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Properties

Label 134.2.e
Level $134$
Weight $2$
Character orbit 134.e
Rep. character $\chi_{134}(9,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $70$
Newform subspaces $2$
Sturm bound $34$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 134 = 2 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 134.e (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 67 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 2 \)
Sturm bound: \(34\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(134, [\chi])\).

Total New Old
Modular forms 190 70 120
Cusp forms 150 70 80
Eisenstein series 40 0 40

Trace form

\( 70 q - q^{2} - 8 q^{3} - 7 q^{4} - 6 q^{5} - 6 q^{6} - 8 q^{7} - q^{8} - 21 q^{9} + O(q^{10}) \) \( 70 q - q^{2} - 8 q^{3} - 7 q^{4} - 6 q^{5} - 6 q^{6} - 8 q^{7} - q^{8} - 21 q^{9} - 8 q^{11} + 3 q^{12} - 22 q^{13} - 8 q^{14} + 28 q^{15} - 7 q^{16} - q^{17} - 5 q^{18} + 12 q^{19} - 6 q^{20} + 2 q^{21} - 10 q^{22} + 12 q^{23} + 16 q^{24} - 35 q^{25} - 32 q^{27} - 8 q^{28} + 4 q^{29} + 36 q^{30} - 4 q^{31} - q^{32} + 6 q^{33} - 18 q^{34} - 28 q^{35} - 21 q^{36} - 20 q^{37} + 46 q^{38} + 26 q^{39} + 28 q^{41} - 32 q^{42} - 4 q^{43} - 8 q^{44} - 44 q^{45} - 32 q^{46} - 4 q^{47} + 14 q^{48} - 79 q^{49} - 39 q^{50} - 80 q^{51} + 22 q^{52} - 20 q^{53} - 27 q^{54} + 22 q^{55} - 8 q^{56} - 34 q^{57} + 26 q^{58} + 105 q^{59} + 28 q^{60} + 100 q^{61} - 18 q^{62} + 70 q^{63} - 7 q^{64} - 8 q^{65} + 186 q^{66} - 23 q^{67} + 10 q^{68} - 68 q^{69} + 152 q^{70} + 2 q^{71} - 5 q^{72} + 50 q^{73} - 12 q^{74} + 153 q^{75} + 12 q^{76} + 182 q^{77} - 16 q^{78} + 48 q^{79} + 16 q^{80} + 27 q^{81} - 13 q^{82} - 47 q^{83} + 46 q^{84} - 80 q^{85} - 46 q^{86} - 42 q^{87} - 10 q^{88} - 46 q^{89} - 36 q^{90} - 128 q^{91} - 10 q^{92} + 2 q^{93} - 24 q^{94} - 54 q^{95} - 6 q^{96} - 70 q^{97} + 3 q^{98} - 14 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(134, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
134.2.e.a 134.e 67.e $30$ $1.070$ None \(3\) \(-1\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{11}]$
134.2.e.b 134.e 67.e $40$ $1.070$ None \(-4\) \(-7\) \(-3\) \(-8\) $\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{2}^{\mathrm{old}}(134, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(134, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 2}\)