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Properties

Label 49.2.a
Level $49$
Weight $2$
Character orbit 49.a
Rep. character $\chi_{49}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(49))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7
49.2.a.a \(1\) \(0.391\) \(\Q\) \(\Q(\sqrt{-7}) \) \(1\) \(0\) \(0\) \(0\) \(-\) \(q+q^{2}-q^{4}-3q^{8}-3q^{9}+4q^{11}+\cdots\)