Properties

Label 231.2.y
Level 231
Weight 2
Character orbit y
Rep. character \(\chi_{231}(4,\cdot)\)
Character field \(\Q(\zeta_{15})\)
Dimension 128
Newform subspaces 2
Sturm bound 64
Trace bound 2

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 231.y (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 77 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 2 \)
Sturm bound: \(64\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

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

\( 128q + 4q^{2} + 20q^{4} - 4q^{5} - 8q^{6} - 2q^{7} + 16q^{8} + 16q^{9} + O(q^{10}) \) \( 128q + 4q^{2} + 20q^{4} - 4q^{5} - 8q^{6} - 2q^{7} + 16q^{8} + 16q^{9} - 36q^{10} - 2q^{11} - 16q^{13} - 20q^{14} - 12q^{15} - 6q^{18} + 8q^{19} + 48q^{20} - 52q^{22} - 8q^{23} + 30q^{24} - 12q^{25} + 8q^{26} - 38q^{28} - 56q^{29} + 8q^{30} + 6q^{31} + 8q^{32} - 6q^{33} - 144q^{34} + 36q^{35} - 40q^{36} - 32q^{37} - 8q^{38} + 42q^{40} - 48q^{41} - 2q^{42} - 8q^{43} - 26q^{44} - 4q^{45} - 38q^{46} - 44q^{47} + 66q^{49} - 56q^{50} + 12q^{51} + 12q^{52} - 52q^{53} - 16q^{54} - 56q^{55} - 24q^{56} - 16q^{57} + 12q^{58} + 8q^{59} - 18q^{61} + 96q^{62} - 14q^{63} - 96q^{64} + 16q^{65} - 12q^{66} + 72q^{67} - 56q^{68} + 24q^{69} + 58q^{70} + 128q^{71} + 2q^{72} - 6q^{73} + 4q^{74} - 8q^{75} + 272q^{76} + 4q^{77} + 120q^{78} - 6q^{79} - 88q^{80} + 16q^{81} + 128q^{83} - 12q^{84} + 172q^{85} - 34q^{86} - 100q^{87} + 28q^{88} + 72q^{89} - 8q^{90} + 300q^{92} - 44q^{93} - 52q^{94} - 10q^{95} + 4q^{96} + 32q^{97} - 240q^{98} + 44q^{99} + O(q^{100}) \)

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.y.a \(64\) \(1.845\) None \(0\) \(-8\) \(0\) \(-1\)
231.2.y.b \(64\) \(1.845\) None \(4\) \(8\) \(-4\) \(-1\)

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