Defining parameters
Level: | \( N \) | = | \( 49 = 7^{2} \) |
Weight: | \( k \) | = | \( 2 \) |
Character orbit: | \([\chi]\) | = | 49.a (trivial) |
Character field: | \(\Q\) | ||
Newforms: | \( 1 \) | ||
Sturm bound: | \(9\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(49))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 8 | 6 | 2 |
Cusp forms | 1 | 1 | 0 |
Eisenstein series | 7 | 5 | 2 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(7\) | Dim. |
---|---|
\(-\) | \(1\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(49))\) into irreducible Hecke orbits
Label | Dim. | \(A\) | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | 7 | |||||||
49.2.a.a | \(1\) | \(0.391\) | \(\Q\) | \(\Q(\sqrt{-7}) \) | \(1\) | \(0\) | \(0\) | \(0\) | \(-\) | \(q+q^{2}-q^{4}-3q^{8}-3q^{9}+4q^{11}+\cdots\) |