Properties

Label 49.2.a
Level 49
Weight 2
Character orbit a
Rep. character \(\chi_{49}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 9
Trace bound 0

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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

\(q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut q^{16} \) \(\mathstrut -\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut -\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 5q^{32} \) \(\mathstrut +\mathstrut 3q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut -\mathstrut 12q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 8q^{46} \) \(\mathstrut -\mathstrut 5q^{50} \) \(\mathstrut -\mathstrut 10q^{53} \) \(\mathstrut +\mathstrut 2q^{58} \) \(\mathstrut +\mathstrut 7q^{64} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 16q^{71} \) \(\mathstrut +\mathstrut 9q^{72} \) \(\mathstrut -\mathstrut 6q^{74} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 9q^{81} \) \(\mathstrut -\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 12q^{88} \) \(\mathstrut -\mathstrut 8q^{92} \) \(\mathstrut -\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \(1\) \(0.391\) \(\Q\) \(\Q(\sqrt{-7}) \) \(1\) \(0\) \(0\) \(0\) \(-\) \(q+q^{2}-q^{4}-3q^{8}-3q^{9}+4q^{11}+\cdots\)