Defining parameters
Level: | \( N \) | \(=\) | \( 520 = 2^{3} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 520.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(168\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(520, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 92 | 18 | 74 |
Cusp forms | 76 | 18 | 58 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(520, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
520.2.d.a | $2$ | $4.152$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(4\) | \(0\) | \(q+(2+i)q^{5}-4iq^{7}+3q^{9}-2q^{11}+\cdots\) |
520.2.d.b | $6$ | $4.152$ | 6.0.350464.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\beta _{3}+\beta _{4})q^{3}+(\beta _{1}+\beta _{4})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\) |
520.2.d.c | $10$ | $4.152$ | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) | None | \(0\) | \(0\) | \(-4\) | \(0\) | \(q-\beta _{9}q^{3}-\beta _{1}q^{5}-\beta _{4}q^{7}+(-4-\beta _{5}+\cdots)q^{9}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(520, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 2}\)