Defining parameters
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.k (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 16 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(19\) | ||
Distinguishing \(T_p\): | \(5\), \(11\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1152, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 448 | 44 | 404 |
Cusp forms | 320 | 36 | 284 |
Eisenstein series | 128 | 8 | 120 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1152, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1152.2.k.a | $2$ | $9.199$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q+(-1-i)q^{5}+2iq^{7}+(-1-i)q^{11}+\cdots\) |
1152.2.k.b | $2$ | $9.199$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q+(-1-i)q^{5}-2iq^{7}+(1+i)q^{11}+\cdots\) |
1152.2.k.c | $8$ | $9.199$ | 8.0.18939904.2 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\beta _{4}-\beta _{6})q^{5}+(-\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\) |
1152.2.k.d | $8$ | $9.199$ | 8.0.629407744.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{5}+(\beta _{3}-\beta _{7})q^{7}+(-\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\) |
1152.2.k.e | $8$ | $9.199$ | 8.0.629407744.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{5}+(-\beta _{3}+\beta _{7})q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\) |
1152.2.k.f | $8$ | $9.199$ | 8.0.18939904.2 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\beta _{4}-\beta _{6})q^{5}+(\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1152, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1152, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)