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Properties

Label 201.2.i
Level $201$
Weight $2$
Character orbit 201.i
Rep. character $\chi_{201}(22,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $120$
Newform subspaces $2$
Sturm bound $45$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 201.i (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 67 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 2 \)
Sturm bound: \(45\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(201, [\chi])\).

Total New Old
Modular forms 240 120 120
Cusp forms 200 120 80
Eisenstein series 40 0 40

Trace form

\( 120 q - 4 q^{2} - 2 q^{3} - 18 q^{4} - 8 q^{7} + 42 q^{8} - 12 q^{9} + O(q^{10}) \) \( 120 q - 4 q^{2} - 2 q^{3} - 18 q^{4} - 8 q^{7} + 42 q^{8} - 12 q^{9} + 54 q^{10} - 12 q^{11} - 6 q^{12} - 20 q^{13} - 24 q^{14} + 18 q^{15} - 30 q^{16} - 14 q^{17} - 4 q^{18} + 8 q^{19} - 32 q^{20} - 12 q^{21} - 26 q^{22} - 14 q^{23} - 12 q^{24} - 20 q^{25} - 20 q^{26} - 2 q^{27} - 42 q^{28} - 12 q^{29} + 24 q^{30} + 4 q^{31} + 38 q^{32} - 4 q^{33} - 44 q^{34} - 60 q^{35} + 4 q^{36} - 20 q^{37} - 36 q^{38} - 20 q^{39} + 50 q^{40} + 42 q^{41} - 16 q^{42} + 14 q^{43} - 64 q^{44} - 34 q^{46} - 12 q^{47} - 30 q^{48} - 68 q^{49} - 26 q^{50} - 24 q^{51} + 34 q^{52} - 30 q^{53} - 50 q^{55} + 92 q^{56} + 78 q^{57} - 24 q^{58} + 22 q^{59} + 48 q^{60} + 8 q^{61} - 56 q^{62} + 14 q^{63} - 40 q^{64} + 28 q^{65} + 64 q^{66} - 42 q^{67} + 456 q^{68} - 2 q^{69} + 44 q^{70} + 8 q^{71} + 20 q^{72} + 42 q^{73} - 112 q^{74} + 6 q^{75} - 28 q^{76} + 68 q^{77} - 20 q^{78} + 12 q^{79} - 60 q^{80} - 12 q^{81} + 96 q^{82} - 66 q^{83} + 146 q^{84} - 72 q^{85} + 32 q^{86} - 40 q^{87} - 76 q^{88} + 4 q^{89} + 54 q^{90} + 12 q^{91} - 108 q^{92} - 28 q^{93} - 116 q^{94} - 118 q^{95} - 24 q^{96} + 4 q^{97} - 100 q^{98} - 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(201, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
201.2.i.a 201.i 67.e $50$ $1.605$ None \(-2\) \(5\) \(2\) \(2\) $\mathrm{SU}(2)[C_{11}]$
201.2.i.b 201.i 67.e $70$ $1.605$ None \(-2\) \(-7\) \(-2\) \(-10\) $\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{2}^{\mathrm{old}}(201, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(201, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 2}\)