Defining parameters
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(2412\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8020))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1212 | 132 | 1080 |
Cusp forms | 1201 | 132 | 1069 |
Eisenstein series | 11 | 0 | 11 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(5\) | \(401\) | Fricke | Dim |
---|---|---|---|---|
\(-\) | \(+\) | \(+\) | $-$ | \(37\) |
\(-\) | \(+\) | \(-\) | $+$ | \(29\) |
\(-\) | \(-\) | \(+\) | $+$ | \(29\) |
\(-\) | \(-\) | \(-\) | $-$ | \(37\) |
Plus space | \(+\) | \(58\) | ||
Minus space | \(-\) | \(74\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8020))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 5 | 401 | |||||||
8020.2.a.a | $1$ | $64.040$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(-2\) | $-$ | $+$ | $-$ | \(q-q^{5}-2q^{7}-3q^{9}-4q^{11}+4q^{13}+\cdots\) | |
8020.2.a.b | $2$ | $64.040$ | \(\Q(\sqrt{3}) \) | None | \(0\) | \(-2\) | \(-2\) | \(0\) | $-$ | $+$ | $+$ | \(q+(-1+\beta )q^{3}-q^{5}+2\beta q^{7}+(1-2\beta )q^{9}+\cdots\) | |
8020.2.a.c | $28$ | $64.040$ | None | \(0\) | \(3\) | \(-28\) | \(-4\) | $-$ | $+$ | $-$ | |||
8020.2.a.d | $29$ | $64.040$ | None | \(0\) | \(-3\) | \(29\) | \(-8\) | $-$ | $-$ | $+$ | |||
8020.2.a.e | $35$ | $64.040$ | None | \(0\) | \(-1\) | \(-35\) | \(6\) | $-$ | $+$ | $+$ | |||
8020.2.a.f | $37$ | $64.040$ | None | \(0\) | \(3\) | \(37\) | \(4\) | $-$ | $-$ | $-$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8020))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8020)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(1604))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(401))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(802))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2005))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4010))\)\(^{\oplus 2}\)