Properties

Label 231.2.ba
Level 231
Weight 2
Character orbit ba
Rep. character \(\chi_{231}(19,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 128
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.ba (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 77 \)
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 288 128 160
Cusp forms 224 128 96
Eisenstein series 64 0 64

Trace form

\( 128q - 12q^{4} + 12q^{5} - 10q^{7} - 40q^{8} - 16q^{9} + O(q^{10}) \) \( 128q - 12q^{4} + 12q^{5} - 10q^{7} - 40q^{8} - 16q^{9} - 2q^{11} + 12q^{14} + 12q^{15} + 40q^{16} - 60q^{17} - 10q^{18} + 52q^{22} - 24q^{23} - 90q^{24} - 20q^{25} + 24q^{26} + 30q^{28} + 40q^{29} - 18q^{31} + 18q^{33} - 80q^{35} - 24q^{36} - 8q^{37} - 24q^{38} - 90q^{40} + 14q^{42} - 82q^{44} + 12q^{45} + 70q^{46} - 24q^{47} - 94q^{49} - 20q^{51} + 4q^{53} - 104q^{56} - 32q^{58} + 48q^{59} + 30q^{61} - 10q^{63} - 48q^{64} + 36q^{66} - 40q^{67} + 180q^{68} + 146q^{70} - 32q^{71} + 10q^{72} + 90q^{73} + 40q^{74} - 24q^{75} - 72q^{78} + 50q^{79} + 228q^{80} + 16q^{81} + 168q^{82} - 60q^{84} - 20q^{85} + 146q^{86} + 16q^{88} + 48q^{91} - 204q^{92} + 44q^{93} + 10q^{95} - 44q^{99} + O(q^{100}) \)

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.ba.a \(128\) \(1.845\) None \(0\) \(0\) \(12\) \(-10\)

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