Properties

Label 134.2.c
Level 134
Weight 2
Character orbit c
Rep. character \(\chi_{134}(29,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 10
Newforms 3
Sturm bound 34
Trace bound 2

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 38 10 28
Cusp forms 30 10 20
Eisenstein series 8 0 8

Trace form

\(10q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 5q^{4} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(10q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 5q^{4} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut -\mathstrut 2q^{11} \) \(\mathstrut -\mathstrut 3q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut 8q^{14} \) \(\mathstrut -\mathstrut 16q^{15} \) \(\mathstrut -\mathstrut 5q^{16} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut +\mathstrut 2q^{21} \) \(\mathstrut +\mathstrut 20q^{22} \) \(\mathstrut -\mathstrut 10q^{23} \) \(\mathstrut -\mathstrut 6q^{24} \) \(\mathstrut -\mathstrut 18q^{25} \) \(\mathstrut +\mathstrut 30q^{27} \) \(\mathstrut +\mathstrut 2q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 14q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 3q^{34} \) \(\mathstrut +\mathstrut 14q^{35} \) \(\mathstrut -\mathstrut 4q^{36} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 5q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 2q^{41} \) \(\mathstrut -\mathstrut 20q^{42} \) \(\mathstrut -\mathstrut 14q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 48q^{45} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut -\mathstrut 3q^{48} \) \(\mathstrut +\mathstrut 5q^{49} \) \(\mathstrut +\mathstrut 9q^{50} \) \(\mathstrut +\mathstrut 13q^{51} \) \(\mathstrut +\mathstrut 12q^{52} \) \(\mathstrut +\mathstrut 36q^{53} \) \(\mathstrut -\mathstrut 15q^{54} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 4q^{56} \) \(\mathstrut -\mathstrut 3q^{57} \) \(\mathstrut +\mathstrut 12q^{58} \) \(\mathstrut -\mathstrut 6q^{59} \) \(\mathstrut +\mathstrut 8q^{60} \) \(\mathstrut +\mathstrut 8q^{61} \) \(\mathstrut +\mathstrut 8q^{62} \) \(\mathstrut -\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 18q^{65} \) \(\mathstrut +\mathstrut 40q^{66} \) \(\mathstrut +\mathstrut 34q^{67} \) \(\mathstrut -\mathstrut 6q^{68} \) \(\mathstrut +\mathstrut 2q^{69} \) \(\mathstrut -\mathstrut 8q^{70} \) \(\mathstrut -\mathstrut 14q^{71} \) \(\mathstrut +\mathstrut 4q^{72} \) \(\mathstrut +\mathstrut 25q^{73} \) \(\mathstrut -\mathstrut 10q^{74} \) \(\mathstrut -\mathstrut 6q^{75} \) \(\mathstrut +\mathstrut 2q^{76} \) \(\mathstrut -\mathstrut 14q^{77} \) \(\mathstrut +\mathstrut 22q^{79} \) \(\mathstrut -\mathstrut 14q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 56q^{83} \) \(\mathstrut +\mathstrut 2q^{84} \) \(\mathstrut +\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 7q^{86} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut -\mathstrut 10q^{88} \) \(\mathstrut +\mathstrut 26q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 20q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 40q^{94} \) \(\mathstrut -\mathstrut 30q^{95} \) \(\mathstrut +\mathstrut 3q^{96} \) \(\mathstrut +\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 17q^{98} \) \(\mathstrut -\mathstrut 16q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(134, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
134.2.c.a \(2\) \(1.070\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-2\) \(4\) \(4\) \(q+(-1+\zeta_{6})q^{2}-q^{3}-\zeta_{6}q^{4}+2q^{5}+\cdots\)
134.2.c.b \(4\) \(1.070\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(-2\) \(2\) \(-4\) \(-1\) \(q+\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(-1-\beta _{1})q^{4}+\cdots\)
134.2.c.c \(4\) \(1.070\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(2\) \(6\) \(0\) \(-1\) \(q+(1+\beta _{3})q^{2}+(1-\beta _{2})q^{3}+\beta _{3}q^{4}+\cdots\)

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

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