Defining parameters
Level: | \( N \) | \(=\) | \( 6011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6011.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(1002\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6011))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 502 | 502 | 0 |
Cusp forms | 501 | 501 | 0 |
Eisenstein series | 1 | 1 | 0 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(6011\) | Dim |
---|---|
\(+\) | \(224\) |
\(-\) | \(277\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6011))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 6011 | |||||||
6011.2.a.a | $1$ | $47.998$ | \(\Q\) | None | \(-2\) | \(0\) | \(-2\) | \(1\) | $-$ | \(q-2q^{2}+2q^{4}-2q^{5}+q^{7}-3q^{9}+\cdots\) | |
6011.2.a.b | $1$ | $47.998$ | \(\Q\) | None | \(0\) | \(3\) | \(1\) | \(-1\) | $-$ | \(q+3q^{3}-2q^{4}+q^{5}-q^{7}+6q^{9}+6q^{11}+\cdots\) | |
6011.2.a.c | $1$ | $47.998$ | \(\Q\) | None | \(1\) | \(-1\) | \(-3\) | \(1\) | $+$ | \(q+q^{2}-q^{3}-q^{4}-3q^{5}-q^{6}+q^{7}+\cdots\) | |
6011.2.a.d | $2$ | $47.998$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(4\) | \(0\) | \(-2\) | $+$ | \(q+\beta q^{2}+2q^{3}+2\beta q^{5}+2\beta q^{6}-q^{7}+\cdots\) | |
6011.2.a.e | $221$ | $47.998$ | None | \(-15\) | \(-17\) | \(-32\) | \(-40\) | $+$ | |||
6011.2.a.f | $275$ | $47.998$ | None | \(16\) | \(9\) | \(36\) | \(41\) | $-$ |