Properties

Label 84.1.p
Level 84
Weight 1
Character orbit p
Rep. character \(\chi_{84}(53,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 2
Newforms 1
Sturm bound 16
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 84.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(84, [\chi])\).

Total New Old
Modular forms 14 2 12
Cusp forms 2 2 0
Eisenstein series 12 0 12

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

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

Decomposition of \(S_{1}^{\mathrm{new}}(84, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
84.1.p.a \(2\) \(0.042\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}-q^{13}+\cdots\)