Defining parameters
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(10\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(25))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 11 | 6 | 5 |
Cusp forms | 5 | 3 | 2 |
Eisenstein series | 6 | 3 | 3 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(5\) | Dim |
---|---|
\(+\) | \(2\) |
\(-\) | \(1\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(25))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 5 | |||||||
25.4.a.a | $1$ | $1.475$ | \(\Q\) | None | \(-1\) | \(-7\) | \(0\) | \(-6\) | $-$ | \(q-q^{2}-7q^{3}-7q^{4}+7q^{6}-6q^{7}+\cdots\) | |
25.4.a.b | $1$ | $1.475$ | \(\Q\) | None | \(1\) | \(7\) | \(0\) | \(6\) | $+$ | \(q+q^{2}+7q^{3}-7q^{4}+7q^{6}+6q^{7}+\cdots\) | |
25.4.a.c | $1$ | $1.475$ | \(\Q\) | None | \(4\) | \(-2\) | \(0\) | \(-6\) | $+$ | \(q+4q^{2}-2q^{3}+8q^{4}-8q^{6}-6q^{7}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(25))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(25)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)