Properties

Label 231.2.s
Level 231
Weight 2
Character orbit s
Rep. character \(\chi_{231}(8,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 96
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.s (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 33 \)
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 96 48
Cusp forms 112 96 16
Eisenstein series 32 0 32

Trace form

\( 96q + 6q^{3} - 24q^{4} - 10q^{6} - 20q^{9} + O(q^{10}) \) \( 96q + 6q^{3} - 24q^{4} - 10q^{6} - 20q^{9} - 20q^{12} - 32q^{16} - 10q^{18} - 60q^{19} + 30q^{24} + 12q^{25} - 40q^{28} + 60q^{30} + 40q^{31} - 44q^{33} + 8q^{34} + 2q^{36} + 16q^{37} - 10q^{39} - 96q^{45} - 40q^{46} + 48q^{48} + 24q^{49} - 30q^{51} - 40q^{52} + 28q^{55} - 30q^{57} + 36q^{58} - 32q^{60} + 40q^{61} - 28q^{64} + 118q^{66} - 56q^{67} + 26q^{69} + 20q^{70} + 150q^{72} + 40q^{73} + 2q^{75} - 20q^{78} - 40q^{79} + 8q^{81} - 16q^{82} + 40q^{84} - 60q^{85} - 156q^{88} + 100q^{90} + 36q^{91} - 36q^{93} + 160q^{96} - 88q^{97} - 94q^{99} + O(q^{100}) \)

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.s.a \(96\) \(1.845\) 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