Defining parameters
Level: | \( N \) | \(=\) | \( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 510.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 85 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(216\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(510, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 116 | 20 | 96 |
Cusp forms | 100 | 20 | 80 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(510, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
510.2.f.a | $4$ | $4.072$ | \(\Q(i, \sqrt{6})\) | None | \(0\) | \(-4\) | \(4\) | \(-8\) | \(q+\beta _{2}q^{2}-q^{3}-q^{4}+(1+\beta _{2}-\beta _{3})q^{5}+\cdots\) |
510.2.f.b | $4$ | $4.072$ | \(\Q(i, \sqrt{6})\) | None | \(0\) | \(4\) | \(-4\) | \(8\) | \(q+\beta _{2}q^{2}+q^{3}-q^{4}+(-1-\beta _{2}-\beta _{3})q^{5}+\cdots\) |
510.2.f.c | $6$ | $4.072$ | 6.0.350464.1 | None | \(0\) | \(-6\) | \(-2\) | \(4\) | \(q+\beta _{4}q^{2}-q^{3}-q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\) |
510.2.f.d | $6$ | $4.072$ | 6.0.350464.1 | None | \(0\) | \(6\) | \(2\) | \(-4\) | \(q-\beta _{4}q^{2}+q^{3}-q^{4}+(-\beta _{1}-\beta _{5})q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(510, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(510, [\chi]) \cong \)