Properties

Label 231.2.n
Level 231
Weight 2
Character orbit n
Rep. character \(\chi_{231}(89,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 52
Newform subspaces 1
Sturm bound 64
Trace bound 0

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Defining parameters

Level: \( N \) = \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 231.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(231, [\chi])\).

Total New Old
Modular forms 72 52 20
Cusp forms 56 52 4
Eisenstein series 16 0 16

Trace form

\( 52q + 24q^{4} - 6q^{7} - 4q^{9} + O(q^{10}) \) \( 52q + 24q^{4} - 6q^{7} - 4q^{9} - 30q^{12} - 4q^{15} - 20q^{16} - 18q^{18} + 6q^{19} - 2q^{21} + 36q^{24} - 22q^{25} - 40q^{28} - 20q^{30} - 54q^{31} + 36q^{36} + 2q^{37} + 20q^{39} + 60q^{40} - 36q^{42} + 36q^{43} - 54q^{45} + 4q^{46} + 22q^{49} - 16q^{51} + 12q^{52} + 66q^{54} - 44q^{57} - 16q^{58} + 20q^{60} - 36q^{61} - 24q^{63} - 48q^{64} - 30q^{66} - 6q^{67} - 116q^{70} + 36q^{72} - 6q^{73} + 72q^{75} + 112q^{78} + 14q^{79} + 52q^{81} - 84q^{82} + 8q^{84} + 8q^{85} + 18q^{87} - 12q^{88} + 46q^{91} + 6q^{93} + 48q^{94} - 18q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(231, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
231.2.n.a \(52\) \(1.845\) None \(0\) \(0\) \(0\) \(-6\)

Decomposition of \(S_{2}^{\mathrm{old}}(231, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(231, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database