Properties

Label 231.2.p
Level 231
Weight 2
Character orbit p
Rep. character \(\chi_{231}(10,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 32
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.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 77 \)
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 32 40
Cusp forms 56 32 24
Eisenstein series 16 0 16

Trace form

\( 32q + 12q^{4} - 12q^{5} + 16q^{9} + O(q^{10}) \) \( 32q + 12q^{4} - 12q^{5} + 16q^{9} + 2q^{11} - 32q^{14} + 8q^{15} - 20q^{16} + 8q^{22} + 24q^{23} - 24q^{26} - 12q^{31} - 18q^{33} + 24q^{36} - 32q^{37} + 24q^{38} - 24q^{42} - 28q^{44} - 12q^{45} + 24q^{47} - 36q^{49} + 36q^{53} - 56q^{56} + 12q^{58} - 48q^{59} + 8q^{64} - 36q^{66} + 20q^{67} + 24q^{70} + 72q^{71} + 24q^{75} - 48q^{78} + 72q^{80} - 16q^{81} - 48q^{82} + 64q^{86} + 24q^{88} + 60q^{89} - 28q^{91} - 16q^{92} + 16q^{93} + 4q^{99} + O(q^{100}) \)

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.p.a \(32\) \(1.845\) None \(0\) \(0\) \(-12\) \(0\)

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

\( S_{2}^{\mathrm{old}}(231, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database