Properties

Label 55.1.d
Level 55
Weight 1
Character orbit d
Rep. character \(\chi_{55}(54,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 55 = 5 \cdot 11 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 55.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 55 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(55, [\chi])\).

Total New Old
Modular forms 3 3 0
Cusp forms 1 1 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 1 0 0 0

Trace form

\(q \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut -\mathstrut q^{11} \) \(\mathstrut +\mathstrut q^{16} \) \(\mathstrut +\mathstrut q^{20} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut -\mathstrut 2q^{31} \) \(\mathstrut -\mathstrut q^{36} \) \(\mathstrut +\mathstrut q^{44} \) \(\mathstrut -\mathstrut q^{45} \) \(\mathstrut -\mathstrut q^{49} \) \(\mathstrut +\mathstrut q^{55} \) \(\mathstrut +\mathstrut 2q^{59} \) \(\mathstrut -\mathstrut q^{64} \) \(\mathstrut +\mathstrut 2q^{71} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut q^{81} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut -\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(55, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
55.1.d.a \(1\) \(0.027\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q-q^{4}-q^{5}+q^{9}-q^{11}+q^{16}+q^{20}+\cdots\)