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

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

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 7
49.2.a.a 49.a 1.a $1$ $0.391$ \(\Q\) \(\Q(\sqrt{-7}) \) \(1\) \(0\) \(0\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q+q^{2}-q^{4}-3q^{8}-3q^{9}+4q^{11}+\cdots\)