Properties

Label 1152.3.e
Level 11521152
Weight 33
Character orbit 1152.e
Rep. character χ1152(1025,)\chi_{1152}(1025,\cdot)
Character field Q\Q
Dimension 3232
Newform subspaces 88
Sturm bound 576576
Trace bound 2525

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Defining parameters

Level: N N == 1152=2732 1152 = 2^{7} \cdot 3^{2}
Weight: k k == 3 3
Character orbit: [χ][\chi] == 1152.e (of order 22 and degree 11)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 3 3
Character field: Q\Q
Newform subspaces: 8 8
Sturm bound: 576576
Trace bound: 2525
Distinguishing TpT_p: 55, 77, 1313

Dimensions

The following table gives the dimensions of various subspaces of M3(1152,[χ])M_{3}(1152, [\chi]).

Total New Old
Modular forms 416 32 384
Cusp forms 352 32 320
Eisenstein series 64 0 64

Trace form

32q160q25+96q49+640q73768q97+O(q100) 32 q - 160 q^{25} + 96 q^{49} + 640 q^{73} - 768 q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S3new(1152,[χ])S_{3}^{\mathrm{new}}(1152, [\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}
1152.3.e.a 1152.e 3.b 44 31.39031.390 Q(2,11)\Q(\sqrt{-2}, \sqrt{-11}) None 1152.3.e.a 00 00 00 8-8 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(β1β3)q52q7+(6β12β3)q11+q+(\beta _{1}-\beta _{3})q^{5}-2q^{7}+(6\beta _{1}-2\beta _{3})q^{11}+\cdots
1152.3.e.b 1152.e 3.b 44 31.39031.390 Q(2,3)\Q(\sqrt{-2}, \sqrt{-3}) None 1152.3.e.b 00 00 00 8-8 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(β1+β2)q5+(2+2β3)q7+q+(-\beta _{1}+\beta _{2})q^{5}+(-2+2\beta _{3})q^{7}+\cdots
1152.3.e.c 1152.e 3.b 44 31.39031.390 Q(2,11)\Q(\sqrt{-2}, \sqrt{-11}) None 1152.3.e.a 00 00 00 8-8 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(β1β3)q52q7+(6β12β3)q11+q+(\beta _{1}-\beta _{3})q^{5}-2q^{7}+(6\beta _{1}-2\beta _{3})q^{11}+\cdots
1152.3.e.d 1152.e 3.b 44 31.39031.390 Q(2,3)\Q(\sqrt{-2}, \sqrt{-3}) None 1152.3.e.b 00 00 00 8-8 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(β1+β2)q5+(2+2β3)q7+q+(-\beta _{1}+\beta _{2})q^{5}+(-2+2\beta _{3})q^{7}+\cdots
1152.3.e.e 1152.e 3.b 44 31.39031.390 Q(2,11)\Q(\sqrt{-2}, \sqrt{-11}) None 1152.3.e.a 00 00 00 88 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(β1β3)q5+2q7+(6β1+2β3)q11+q+(\beta _{1}-\beta _{3})q^{5}+2q^{7}+(-6\beta _{1}+2\beta _{3})q^{11}+\cdots
1152.3.e.f 1152.e 3.b 44 31.39031.390 Q(2,3)\Q(\sqrt{-2}, \sqrt{-3}) None 1152.3.e.b 00 00 00 88 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(β1+β2)q5+(22β3)q7+(2β1+)q11+q+(-\beta _{1}+\beta _{2})q^{5}+(2-2\beta _{3})q^{7}+(-2\beta _{1}+\cdots)q^{11}+\cdots
1152.3.e.g 1152.e 3.b 44 31.39031.390 Q(2,11)\Q(\sqrt{-2}, \sqrt{-11}) None 1152.3.e.a 00 00 00 88 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(β1β3)q5+2q7+(6β1+2β3)q11+q+(\beta _{1}-\beta _{3})q^{5}+2q^{7}+(-6\beta _{1}+2\beta _{3})q^{11}+\cdots
1152.3.e.h 1152.e 3.b 44 31.39031.390 Q(2,3)\Q(\sqrt{-2}, \sqrt{-3}) None 1152.3.e.b 00 00 00 88 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(β1+β2)q5+(22β3)q7+(2β1+)q11+q+(-\beta _{1}+\beta _{2})q^{5}+(2-2\beta _{3})q^{7}+(-2\beta _{1}+\cdots)q^{11}+\cdots

Decomposition of S3old(1152,[χ])S_{3}^{\mathrm{old}}(1152, [\chi]) into lower level spaces