Properties

Label 41.2.b
Level 41
Weight 2
Character orbit b
Rep. character \(\chi_{41}(40,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 7
Trace bound 0

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Defining parameters

Level: \( N \) = \( 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 41.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 41 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(41, [\chi])\).

Total New Old
Modular forms 4 4 0
Cusp forms 2 2 0
Eisenstein series 2 2 0

Trace form

\( 2q - 2q^{2} - 2q^{4} + 4q^{5} + 6q^{8} - 10q^{9} + O(q^{10}) \) \( 2q - 2q^{2} - 2q^{4} + 4q^{5} + 6q^{8} - 10q^{9} - 4q^{10} - 2q^{16} + 10q^{18} - 4q^{20} + 16q^{21} - 2q^{25} - 16q^{31} - 10q^{32} - 16q^{33} + 10q^{36} + 4q^{37} + 32q^{39} + 12q^{40} - 6q^{41} - 16q^{42} + 8q^{43} - 20q^{45} - 2q^{49} + 2q^{50} - 16q^{57} + 8q^{59} - 4q^{61} + 16q^{62} + 14q^{64} + 16q^{66} - 30q^{72} + 28q^{73} - 4q^{74} + 16q^{77} - 32q^{78} - 4q^{80} + 2q^{81} + 6q^{82} - 24q^{83} - 16q^{84} - 8q^{86} + 32q^{87} + 20q^{90} - 32q^{91} + 2q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(41, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
41.2.b.a \(2\) \(0.327\) \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(4\) \(0\) \(q-q^{2}+\beta q^{3}-q^{4}+2q^{5}-\beta q^{6}-\beta q^{7}+\cdots\)