Defining parameters
Level: | \( N \) | \(=\) | \( 520 = 2^{3} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 520.k (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
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 | 14 | 78 |
Cusp forms | 76 | 14 | 62 |
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.k.a | $6$ | $4.152$ | 6.0.350464.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(\beta _{3}-\beta _{4}+\beta _{5})q^{7}+\cdots\) |
520.2.k.b | $8$ | $4.152$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(4\) | \(0\) | \(0\) | \(q-\beta _{3}q^{3}-\beta _{2}q^{5}+(\beta _{2}+\beta _{4}-\beta _{5})q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(520, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 2}\)