Defining parameters
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(696\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4033))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 348 | 325 | 23 |
Cusp forms | 345 | 325 | 20 |
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.
\(37\) | \(109\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(80\) |
\(+\) | \(-\) | $-$ | \(83\) |
\(-\) | \(+\) | $-$ | \(85\) |
\(-\) | \(-\) | $+$ | \(77\) |
Plus space | \(+\) | \(157\) | |
Minus space | \(-\) | \(168\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4033))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 37 | 109 | |||||||
4033.2.a.a | $1$ | $32.204$ | \(\Q\) | None | \(-1\) | \(0\) | \(2\) | \(0\) | $+$ | $+$ | \(q-q^{2}-q^{4}+2q^{5}+3q^{8}-3q^{9}-2q^{10}+\cdots\) | |
4033.2.a.b | $1$ | $32.204$ | \(\Q\) | None | \(1\) | \(0\) | \(-2\) | \(2\) | $+$ | $-$ | \(q+q^{2}-q^{4}-2q^{5}+2q^{7}-3q^{8}-3q^{9}+\cdots\) | |
4033.2.a.c | $77$ | $32.204$ | None | \(-9\) | \(-27\) | \(-16\) | \(-23\) | $-$ | $-$ | |||
4033.2.a.d | $79$ | $32.204$ | None | \(-11\) | \(-11\) | \(-16\) | \(-15\) | $+$ | $+$ | |||
4033.2.a.e | $82$ | $32.204$ | None | \(10\) | \(17\) | \(22\) | \(15\) | $+$ | $-$ | |||
4033.2.a.f | $85$ | $32.204$ | None | \(11\) | \(21\) | \(12\) | \(17\) | $-$ | $+$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4033))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(4033)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(109))\)\(^{\oplus 2}\)