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Properties

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

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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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(231, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
231.2.y.a 231.y 77.m $64$ $1.845$ None \(0\) \(-8\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{15}]$
231.2.y.b 231.y 77.m $64$ $1.845$ None \(4\) \(8\) \(-4\) \(-1\) $\mathrm{SU}(2)[C_{15}]$

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

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