Defining parameters
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(600, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 144 | 10 | 134 |
Cusp forms | 96 | 10 | 86 |
Eisenstein series | 48 | 0 | 48 |
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.f.a | $2$ | $4.791$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{3}+5iq^{7}-q^{9}-6q^{11}-3iq^{13}+\cdots\) |
600.2.f.b | $2$ | $4.791$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{3}-q^{9}-4q^{11}+6iq^{13}+6iq^{17}+\cdots\) |
600.2.f.c | $2$ | $4.791$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{3}-4iq^{7}-q^{9}-6iq^{13}+2iq^{17}+\cdots\) |
600.2.f.d | $2$ | $4.791$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{3}-3iq^{7}-q^{9}+2q^{11}-3iq^{13}+\cdots\) |
600.2.f.e | $2$ | $4.791$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{3}-q^{9}+4q^{11}+2iq^{13}+2iq^{17}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(600, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)