Properties

Label 231.2.be
Level 231
Weight 2
Character orbit be
Rep. character \(\chi_{231}(2,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 224
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.be (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 231 \)
Character field: \(\Q(\zeta_{30})\)
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 288 288 0
Cusp forms 224 224 0
Eisenstein series 64 64 0

Trace form

\( 224q - 3q^{3} + 18q^{4} - 20q^{6} - 20q^{7} - 9q^{9} + O(q^{10}) \) \( 224q - 3q^{3} + 18q^{4} - 20q^{6} - 20q^{7} - 9q^{9} - 16q^{12} - 40q^{13} + 12q^{15} + 34q^{16} - 5q^{18} - 10q^{19} - 76q^{22} - 25q^{24} - 18q^{25} + 6q^{27} + 10q^{28} - 35q^{30} - 8q^{33} - 96q^{34} - 48q^{36} - 10q^{37} - 45q^{39} - 120q^{40} + 34q^{42} - 24q^{45} - 50q^{46} + 14q^{48} - 56q^{49} - 45q^{51} - 10q^{52} + 48q^{55} + 60q^{57} + 44q^{58} - 47q^{60} - 50q^{61} + 60q^{63} - 72q^{64} + 77q^{66} - 80q^{67} + 78q^{69} + 36q^{70} + 55q^{72} - 70q^{73} - 11q^{75} + 36q^{78} - 90q^{79} + 23q^{81} - 6q^{82} + 125q^{84} + 160q^{85} + 86q^{88} + 30q^{90} - 128q^{91} - 38q^{93} - 210q^{94} + 135q^{96} + 40q^{97} + 80q^{99} + O(q^{100}) \)

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.be.a \(224\) \(1.845\) None \(0\) \(-3\) \(0\) \(-20\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database