Defining parameters
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.h (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 20 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(540\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(400, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 498 | 72 | 426 |
Cusp forms | 462 | 72 | 390 |
Eisenstein series | 36 | 0 | 36 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(400, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
400.9.h.a | $4$ | $162.951$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{12}^{2}q^{3}-238\zeta_{12}^{2}q^{7}-6369q^{9}+\cdots\) |
400.9.h.b | $4$ | $162.951$ | \(\Q(i, \sqrt{35})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{3}-18\beta _{2}q^{7}+13599q^{9}-3^{3}\beta _{3}q^{11}+\cdots\) |
400.9.h.c | $8$ | $162.951$ | 8.0.12960000.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{3}+(28\beta _{1}-7\beta _{4})q^{7}+(-3111+\cdots)q^{9}+\cdots\) |
400.9.h.d | $12$ | $162.951$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{6}q^{3}+(7\beta _{6}-\beta _{7})q^{7}+(1794+\beta _{1}+\cdots)q^{9}+\cdots\) |
400.9.h.e | $20$ | $162.951$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{3}-\beta _{4}q^{7}+(2994+\beta _{5})q^{9}+\cdots\) |
400.9.h.f | $24$ | $162.951$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{9}^{\mathrm{old}}(400, [\chi])\) into lower level spaces
\( S_{9}^{\mathrm{old}}(400, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)