Properties

Label 20.7.d
Level 2020
Weight 77
Character orbit 20.d
Rep. character χ20(19,)\chi_{20}(19,\cdot)
Character field Q\Q
Dimension 1616
Newform subspaces 44
Sturm bound 2121
Trace bound 22

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Defining parameters

Level: N N == 20=225 20 = 2^{2} \cdot 5
Weight: k k == 7 7
Character orbit: [χ][\chi] == 20.d (of order 22 and degree 11)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 20 20
Character field: Q\Q
Newform subspaces: 4 4
Sturm bound: 2121
Trace bound: 22
Distinguishing TpT_p: 33

Dimensions

The following table gives the dimensions of various subspaces of M7(20,[χ])M_{7}(20, [\chi]).

Total New Old
Modular forms 20 20 0
Cusp forms 16 16 0
Eisenstein series 4 4 0

Trace form

16q+64q424q5+32q6+2912q9+1296q107872q144544q1614784q20+5104q21+24128q24944q2512000q26+9888q294480q30+100800q34++10556672q96+O(q100) 16 q + 64 q^{4} - 24 q^{5} + 32 q^{6} + 2912 q^{9} + 1296 q^{10} - 7872 q^{14} - 4544 q^{16} - 14784 q^{20} + 5104 q^{21} + 24128 q^{24} - 944 q^{25} - 12000 q^{26} + 9888 q^{29} - 4480 q^{30} + 100800 q^{34}+ \cdots + 10556672 q^{96}+O(q^{100}) Copy content Toggle raw display

Decomposition of S7new(20,[χ])S_{7}^{\mathrm{new}}(20, [\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}
20.7.d.a 20.d 20.d 11 4.6014.601 Q\Q Q(5)\Q(\sqrt{-5}) 20.7.d.a 8-8 44-44 125-125 524524 U(1)[D2]\mathrm{U}(1)[D_{2}] q8q244q3+26q453q5+352q6+q-8q^{2}-44q^{3}+2^{6}q^{4}-5^{3}q^{5}+352q^{6}+\cdots
20.7.d.b 20.d 20.d 11 4.6014.601 Q\Q Q(5)\Q(\sqrt{-5}) 20.7.d.a 88 4444 125-125 524-524 U(1)[D2]\mathrm{U}(1)[D_{2}] q+8q2+44q3+26q453q5+352q6+q+8q^{2}+44q^{3}+2^{6}q^{4}-5^{3}q^{5}+352q^{6}+\cdots
20.7.d.c 20.d 20.d 22 4.6014.601 Q(1)\Q(\sqrt{-1}) Q(1)\Q(\sqrt{-1}) 20.7.d.c 00 00 234-234 00 U(1)[D2]\mathrm{U}(1)[D_{2}] q+2βq264q4+(11β117)q5+q+2\beta q^{2}-64 q^{4}+(11\beta-117)q^{5}+\cdots
20.7.d.d 20.d 20.d 1212 4.6014.601 Q[x]/(x12+)\mathbb{Q}[x]/(x^{12} + \cdots) None 20.7.d.d 00 00 460460 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qβ1q2+(β1+β2)q3+(6+β4β8+)q4+q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(6+\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots