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Properties

Label 133.2.f
Level $133$
Weight $2$
Character orbit 133.f
Rep. character $\chi_{133}(39,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $24$
Newform subspaces $4$
Sturm bound $26$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 133 = 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 133.f (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(26\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(133, [\chi])\).

Total New Old
Modular forms 32 24 8
Cusp forms 24 24 0
Eisenstein series 8 0 8

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(133, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
133.2.f.a 133.f 7.c $2$ $1.062$ \(\Q(\sqrt{-3}) \) None \(-2\) \(-2\) \(-3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
133.2.f.b 133.f 7.c $4$ $1.062$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}-2\beta _{1}q^{5}+\cdots\)
133.2.f.c 133.f 7.c $4$ $1.062$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots\)
133.2.f.d 133.f 7.c $14$ $1.062$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-2\) \(2\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{10}q^{2}+\beta _{8}q^{3}+(-2-\beta _{5}-\beta _{6}+\cdots)q^{4}+\cdots\)