Properties

Label 231.2.bc
Level 231
Weight 2
Character orbit bc
Rep. character \(\chi_{231}(5,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 224
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.bc (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 231 \)
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 288 288 0
Cusp forms 224 224 0
Eisenstein series 64 64 0

Trace form

\( 224q - 9q^{3} - 30q^{4} - 16q^{7} + 3q^{9} + O(q^{10}) \) \( 224q - 9q^{3} - 30q^{4} - 16q^{7} + 3q^{9} - 60q^{10} - 12q^{12} - 36q^{15} + 18q^{16} + 13q^{18} - 18q^{19} - 6q^{21} + 20q^{22} - 51q^{24} - 18q^{25} - 26q^{28} - 15q^{30} - 36q^{31} + 60q^{33} - 32q^{36} - 10q^{37} + 9q^{39} - 114q^{42} - 96q^{43} + 24q^{45} - 54q^{46} - 56q^{49} - 29q^{51} - 30q^{52} - 96q^{54} + 68q^{57} - 64q^{58} + 125q^{60} - 18q^{61} - 26q^{63} + 56q^{64} + 135q^{66} + 48q^{67} - 44q^{70} + 19q^{72} + 30q^{73} + 63q^{75} + 28q^{78} + 30q^{79} + 31q^{81} + 54q^{82} + 99q^{84} - 248q^{85} + 102q^{87} + 82q^{88} - 144q^{91} + 34q^{93} + 162q^{94} - 87q^{96} - 100q^{99} + O(q^{100}) \)

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.bc.a \(224\) \(1.845\) None \(0\) \(-9\) \(0\) \(-16\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database