Properties

Label 145.1.f
Level $145$
Weight $1$
Character orbit 145.f
Rep. character $\chi_{145}(99,\cdot)$
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.f (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

\( 2 q + O(q^{10}) \) \( 2 q - 2 q^{11} - 2 q^{16} - 2 q^{19} + 2 q^{20} - 2 q^{25} + 2 q^{31} - 2 q^{36} + 2 q^{41} + 2 q^{44} + 2 q^{45} + 2 q^{49} - 2 q^{55} + 2 q^{61} + 2 q^{76} - 2 q^{79} - 2 q^{81} - 2 q^{89} - 2 q^{95} + 2 q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
145.1.f.a \(2\) \(0.072\) \(\Q(\sqrt{-1}) \) \(D_{4}\) None \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{4}-iq^{5}+iq^{9}+(-1-i)q^{11}+\cdots\)