Properties

Label 133.1.m
Level 133133
Weight 11
Character orbit 133.m
Rep. character χ133(83,)\chi_{133}(83,\cdot)
Character field Q(ζ6)\Q(\zeta_{6})
Dimension 44
Newform subspaces 11
Sturm bound 1313
Trace bound 00

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Defining parameters

Level: N N == 133=719 133 = 7 \cdot 19
Weight: k k == 1 1
Character orbit: [χ][\chi] == 133.m (of order 66 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 133 133
Character field: Q(ζ6)\Q(\zeta_{6})
Newform subspaces: 1 1
Sturm bound: 1313
Trace bound: 00

Dimensions

The following table gives the dimensions of various subspaces of M1(133,[χ])M_{1}(133, [\chi]).

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

The following table gives the dimensions of subspaces with specified projective image type.

DnD_n A4A_4 S4S_4 A5A_5
Dimension 0 4 0 0

Trace form

4q2q24q82q15+2q16+2q212q23+2q29+4q302q354q39+2q422q43+4q464q49+2q51+2q532q574q58+4q64++2q98+O(q100) 4 q - 2 q^{2} - 4 q^{8} - 2 q^{15} + 2 q^{16} + 2 q^{21} - 2 q^{23} + 2 q^{29} + 4 q^{30} - 2 q^{35} - 4 q^{39} + 2 q^{42} - 2 q^{43} + 4 q^{46} - 4 q^{49} + 2 q^{51} + 2 q^{53} - 2 q^{57} - 4 q^{58} + 4 q^{64}+ \cdots + 2 q^{98}+O(q^{100}) Copy content Toggle raw display

Decomposition of S1new(133,[χ])S_{1}^{\mathrm{new}}(133, [\chi]) into newform subspaces

Label Char Prim Dim AA Field Image CM RM Minimal twist Traces Sato-Tate qq-expansion
a2a_{2} a3a_{3} a5a_{5} a7a_{7}
133.1.m.a 133.m 133.m 44 0.0660.066 Q(ζ12)\Q(\zeta_{12}) A4A_{4} None None 133.1.m.a 2-2 00 00 00 qζ122q2+ζ125q3ζ125q5+q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{5}q^{5}+\cdots