Properties

Label 145.1.h
Level $145$
Weight $1$
Character orbit 145.h
Rep. character $\chi_{145}(28,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $2$
Newform subspaces $1$
Sturm bound $15$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 145 = 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 145.h (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 145 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(15\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(145, [\chi])\).

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

\( 2 q - 2 q^{7} + O(q^{10}) \) \( 2 q - 2 q^{7} + 2 q^{13} - 2 q^{16} - 2 q^{20} - 2 q^{23} - 2 q^{25} + 2 q^{28} + 2 q^{35} + 2 q^{36} + 2 q^{45} + 2 q^{52} - 2 q^{53} - 2 q^{63} + 2 q^{65} + 2 q^{67} - 2 q^{81} + 2 q^{83} - 4 q^{91} - 2 q^{92} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(145, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
145.1.h.a 145.h 145.h $2$ $0.072$ \(\Q(\sqrt{-1}) \) $D_{4}$ None \(\Q(\sqrt{29}) \) 145.1.h.a \(0\) \(0\) \(0\) \(-2\) \(q-iq^{4}-iq^{5}+(-1+i)q^{7}+iq^{9}+\cdots\)