Properties

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

Related objects

Downloads

Learn more

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: \(\Q\)
Newform subspaces: \( 2 \)
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

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

Decomposition of \(S_{1}^{\mathrm{new}}(152, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
152.1.g.a 152.g 152.g $1$ $0.076$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-38}) \) None 152.1.g.a \(-1\) \(1\) \(0\) \(-1\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
152.1.g.b 152.g 152.g $1$ $0.076$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-38}) \) None 152.1.g.a \(1\) \(-1\) \(0\) \(-1\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)