Properties

Label 50.2.a
Level 50
Weight 2
Character orbit a
Rep. character \(\chi_{50}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 2
Sturm bound 15
Trace bound 2

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 50.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(15\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(50))\).

Total New Old
Modular forms 13 2 11
Cusp forms 2 2 0
Eisenstein series 11 0 11

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(5\)FrickeDim.
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(2\)

Trace form

\(2q \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 2q^{16} \) \(\mathstrut +\mathstrut 10q^{19} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 2q^{24} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 6q^{34} \) \(\mathstrut -\mathstrut 4q^{36} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 12q^{46} \) \(\mathstrut -\mathstrut 6q^{49} \) \(\mathstrut -\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 10q^{54} \) \(\mathstrut -\mathstrut 4q^{56} \) \(\mathstrut +\mathstrut 4q^{61} \) \(\mathstrut +\mathstrut 2q^{64} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 24q^{71} \) \(\mathstrut -\mathstrut 4q^{74} \) \(\mathstrut +\mathstrut 10q^{76} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 2q^{81} \) \(\mathstrut +\mathstrut 4q^{84} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 30q^{89} \) \(\mathstrut -\mathstrut 16q^{91} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 2q^{96} \) \(\mathstrut +\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(50))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5
50.2.a.a \(1\) \(0.399\) \(\Q\) None \(-1\) \(1\) \(0\) \(2\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
50.2.a.b \(1\) \(0.399\) \(\Q\) None \(1\) \(-1\) \(0\) \(-2\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)