Defining parameters
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.j (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 20 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(720\) | ||
Trace bound: | \(29\) | ||
Distinguishing \(T_p\): | \(7\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(1200, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 516 | 36 | 480 |
Cusp forms | 444 | 36 | 408 |
Eisenstein series | 72 | 0 | 72 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1200.3.j.a | $4$ | $32.698$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{12}q^{3}-4\zeta_{12}q^{7}+3q^{9}-6\zeta_{12}^{2}q^{11}+\cdots\) |
1200.3.j.b | $4$ | $32.698$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{12}^{3}q^{3}-3\zeta_{12}^{3}q^{7}+3q^{9}+2\zeta_{12}^{2}q^{11}+\cdots\) |
1200.3.j.c | $4$ | $32.698$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{12}^{3}q^{3}-\zeta_{12}^{3}q^{7}+3q^{9}-2\zeta_{12}^{2}q^{11}+\cdots\) |
1200.3.j.d | $8$ | $32.698$ | 8.0.303595776.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{5})q^{7}+3q^{9}-\beta _{4}q^{11}+\cdots\) |
1200.3.j.e | $8$ | $32.698$ | 8.0.12960000.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{3}+(-2\beta _{1}-\beta _{6})q^{7}+3q^{9}+\cdots\) |
1200.3.j.f | $8$ | $32.698$ | 8.0.12960000.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{3}+(-2\beta _{1}+\beta _{6})q^{7}+3q^{9}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(1200, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)