Defining parameters
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.k (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(600, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 132 | 38 | 94 |
Cusp forms | 108 | 38 | 70 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(600, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
600.2.k.a | $2$ | $4.791$ | \(\Q(\sqrt{-1}) \) | None | \(-2\) | \(0\) | \(0\) | \(-4\) | \(q+(i-1)q^{2}-i q^{3}-2 i q^{4}+(i+1)q^{6}+\cdots\) |
600.2.k.b | $2$ | $4.791$ | \(\Q(\sqrt{-1}) \) | None | \(2\) | \(0\) | \(0\) | \(4\) | \(q+(i+1)q^{2}+i q^{3}+2 i q^{4}+(i-1)q^{6}+\cdots\) |
600.2.k.c | $6$ | $4.791$ | 6.0.399424.1 | None | \(-2\) | \(0\) | \(0\) | \(-4\) | \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(\beta _{2}-\beta _{3})q^{4}+\beta _{4}q^{6}+\cdots\) |
600.2.k.d | $8$ | $4.791$ | 8.0.214798336.3 | None | \(-2\) | \(0\) | \(0\) | \(8\) | \(q+\beta _{3}q^{2}+\beta _{2}q^{3}+(-\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\) |
600.2.k.e | $8$ | $4.791$ | 8.0.214798336.3 | None | \(2\) | \(0\) | \(0\) | \(-8\) | \(q-\beta _{3}q^{2}-\beta _{2}q^{3}+(-\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\) |
600.2.k.f | $12$ | $4.791$ | 12.0.\(\cdots\).1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}-\beta _{5}q^{6}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(600, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(600, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)