Properties

Label 798.2.bx
Level 798798
Weight 22
Character orbit 798.bx
Rep. character χ798(13,)\chi_{798}(13,\cdot)
Character field Q(ζ18)\Q(\zeta_{18})
Dimension 168168
Newform subspaces 22
Sturm bound 320320
Trace bound 1010

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Defining parameters

Level: N N == 798=23719 798 = 2 \cdot 3 \cdot 7 \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 798.bx (of order 1818 and degree 66)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 133 133
Character field: Q(ζ18)\Q(\zeta_{18})
Newform subspaces: 2 2
Sturm bound: 320320
Trace bound: 1010
Distinguishing TpT_p: 55

Dimensions

The following table gives the dimensions of various subspaces of M2(798,[χ])M_{2}(798, [\chi]).

Total New Old
Modular forms 1008 168 840
Cusp forms 912 168 744
Eisenstein series 96 0 96

Trace form

168q12q724q11+24q14+24q2112q22+24q23+12q2572q29+60q35+12q42120q43+24q4436q46+24q4924q53+12q57+84q64+24q99+O(q100) 168 q - 12 q^{7} - 24 q^{11} + 24 q^{14} + 24 q^{21} - 12 q^{22} + 24 q^{23} + 12 q^{25} - 72 q^{29} + 60 q^{35} + 12 q^{42} - 120 q^{43} + 24 q^{44} - 36 q^{46} + 24 q^{49} - 24 q^{53} + 12 q^{57} + 84 q^{64}+ \cdots - 24 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(798,[χ])S_{2}^{\mathrm{new}}(798, [\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}
798.2.bx.a 798.bx 133.aa 8484 6.3726.372 None 798.2.bx.a 00 00 00 6-6 SU(2)[C18]\mathrm{SU}(2)[C_{18}]
798.2.bx.b 798.bx 133.aa 8484 6.3726.372 None 798.2.bx.a 00 00 00 6-6 SU(2)[C18]\mathrm{SU}(2)[C_{18}]

Decomposition of S2old(798,[χ])S_{2}^{\mathrm{old}}(798, [\chi]) into lower level spaces

S2old(798,[χ]) S_{2}^{\mathrm{old}}(798, [\chi]) \simeq S2new(133,[χ])S_{2}^{\mathrm{new}}(133, [\chi])4^{\oplus 4}\oplusS2new(266,[χ])S_{2}^{\mathrm{new}}(266, [\chi])2^{\oplus 2}\oplusS2new(399,[χ])S_{2}^{\mathrm{new}}(399, [\chi])2^{\oplus 2}