Defining parameters
Level: | \( N \) | \(=\) | \( 473 = 11 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 473.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 473 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(88\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\), \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(473, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 46 | 46 | 0 |
Cusp forms | 42 | 42 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(473, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
473.2.d.a | $2$ | $3.777$ | \(\Q(\sqrt{-43}) \) | \(\Q(\sqrt{-43}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-2q^{4}+3q^{9}+(1-\beta )q^{11}+(-1+2\beta )q^{13}+\cdots\) |
473.2.d.b | $4$ | $3.777$ | \(\Q(\sqrt{-2}, \sqrt{13})\) | None | \(-2\) | \(0\) | \(0\) | \(-4\) | \(q-\beta _{3}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(1+\beta _{3})q^{4}+\cdots\) |
473.2.d.c | $4$ | $3.777$ | \(\Q(\sqrt{-2}, \sqrt{-5})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{3}q^{3}-2q^{4}+\beta _{3}q^{5}+(-2\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\) |
473.2.d.d | $4$ | $3.777$ | \(\Q(\sqrt{-2}, \sqrt{13})\) | None | \(2\) | \(0\) | \(0\) | \(4\) | \(q+\beta _{3}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(1+\beta _{3})q^{4}+\cdots\) |
473.2.d.e | $28$ | $3.777$ | None | \(0\) | \(0\) | \(0\) | \(0\) |