Properties

Label 1872.1.gc
Level 18721872
Weight 11
Character orbit 1872.gc
Rep. character χ1872(145,)\chi_{1872}(145,\cdot)
Character field Q(ζ12)\Q(\zeta_{12})
Dimension 44
Newform subspaces 11
Sturm bound 336336
Trace bound 00

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Defining parameters

Level: N N == 1872=243213 1872 = 2^{4} \cdot 3^{2} \cdot 13
Weight: k k == 1 1
Character orbit: [χ][\chi] == 1872.gc (of order 1212 and degree 44)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 13 13
Character field: Q(ζ12)\Q(\zeta_{12})
Newform subspaces: 1 1
Sturm bound: 336336
Trace bound: 00

Dimensions

The following table gives the dimensions of various subspaces of M1(1872,[χ])M_{1}(1872, [\chi]).

Total New Old
Modular forms 112 8 104
Cusp forms 16 4 12
Eisenstein series 96 4 92

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

DnD_n A4A_4 S4S_4 A5A_5
Dimension 4 0 0 0

Trace form

4q2q72q19+2q312q37+6q436q49+4q67+2q732q912q97+O(q100) 4 q - 2 q^{7} - 2 q^{19} + 2 q^{31} - 2 q^{37} + 6 q^{43} - 6 q^{49} + 4 q^{67} + 2 q^{73} - 2 q^{91} - 2 q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S1new(1872,[χ])S_{1}^{\mathrm{new}}(1872, [\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}
1872.1.gc.a 1872.gc 13.f 44 0.9340.934 Q(ζ12)\Q(\zeta_{12}) D12D_{12} Q(3)\Q(\sqrt{-3}) None 468.1.cd.a 00 00 00 2-2 q+(ζ122ζ123)q7ζ12q13+q+(-\zeta_{12}^{2}-\zeta_{12}^{3})q^{7}-\zeta_{12}q^{13}+\cdots

Decomposition of S1old(1872,[χ])S_{1}^{\mathrm{old}}(1872, [\chi]) into lower level spaces

S1old(1872,[χ]) S_{1}^{\mathrm{old}}(1872, [\chi]) \simeq S1new(468,[χ])S_{1}^{\mathrm{new}}(468, [\chi])3^{\oplus 3}