Defining parameters
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.x (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 37 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(456\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1110, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 472 | 56 | 416 |
Cusp forms | 440 | 56 | 384 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1110, [\chi])\) into newform subspaces
Label | Dim. | \(A\) | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||
1110.2.x.a | \(4\) | \(8.863\) | \(\Q(\zeta_{12})\) | None | \(0\) | \(2\) | \(0\) | \(2\) | \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}+\cdots)q^{5}+\cdots\) |
1110.2.x.b | \(4\) | \(8.863\) | \(\Q(\zeta_{12})\) | None | \(0\) | \(2\) | \(0\) | \(2\) | \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+(\zeta_{12}+\cdots)q^{5}+\cdots\) |
1110.2.x.c | \(16\) | \(8.863\) | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(-8\) | \(0\) | \(-2\) | \(q+(-\beta _{6}+\beta _{10})q^{2}+\beta _{9}q^{3}-\beta _{9}q^{4}+\cdots\) |
1110.2.x.d | \(16\) | \(8.863\) | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(-8\) | \(0\) | \(-2\) | \(q+(\beta _{3}+\beta _{5})q^{2}-\beta _{9}q^{3}+\beta _{9}q^{4}+\beta _{3}q^{5}+\cdots\) |
1110.2.x.e | \(16\) | \(8.863\) | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(8\) | \(0\) | \(-4\) | \(q+\beta _{6}q^{2}-\beta _{1}q^{3}-\beta _{1}q^{4}-\beta _{7}q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1110, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1110, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 2}\)