Properties

Label 231.2.u
Level 231
Weight 2
Character orbit u
Rep. character \(\chi_{231}(20,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 112
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.u (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 231 \)
Character field: \(\Q(\zeta_{10})\)
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 144 144 0
Cusp forms 112 112 0
Eisenstein series 32 32 0

Trace form

\( 112q + 12q^{4} - 2q^{7} - 12q^{9} + O(q^{10}) \) \( 112q + 12q^{4} - 2q^{7} - 12q^{9} - 60q^{16} + 2q^{18} - 80q^{22} - 36q^{25} + 8q^{28} + 24q^{30} - 34q^{36} + 4q^{37} - 66q^{39} - 30q^{42} + 36q^{46} + 26q^{49} + 38q^{51} - 86q^{57} - 116q^{58} + 88q^{60} + 44q^{63} - 32q^{64} + 110q^{70} + 86q^{72} - 52q^{78} - 156q^{79} + 68q^{81} - 30q^{84} + 8q^{85} - 112q^{88} + 42q^{91} + 56q^{93} + 70q^{99} + O(q^{100}) \)

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.u.a \(112\) \(1.845\) None \(0\) \(0\) \(0\) \(-2\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database