Defining parameters
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 10 \) | ||
Sturm bound: | \(1584\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8041))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 796 | 559 | 237 |
Cusp forms | 789 | 559 | 230 |
Eisenstein series | 7 | 0 | 7 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(11\) | \(17\) | \(43\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(74\) |
\(+\) | \(+\) | \(-\) | $-$ | \(66\) |
\(+\) | \(-\) | \(+\) | $-$ | \(67\) |
\(+\) | \(-\) | \(-\) | $+$ | \(69\) |
\(-\) | \(+\) | \(+\) | $-$ | \(78\) |
\(-\) | \(+\) | \(-\) | $+$ | \(62\) |
\(-\) | \(-\) | \(+\) | $+$ | \(61\) |
\(-\) | \(-\) | \(-\) | $-$ | \(82\) |
Plus space | \(+\) | \(266\) | ||
Minus space | \(-\) | \(293\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8041))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 11 | 17 | 43 | |||||||
8041.2.a.a | $1$ | $64.208$ | \(\Q\) | None | \(-2\) | \(-2\) | \(2\) | \(3\) | $-$ | $-$ | $+$ | \(q-2q^{2}-2q^{3}+2q^{4}+2q^{5}+4q^{6}+\cdots\) | |
8041.2.a.b | $1$ | $64.208$ | \(\Q\) | None | \(-1\) | \(3\) | \(-2\) | \(-2\) | $+$ | $-$ | $+$ | \(q-q^{2}+3q^{3}-q^{4}-2q^{5}-3q^{6}-2q^{7}+\cdots\) | |
8041.2.a.c | $60$ | $64.208$ | None | \(-9\) | \(-6\) | \(-15\) | \(-17\) | $-$ | $-$ | $+$ | |||
8041.2.a.d | $62$ | $64.208$ | None | \(-7\) | \(-8\) | \(-13\) | \(-11\) | $-$ | $+$ | $-$ | |||
8041.2.a.e | $66$ | $64.208$ | None | \(7\) | \(3\) | \(4\) | \(14\) | $+$ | $+$ | $-$ | |||
8041.2.a.f | $66$ | $64.208$ | None | \(12\) | \(0\) | \(6\) | \(13\) | $+$ | $-$ | $+$ | |||
8041.2.a.g | $69$ | $64.208$ | None | \(-11\) | \(-3\) | \(-6\) | \(-11\) | $+$ | $-$ | $-$ | |||
8041.2.a.h | $74$ | $64.208$ | None | \(-7\) | \(-3\) | \(-6\) | \(-16\) | $+$ | $+$ | $+$ | |||
8041.2.a.i | $78$ | $64.208$ | None | \(7\) | \(10\) | \(17\) | \(11\) | $-$ | $+$ | $+$ | |||
8041.2.a.j | $82$ | $64.208$ | None | \(8\) | \(6\) | \(11\) | \(8\) | $-$ | $-$ | $-$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8041))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8041)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(187))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(473))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(731))\)\(^{\oplus 2}\)