Defining parameters
Level: | \( N \) | \(=\) | \( 8045 = 5 \cdot 1609 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8045.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(1610\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8045))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 806 | 537 | 269 |
Cusp forms | 803 | 537 | 266 |
Eisenstein series | 3 | 0 | 3 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(5\) | \(1609\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(126\) |
\(+\) | \(-\) | $-$ | \(142\) |
\(-\) | \(+\) | $-$ | \(142\) |
\(-\) | \(-\) | $+$ | \(127\) |
Plus space | \(+\) | \(253\) | |
Minus space | \(-\) | \(284\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8045))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 5 | 1609 | |||||||
8045.2.a.a | $1$ | $64.240$ | \(\Q\) | None | \(1\) | \(0\) | \(-1\) | \(-2\) | $+$ | $-$ | \(q+q^{2}-q^{4}-q^{5}-2q^{7}-3q^{8}-3q^{9}+\cdots\) | |
8045.2.a.b | $126$ | $64.240$ | None | \(5\) | \(-9\) | \(-126\) | \(-23\) | $+$ | $+$ | |||
8045.2.a.c | $127$ | $64.240$ | None | \(-20\) | \(-31\) | \(127\) | \(-63\) | $-$ | $-$ | |||
8045.2.a.d | $141$ | $64.240$ | None | \(-8\) | \(11\) | \(-141\) | \(29\) | $+$ | $-$ | |||
8045.2.a.e | $142$ | $64.240$ | None | \(21\) | \(33\) | \(142\) | \(63\) | $-$ | $+$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8045))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8045)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(1609))\)\(^{\oplus 2}\)