Properties

Label 845.2.b
Level 845845
Weight 22
Character orbit 845.b
Rep. character χ845(339,)\chi_{845}(339,\cdot)
Character field Q\Q
Dimension 6666
Newform subspaces 88
Sturm bound 182182
Trace bound 66

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Defining parameters

Level: N N == 845=5132 845 = 5 \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 845.b (of order 22 and degree 11)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 5 5
Character field: Q\Q
Newform subspaces: 8 8
Sturm bound: 182182
Trace bound: 66
Distinguishing TpT_p: 22, 1111

Dimensions

The following table gives the dimensions of various subspaces of M2(845,[χ])M_{2}(845, [\chi]).

Total New Old
Modular forms 106 88 18
Cusp forms 78 66 12
Eisenstein series 28 22 6

Trace form

66q50q44q642q9+2q10+12q1132q1416q15+18q16+20q20+4q2116q244q25+16q29+26q30+20q3120q344q35+34q36+16q99+O(q100) 66 q - 50 q^{4} - 4 q^{6} - 42 q^{9} + 2 q^{10} + 12 q^{11} - 32 q^{14} - 16 q^{15} + 18 q^{16} + 20 q^{20} + 4 q^{21} - 16 q^{24} - 4 q^{25} + 16 q^{29} + 26 q^{30} + 20 q^{31} - 20 q^{34} - 4 q^{35} + 34 q^{36}+ \cdots - 16 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(845,[χ])S_{2}^{\mathrm{new}}(845, [\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}
845.2.b.a 845.b 5.b 22 6.7476.747 Q(1)\Q(\sqrt{-1}) None 65.2.d.a 00 00 4-4 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+iq22iq3+q4+(i2)q5+q+i q^{2}-2 i q^{3}+q^{4}+(i-2)q^{5}+\cdots
845.2.b.b 845.b 5.b 22 6.7476.747 Q(1)\Q(\sqrt{-1}) None 65.2.d.a 00 00 44 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+iq2+2iq3+q4+(i+2)q5+q+i q^{2}+2 i q^{3}+q^{4}+(i+2)q^{5}+\cdots
845.2.b.c 845.b 5.b 66 6.7476.747 6.0.350464.1 None 65.2.b.a 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(β3β5)q2+(β3+β4)q3+(2+)q4+q+(\beta _{3}-\beta _{5})q^{2}+(\beta _{3}+\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots
845.2.b.d 845.b 5.b 66 6.7476.747 6.0.49843600.1 None 65.2.n.a 00 00 3-3 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β1q2+(β1+β5)q3+(1+β2+)q4+q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{5})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots
845.2.b.e 845.b 5.b 66 6.7476.747 6.0.49843600.1 None 65.2.n.a 00 00 33 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β1q2+(β1β5)q3+(1+β2+)q4+q+\beta _{1}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots
845.2.b.f 845.b 5.b 88 6.7476.747 8.0.49787136.1 None 65.2.l.a 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β6q2+β3q3+β4q4+(β2β7)q5+q+\beta _{6}q^{2}+\beta _{3}q^{3}+\beta _{4}q^{4}+(-\beta _{2}-\beta _{7})q^{5}+\cdots
845.2.b.g 845.b 5.b 1818 6.7476.747 Q[x]/(x18+)\mathbb{Q}[x]/(x^{18} + \cdots) None 845.2.b.g 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β1q2β15q3+(1+β2)q4+q+\beta _{1}q^{2}-\beta _{15}q^{3}+(-1+\beta _{2})q^{4}+\cdots
845.2.b.h 845.b 5.b 1818 6.7476.747 Q[x]/(x18+)\mathbb{Q}[x]/(x^{18} + \cdots) None 845.2.b.g 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β1q2+β15q3+(1+β2)q4+q+\beta _{1}q^{2}+\beta _{15}q^{3}+(-1+\beta _{2})q^{4}+\cdots

Decomposition of S2old(845,[χ])S_{2}^{\mathrm{old}}(845, [\chi]) into lower level spaces

S2old(845,[χ]) S_{2}^{\mathrm{old}}(845, [\chi]) \simeq S2new(65,[χ])S_{2}^{\mathrm{new}}(65, [\chi])2^{\oplus 2}