Defining parameters
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.m (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 120 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(6\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(29\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(600, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 132 | 76 | 56 |
Cusp forms | 108 | 68 | 40 |
Eisenstein series | 24 | 8 | 16 |
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.m.a | $4$ | $4.791$ | \(\Q(\zeta_{8})\) | \(\Q(\sqrt{-2}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{8}^{3}q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+2q^{4}+\cdots\) |
600.2.m.b | $8$ | $4.791$ | \(\Q(\zeta_{24})\) | \(\Q(\sqrt{-2}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{24}^{2}q^{2}-\zeta_{24}^{3}q^{3}+2q^{4}+(-1+\cdots)q^{6}+\cdots\) |
600.2.m.c | $16$ | $4.791$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+(-1+\beta _{11}+\cdots)q^{6}+\cdots\) |
600.2.m.d | $16$ | $4.791$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+\beta _{6}q^{3}+\beta _{2}q^{4}-\beta _{14}q^{6}+\cdots\) |
600.2.m.e | $24$ | $4.791$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(600, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)