Properties

Label 152.1.g
Level 152
Weight 1
Character orbit g
Rep. character \(\chi_{152}(37,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 2
Sturm bound 20
Trace bound 2

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Defining parameters

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

Dimensions

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

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

\( 2q + 2q^{4} - 2q^{6} - 2q^{7} + O(q^{10}) \) \( 2q + 2q^{4} - 2q^{6} - 2q^{7} + 2q^{16} - 2q^{17} - 2q^{23} - 2q^{24} + 2q^{25} - 2q^{26} - 2q^{28} + 2q^{38} + 2q^{39} + 2q^{42} + 4q^{47} + 2q^{54} - 2q^{57} - 2q^{58} + 2q^{64} - 2q^{68} - 2q^{73} + 4q^{74} - 2q^{81} + 2q^{87} - 2q^{92} - 2q^{96} + O(q^{100}) \)

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.g.a \(1\) \(0.076\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-38}) \) None \(-1\) \(1\) \(0\) \(-1\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
152.1.g.b \(1\) \(0.076\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-38}) \) None \(1\) \(-1\) \(0\) \(-1\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)