Defining parameters
Level: | \( N \) | \(=\) | \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1872.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 12 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(672\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1872, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 360 | 24 | 336 |
Cusp forms | 312 | 24 | 288 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1872, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1872.2.d.a | $4$ | $14.948$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{8}^{3}q^{11}-q^{13}-\zeta_{8}^{2}q^{17}-\zeta_{8}q^{19}+\cdots\) |
1872.2.d.b | $4$ | $14.948$ | \(\Q(\sqrt{-2}, \sqrt{-5})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-2\beta _{1}q^{5}-\beta _{3}q^{7}+\beta _{2}q^{11}+q^{13}+\cdots\) |
1872.2.d.c | $8$ | $14.948$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{24}^{5}q^{5}+(-\zeta_{24}+\zeta_{24}^{3})q^{7}+\zeta_{24}^{2}q^{11}+\cdots\) |
1872.2.d.d | $8$ | $14.948$ | 8.0.3317760000.8 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{5}-\beta _{1}q^{7}+\beta _{5}q^{11}+q^{13}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1872, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1872, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 2}\)