Defining parameters
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 11 \) | ||
Sturm bound: | \(2120\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8018))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1064 | 315 | 749 |
Cusp forms | 1057 | 315 | 742 |
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.
\(2\) | \(19\) | \(211\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(36\) |
\(+\) | \(+\) | \(-\) | $-$ | \(42\) |
\(+\) | \(-\) | \(+\) | $-$ | \(45\) |
\(+\) | \(-\) | \(-\) | $+$ | \(34\) |
\(-\) | \(+\) | \(+\) | $-$ | \(47\) |
\(-\) | \(+\) | \(-\) | $+$ | \(32\) |
\(-\) | \(-\) | \(+\) | $+$ | \(30\) |
\(-\) | \(-\) | \(-\) | $-$ | \(49\) |
Plus space | \(+\) | \(132\) | ||
Minus space | \(-\) | \(183\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 19 | 211 | |||||||
8018.2.a.a | $1$ | $64.024$ | \(\Q\) | None | \(-1\) | \(2\) | \(1\) | \(-4\) | $+$ | $+$ | $-$ | \(q-q^{2}+2q^{3}+q^{4}+q^{5}-2q^{6}-4q^{7}+\cdots\) | |
8018.2.a.b | $2$ | $64.024$ | \(\Q(\sqrt{5}) \) | None | \(-2\) | \(1\) | \(0\) | \(4\) | $+$ | $+$ | $+$ | \(q-q^{2}+\beta q^{3}+q^{4}+(-1+2\beta )q^{5}+\cdots\) | |
8018.2.a.c | $2$ | $64.024$ | \(\Q(\sqrt{5}) \) | None | \(-2\) | \(3\) | \(0\) | \(4\) | $+$ | $-$ | $+$ | \(q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1+2\beta )q^{5}+\cdots\) | |
8018.2.a.d | $30$ | $64.024$ | None | \(30\) | \(-10\) | \(-12\) | \(-15\) | $-$ | $-$ | $+$ | |||
8018.2.a.e | $32$ | $64.024$ | None | \(32\) | \(-7\) | \(-6\) | \(-5\) | $-$ | $+$ | $-$ | |||
8018.2.a.f | $34$ | $64.024$ | None | \(-34\) | \(-10\) | \(7\) | \(-6\) | $+$ | $+$ | $+$ | |||
8018.2.a.g | $34$ | $64.024$ | None | \(-34\) | \(-6\) | \(1\) | \(-22\) | $+$ | $-$ | $-$ | |||
8018.2.a.h | $41$ | $64.024$ | None | \(-41\) | \(8\) | \(-9\) | \(7\) | $+$ | $+$ | $-$ | |||
8018.2.a.i | $43$ | $64.024$ | None | \(-43\) | \(0\) | \(0\) | \(19\) | $+$ | $-$ | $+$ | |||
8018.2.a.j | $47$ | $64.024$ | None | \(47\) | \(10\) | \(15\) | \(0\) | $-$ | $+$ | $+$ | |||
8018.2.a.k | $49$ | $64.024$ | None | \(49\) | \(13\) | \(17\) | \(22\) | $-$ | $-$ | $-$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8018))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8018)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(422))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4009))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(211))\)\(^{\oplus 4}\)