Defining parameters
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(720\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(1050, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 504 | 76 | 428 |
Cusp forms | 456 | 76 | 380 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(1050, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1050.3.e.a | $4$ | $28.610$ | \(\Q(\sqrt{-2}, \sqrt{7})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}-2q^{4}+(-2+\cdots)q^{6}+\cdots\) |
1050.3.e.b | $16$ | $28.610$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(-4\) | \(0\) | \(0\) | \(q+\beta _{3}q^{2}+\beta _{2}q^{3}-2q^{4}-\beta _{9}q^{6}+\beta _{6}q^{7}+\cdots\) |
1050.3.e.c | $16$ | $28.610$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(4\) | \(0\) | \(0\) | \(q-\beta _{3}q^{2}-\beta _{2}q^{3}-2q^{4}-\beta _{9}q^{6}-\beta _{6}q^{7}+\cdots\) |
1050.3.e.d | $16$ | $28.610$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(8\) | \(0\) | \(0\) | \(q-\beta _{2}q^{2}+\beta _{6}q^{3}-2q^{4}+(1+\beta _{7})q^{6}+\cdots\) |
1050.3.e.e | $24$ | $28.610$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{3}^{\mathrm{old}}(1050, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(1050, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)