Properties

Label 93.1.l
Level 93
Weight 1
Character orbit l
Rep. character \(\chi_{93}(2,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 4
Newforms 1
Sturm bound 10
Trace bound 0

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Defining parameters

Level: \( N \) = \( 93 = 3 \cdot 31 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 93.l (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 93 \)
Character field: \(\Q(\zeta_{10})\)
Newforms: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(93, [\chi])\).

Total New Old
Modular forms 12 12 0
Cusp forms 4 4 0
Eisenstein series 8 8 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\(4q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut q^{9} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut q^{16} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut +\mathstrut 3q^{21} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut +\mathstrut 3q^{28} \) \(\mathstrut -\mathstrut q^{31} \) \(\mathstrut +\mathstrut 4q^{36} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 3q^{39} \) \(\mathstrut +\mathstrut 3q^{43} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut -\mathstrut 3q^{49} \) \(\mathstrut -\mathstrut 2q^{52} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut 2q^{61} \) \(\mathstrut -\mathstrut 2q^{63} \) \(\mathstrut -\mathstrut q^{64} \) \(\mathstrut -\mathstrut 2q^{67} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut -\mathstrut q^{75} \) \(\mathstrut +\mathstrut 3q^{76} \) \(\mathstrut +\mathstrut 3q^{79} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut -\mathstrut 2q^{84} \) \(\mathstrut +\mathstrut q^{91} \) \(\mathstrut -\mathstrut q^{93} \) \(\mathstrut +\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(93, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
93.1.l.a \(4\) \(0.046\) \(\Q(\zeta_{10})\) \(D_{5}\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-2\) \(q-\zeta_{10}q^{3}-\zeta_{10}^{3}q^{4}+(\zeta_{10}^{2}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots\)