Properties

Label 80.2.c
Level 8080
Weight 22
Character orbit 80.c
Rep. character χ80(49,)\chi_{80}(49,\cdot)
Character field Q\Q
Dimension 22
Newform subspaces 11
Sturm bound 2424
Trace bound 00

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Defining parameters

Level: N N == 80=245 80 = 2^{4} \cdot 5
Weight: k k == 2 2
Character orbit: [χ][\chi] == 80.c (of order 22 and degree 11)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 5 5
Character field: Q\Q
Newform subspaces: 1 1
Sturm bound: 2424
Trace bound: 00

Dimensions

The following table gives the dimensions of various subspaces of M2(80,[χ])M_{2}(80, [\chi]).

Total New Old
Modular forms 18 4 14
Cusp forms 6 2 4
Eisenstein series 12 2 10

Trace form

2q2q52q9+8q118q158q19+8q216q254q29+8q35+16q39+4q41+2q45+6q498q5524q5920q61+16q65+8q69+8q99+O(q100) 2 q - 2 q^{5} - 2 q^{9} + 8 q^{11} - 8 q^{15} - 8 q^{19} + 8 q^{21} - 6 q^{25} - 4 q^{29} + 8 q^{35} + 16 q^{39} + 4 q^{41} + 2 q^{45} + 6 q^{49} - 8 q^{55} - 24 q^{59} - 20 q^{61} + 16 q^{65} + 8 q^{69}+ \cdots - 8 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(80,[χ])S_{2}^{\mathrm{new}}(80, [\chi]) into newform subspaces

Label Char Prim Dim AA Field CM Minimal twist Traces Sato-Tate qq-expansion
a2a_{2} a3a_{3} a5a_{5} a7a_{7}
80.2.c.a 80.c 5.b 22 0.6390.639 Q(1)\Q(\sqrt{-1}) None 40.2.c.a 00 00 2-2 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+βq3+(β1)q5βq7q9+q+\beta q^{3}+(\beta-1)q^{5}-\beta q^{7}-q^{9}+\cdots

Decomposition of S2old(80,[χ])S_{2}^{\mathrm{old}}(80, [\chi]) into lower level spaces

S2old(80,[χ]) S_{2}^{\mathrm{old}}(80, [\chi]) \simeq S2new(40,[χ])S_{2}^{\mathrm{new}}(40, [\chi])2^{\oplus 2}