Defining parameters
Level: | \( N \) | \(=\) | \( 4176 = 2^{4} \cdot 3^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4176.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 12 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(1440\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(5\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4176, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 744 | 56 | 688 |
Cusp forms | 696 | 56 | 640 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(4176, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
4176.2.e.a | $4$ | $33.346$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(2\zeta_{8}-\zeta_{8}^{2})q^{5}+(-\zeta_{8}+2\zeta_{8}^{2})q^{7}+\cdots\) |
4176.2.e.b | $4$ | $33.346$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+2\zeta_{8}q^{5}+(-\zeta_{8}+2\zeta_{8}^{2})q^{7}+(-3+\cdots)q^{11}+\cdots\) |
4176.2.e.c | $4$ | $33.346$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(2\zeta_{8}-\zeta_{8}^{2})q^{5}+(\zeta_{8}-2\zeta_{8}^{2})q^{7}+\cdots\) |
4176.2.e.d | $4$ | $33.346$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+2\zeta_{8}q^{5}+(\zeta_{8}-2\zeta_{8}^{2})q^{7}+(3+\zeta_{8}^{3})q^{11}+\cdots\) |
4176.2.e.e | $40$ | $33.346$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(4176, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(4176, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(348, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(696, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1044, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1392, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2088, [\chi])\)\(^{\oplus 2}\)