Properties

Label 231.2.g
Level 231
Weight 2
Character orbit g
Rep. character \(\chi_{231}(197,\cdot)\)
Character field \(\Q\)
Dimension 24
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.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 33 \)
Character field: \(\Q\)
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 36 24 12
Cusp forms 28 24 4
Eisenstein series 8 0 8

Trace form

\( 24q - 6q^{3} + 24q^{4} + 10q^{9} + O(q^{10}) \) \( 24q - 6q^{3} + 24q^{4} + 10q^{9} - 20q^{12} - 10q^{15} - 8q^{16} - 12q^{25} - 20q^{31} + 14q^{33} - 8q^{34} - 12q^{36} + 4q^{37} + 6q^{45} - 48q^{48} - 24q^{49} - 28q^{55} + 44q^{58} + 32q^{60} - 52q^{64} + 12q^{66} - 4q^{67} + 54q^{69} - 20q^{70} + 68q^{75} - 20q^{78} + 2q^{81} + 16q^{82} - 44q^{88} + 24q^{91} + 26q^{93} - 12q^{97} - 6q^{99} + O(q^{100}) \)

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.g.a \(24\) \(1.845\) None \(0\) \(-6\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(231, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database