Properties

Label 152.1.k
Level 152
Weight 1
Character orbit k
Rep. character \(\chi_{152}(11,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 2
Newforms 1
Sturm bound 20
Trace bound 0

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Defining parameters

Level: \( N \) = \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 152.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 152 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 1 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(152, [\chi])\).

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q - q^{2} + q^{3} - q^{4} + q^{6} + 2q^{8} + O(q^{10}) \) \( 2q - q^{2} + q^{3} - q^{4} + q^{6} + 2q^{8} - 2q^{11} - 2q^{12} - q^{16} - 2q^{17} - q^{19} + q^{22} + q^{24} - q^{25} + 2q^{27} - q^{32} - q^{33} - 2q^{34} + 2q^{38} + q^{41} - 2q^{43} + q^{44} + q^{48} + 2q^{49} + 2q^{50} + 2q^{51} - q^{54} - 2q^{57} + q^{59} + 2q^{64} - q^{66} + q^{67} + 4q^{68} + q^{73} - 2q^{75} - q^{76} + q^{81} + q^{82} - 2q^{83} - 2q^{86} - 2q^{88} - 2q^{89} - 2q^{96} + q^{97} - q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(152, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
152.1.k.a \(2\) \(0.076\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-2}) \) None \(-1\) \(1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)