Defining parameters
Level: | \( N \) | \(=\) | \( 2496 = 2^{6} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2496.m (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 104 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(896\) | ||
Trace bound: | \(17\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(2496, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 472 | 56 | 416 |
Cusp forms | 424 | 56 | 368 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(2496, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
2496.2.m.a | $8$ | $19.931$ | 8.0.40960000.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{3}-\beta _{3}q^{5}-q^{9}-\beta _{7}q^{11}+(2\beta _{3}+\cdots)q^{13}+\cdots\) |
2496.2.m.b | $8$ | $19.931$ | 8.0.1871773696.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{3}-\beta _{3}q^{5}+2\beta _{4}q^{7}-q^{9}-\beta _{6}q^{11}+\cdots\) |
2496.2.m.c | $16$ | $19.931$ | 16.0.\(\cdots\).1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{3}-\beta _{11}q^{5}-\beta _{14}q^{7}-q^{9}+\cdots\) |
2496.2.m.d | $24$ | $19.931$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(2496, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(2496, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(832, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1248, [\chi])\)\(^{\oplus 2}\)