Properties

Label 50.2.b
Level $50$
Weight $2$
Character orbit 50.b
Rep. character $\chi_{50}(49,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $15$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 50.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(15\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(50, [\chi])\).

Total New Old
Modular forms 14 2 12
Cusp forms 2 2 0
Eisenstein series 12 0 12

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(50, [\chi])\) into newform subspaces

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