Defining parameters
Level: | \( N \) | \(=\) | \( 945 = 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 945.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(2\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(945, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 156 | 48 | 108 |
Cusp forms | 132 | 48 | 84 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(945, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
945.2.d.a | $2$ | $7.546$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q+iq^{2}+q^{4}+(-1-2i)q^{5}-iq^{7}+\cdots\) |
945.2.d.b | $2$ | $7.546$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q+iq^{2}+q^{4}+(1-2i)q^{5}+iq^{7}+3iq^{8}+\cdots\) |
945.2.d.c | $8$ | $7.546$ | 8.0.49787136.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{2}+(-1-\beta _{4})q^{4}+(-\beta _{5}+\beta _{6}+\cdots)q^{5}+\cdots\) |
945.2.d.d | $10$ | $7.546$ | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+\beta _{3}q^{5}-\beta _{5}q^{7}+\cdots\) |
945.2.d.e | $10$ | $7.546$ | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+\beta _{4}q^{5}+\beta _{5}q^{7}+\cdots\) |
945.2.d.f | $16$ | $7.546$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{10}q^{2}+(-2-\beta _{7})q^{4}-\beta _{9}q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(945, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(945, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)