Properties

Label 99.1.h
Level 99
Weight 1
Character orbit h
Rep. character \(\chi_{99}(43,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 2
Newforms 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 99.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 99 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(99, [\chi])\).

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

\(2q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut -\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut -\mathstrut q^{9} \) \(\mathstrut -\mathstrut q^{11} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut +\mathstrut q^{15} \) \(\mathstrut -\mathstrut q^{16} \) \(\mathstrut +\mathstrut q^{20} \) \(\mathstrut -\mathstrut 2q^{23} \) \(\mathstrut +\mathstrut 2q^{27} \) \(\mathstrut +\mathstrut q^{31} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 2q^{36} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut q^{47} \) \(\mathstrut +\mathstrut 2q^{48} \) \(\mathstrut -\mathstrut q^{49} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut +\mathstrut q^{59} \) \(\mathstrut -\mathstrut 2q^{60} \) \(\mathstrut +\mathstrut 2q^{64} \) \(\mathstrut +\mathstrut q^{67} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut -\mathstrut 2q^{71} \) \(\mathstrut -\mathstrut 2q^{80} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut +\mathstrut 4q^{89} \) \(\mathstrut -\mathstrut 2q^{92} \) \(\mathstrut +\mathstrut q^{93} \) \(\mathstrut +\mathstrut q^{97} \) \(\mathstrut -\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(99, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
99.1.h.a \(2\) \(0.049\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(1\) \(0\) \(q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}+\cdots\)