Properties

Label 3072.1.i
Level 30723072
Weight 11
Character orbit 3072.i
Rep. character χ3072(257,)\chi_{3072}(257,\cdot)
Character field Q(ζ4)\Q(\zeta_{4})
Dimension 2424
Newform subspaces 88
Sturm bound 512512
Trace bound 3333

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Defining parameters

Level: N N == 3072=2103 3072 = 2^{10} \cdot 3
Weight: k k == 1 1
Character orbit: [χ][\chi] == 3072.i (of order 44 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 48 48
Character field: Q(i)\Q(i)
Newform subspaces: 8 8
Sturm bound: 512512
Trace bound: 3333

Dimensions

The following table gives the dimensions of various subspaces of M1(3072,[χ])M_{1}(3072, [\chi]).

Total New Old
Modular forms 144 40 104
Cusp forms 48 24 24
Eisenstein series 96 16 80

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

DnD_n A4A_4 S4S_4 A5A_5
Dimension 24 0 0 0

Trace form

24q+8q498q8116q97+O(q100) 24 q + 8 q^{49} - 8 q^{81} - 16 q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S1new(3072,[χ])S_{1}^{\mathrm{new}}(3072, [\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}
3072.1.i.a 3072.i 48.i 22 1.5331.533 Q(1)\Q(\sqrt{-1}) D4D_{4} Q(2)\Q(\sqrt{-2}) None 1536.1.e.b 00 2-2 00 00 qq3+q9+(i1)q112iq17+q-q^{3}+q^{9}+(i-1)q^{11}-2 i q^{17}+\cdots
3072.1.i.b 3072.i 48.i 22 1.5331.533 Q(1)\Q(\sqrt{-1}) D4D_{4} Q(2)\Q(\sqrt{-2}) None 1536.1.e.b 00 00 00 00 qiq3q9+(i1)q11+2iq17+q-i q^{3}-q^{9}+(i-1)q^{11}+2 i q^{17}+\cdots
3072.1.i.c 3072.i 48.i 22 1.5331.533 Q(1)\Q(\sqrt{-1}) D4D_{4} Q(2)\Q(\sqrt{-2}) None 1536.1.e.b 00 00 00 00 q+iq3q9+(i+1)q11+2iq17+q+i q^{3}-q^{9}+(-i+1)q^{11}+2 i q^{17}+\cdots
3072.1.i.d 3072.i 48.i 22 1.5331.533 Q(1)\Q(\sqrt{-1}) D4D_{4} Q(2)\Q(\sqrt{-2}) None 1536.1.e.b 00 22 00 00 q+q3+q9+(i+1)q112iq17+q+q^{3}+q^{9}+(-i+1)q^{11}-2 i q^{17}+\cdots
3072.1.i.e 3072.i 48.i 44 1.5331.533 Q(ζ8)\Q(\zeta_{8}) D4D_{4} Q(6)\Q(\sqrt{-6}) None 1536.1.e.a 00 00 4-4 00 q+ζ83q3+(1ζ82)q5+(ζ8+ζ83+)q7+q+\zeta_{8}^{3}q^{3}+(-1-\zeta_{8}^{2})q^{5}+(\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{7}+\cdots
3072.1.i.f 3072.i 48.i 44 1.5331.533 Q(ζ8)\Q(\zeta_{8}) D2D_{2} Q(2)\Q(\sqrt{-2}) , Q(6)\Q(\sqrt{-6}) Q(3)\Q(\sqrt{3}) 384.1.h.a 00 00 00 00 qζ83q3ζ82q9ζ8q11ζ82q25+q-\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{9}-\zeta_{8}q^{11}-\zeta_{8}^{2}q^{25}+\cdots
3072.1.i.g 3072.i 48.i 44 1.5331.533 Q(ζ8)\Q(\zeta_{8}) D2D_{2} Q(3)\Q(\sqrt{-3}) , Q(2)\Q(\sqrt{-2}) Q(6)\Q(\sqrt{6}) 192.1.h.a 00 00 00 00 qζ8q3+ζ82q9ζ8q19ζ82q25+q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{9}-\zeta_{8}q^{19}-\zeta_{8}^{2}q^{25}+\cdots
3072.1.i.h 3072.i 48.i 44 1.5331.533 Q(ζ8)\Q(\zeta_{8}) D4D_{4} Q(6)\Q(\sqrt{-6}) None 1536.1.e.a 00 00 44 00 q+ζ83q3+(1+ζ82)q5+(ζ8ζ83+)q7+q+\zeta_{8}^{3}q^{3}+(1+\zeta_{8}^{2})q^{5}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{7}+\cdots

Decomposition of S1old(3072,[χ])S_{1}^{\mathrm{old}}(3072, [\chi]) into lower level spaces

S1old(3072,[χ]) S_{1}^{\mathrm{old}}(3072, [\chi]) \simeq S1new(768,[χ])S_{1}^{\mathrm{new}}(768, [\chi])3^{\oplus 3}