |
1890.2.b.c | $12$ | $15.092$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(0\) | \(-12\) | \(-4\) | \(q-\beta _{5}q^{2}-q^{4}-q^{5}-\beta _{4}q^{7}+\beta _{5}q^{8}+\cdots\) |
1890.2.b.d | $12$ | $15.092$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(0\) | \(12\) | \(-4\) | \(q-\beta _{5}q^{2}-q^{4}+q^{5}+\beta _{6}q^{7}+\beta _{5}q^{8}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1890, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1890, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)