Properties

Label 84.2.n
Level 84
Weight 2
Character orbit n
Rep. character \(\chi_{84}(11,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 24
Newform subspaces 1
Sturm bound 32
Trace bound 0

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Defining parameters

Level: \( N \) = \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 84.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 84 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(84, [\chi])\).

Total New Old
Modular forms 40 40 0
Cusp forms 24 24 0
Eisenstein series 16 16 0

Trace form

\( 24q - 2q^{4} - 2q^{9} + O(q^{10}) \) \( 24q - 2q^{4} - 2q^{9} - 10q^{10} - 12q^{12} - 24q^{13} - 10q^{16} - 10q^{18} - 6q^{21} + 28q^{22} - 14q^{24} - 12q^{25} + 10q^{28} - 14q^{30} + 10q^{33} - 8q^{34} + 44q^{36} - 8q^{37} + 34q^{40} + 38q^{42} - 18q^{45} + 24q^{46} + 8q^{48} + 16q^{52} + 38q^{54} - 4q^{57} + 14q^{58} + 14q^{60} + 4q^{61} - 68q^{64} + 30q^{66} + 36q^{69} - 90q^{70} + 20q^{72} - 24q^{76} - 104q^{78} + 26q^{81} - 68q^{82} - 76q^{84} - 40q^{85} - 34q^{88} - 40q^{90} - 6q^{93} - 24q^{94} - 62q^{96} + 72q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(84, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
84.2.n.a \(24\) \(0.671\) None \(0\) \(0\) \(0\) \(0\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database