Properties

Label 2880.2.f
Level 28802880
Weight 22
Character orbit 2880.f
Rep. character χ2880(1729,)\chi_{2880}(1729,\cdot)
Character field Q\Q
Dimension 5858
Newform subspaces 2424
Sturm bound 11521152
Trace bound 2525

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Defining parameters

Level: N N == 2880=26325 2880 = 2^{6} \cdot 3^{2} \cdot 5
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2880.f (of order 22 and degree 11)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 5 5
Character field: Q\Q
Newform subspaces: 24 24
Sturm bound: 11521152
Trace bound: 2525
Distinguishing TpT_p: 77, 1111, 1313, 1717, 1919, 2929

Dimensions

The following table gives the dimensions of various subspaces of M2(2880,[χ])M_{2}(2880, [\chi]).

Total New Old
Modular forms 624 62 562
Cusp forms 528 58 470
Eisenstein series 96 4 92

Trace form

58q2q5+2q254q294q4150q4912q6132q85+12q89+O(q100) 58 q - 2 q^{5} + 2 q^{25} - 4 q^{29} - 4 q^{41} - 50 q^{49} - 12 q^{61} - 32 q^{85} + 12 q^{89}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(2880,[χ])S_{2}^{\mathrm{new}}(2880, [\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}
2880.2.f.a 2880.f 5.b 22 22.99722.997 Q(1)\Q(\sqrt{-1}) None 480.2.f.a 00 00 4-4 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(i2)q5+2iq76q11+q+(-i-2)q^{5}+2 i q^{7}-6 q^{11}+\cdots
2880.2.f.b 2880.f 5.b 22 22.99722.997 Q(1)\Q(\sqrt{-1}) None 360.2.f.b 00 00 4-4 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(i2)q5+4iq74q11+4iq13+q+(i-2)q^{5}+4 i q^{7}-4 q^{11}+4 i q^{13}+\cdots
2880.2.f.c 2880.f 5.b 22 22.99722.997 Q(1)\Q(\sqrt{-1}) None 30.2.c.a 00 00 4-4 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(i2)q5+2iq72q116iq13+q+(i-2)q^{5}+2 i q^{7}-2 q^{11}-6 i q^{13}+\cdots
2880.2.f.d 2880.f 5.b 22 22.99722.997 Q(1)\Q(\sqrt{-1}) Q(1)\Q(\sqrt{-1}) 1440.2.f.a 00 00 4-4 00 U(1)[D2]\mathrm{U}(1)[D_{2}] q+(i2)q5+4iq132iq17+(4i+3)q25+q+(i-2)q^{5}+4 i q^{13}-2 i q^{17}+(-4 i+3)q^{25}+\cdots
2880.2.f.e 2880.f 5.b 22 22.99722.997 Q(1)\Q(\sqrt{-1}) None 30.2.c.a 00 00 4-4 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(i2)q5+2iq7+2q11+q+(-i-2)q^{5}+2 i q^{7}+2 q^{11}+\cdots
2880.2.f.f 2880.f 5.b 22 22.99722.997 Q(1)\Q(\sqrt{-1}) None 360.2.f.b 00 00 4-4 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(i2)q5+4iq7+4q11+q+(-i-2)q^{5}+4 i q^{7}+4 q^{11}+\cdots
2880.2.f.g 2880.f 5.b 22 22.99722.997 Q(1)\Q(\sqrt{-1}) None 480.2.f.a 00 00 4-4 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(i2)q5+2iq7+6q11+2iq13+q+(i-2)q^{5}+2 i q^{7}+6 q^{11}+2 i q^{13}+\cdots
2880.2.f.h 2880.f 5.b 22 22.99722.997 Q(1)\Q(\sqrt{-1}) None 40.2.c.a 00 00 2-2 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(β1)q5+βq74q11+2βq13+q+(\beta-1)q^{5}+\beta q^{7}-4 q^{11}+2\beta q^{13}+\cdots
2880.2.f.i 2880.f 5.b 22 22.99722.997 Q(1)\Q(\sqrt{-1}) None 40.2.c.a 00 00 2-2 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(β1)q5+βq7+4q112βq13+q+(-\beta-1)q^{5}+\beta q^{7}+4 q^{11}-2\beta q^{13}+\cdots
2880.2.f.j 2880.f 5.b 22 22.99722.997 Q(5)\Q(\sqrt{-5}) Q(15)\Q(\sqrt{-15}) 45.2.b.a 00 00 00 00 U(1)[D2]\mathrm{U}(1)[D_{2}] qβq5+2βq174q19+4βq23+q-\beta q^{5}+2\beta q^{17}-4q^{19}+4\beta q^{23}+\cdots
2880.2.f.k 2880.f 5.b 22 22.99722.997 Q(5)\Q(\sqrt{-5}) Q(15)\Q(\sqrt{-15}) 45.2.b.a 00 00 00 00 U(1)[D2]\mathrm{U}(1)[D_{2}] qβq5+2βq17+4q194βq23+q-\beta q^{5}+2\beta q^{17}+4q^{19}-4\beta q^{23}+\cdots
2880.2.f.l 2880.f 5.b 22 22.99722.997 Q(1)\Q(\sqrt{-1}) None 60.2.d.a 00 00 22 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(β+1)q5+2βq74q11+q+(-\beta+1)q^{5}+2\beta q^{7}-4 q^{11}+\cdots
2880.2.f.m 2880.f 5.b 22 22.99722.997 Q(1)\Q(\sqrt{-1}) None 480.2.f.c 00 00 22 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(β+1)q5+2βq72βq13+q+(-\beta+1)q^{5}+2\beta q^{7}-2\beta q^{13}+\cdots
2880.2.f.n 2880.f 5.b 22 22.99722.997 Q(1)\Q(\sqrt{-1}) Q(1)\Q(\sqrt{-1}) 160.2.c.a 00 00 22 00 U(1)[D2]\mathrm{U}(1)[D_{2}] q+(β+1)q5+2βq134βq17+q+(-\beta+1)q^{5}+2\beta q^{13}-4\beta q^{17}+\cdots
2880.2.f.o 2880.f 5.b 22 22.99722.997 Q(1)\Q(\sqrt{-1}) None 480.2.f.c 00 00 22 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(β+1)q5+2βq7+2βq13+8q19+q+(\beta+1)q^{5}+2\beta q^{7}+2\beta q^{13}+8 q^{19}+\cdots
2880.2.f.p 2880.f 5.b 22 22.99722.997 Q(1)\Q(\sqrt{-1}) None 60.2.d.a 00 00 22 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(β+1)q5+2βq7+4q11+2βq17+q+(\beta+1)q^{5}+2\beta q^{7}+4 q^{11}+2\beta q^{17}+\cdots
2880.2.f.q 2880.f 5.b 22 22.99722.997 Q(1)\Q(\sqrt{-1}) None 360.2.f.b 00 00 44 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(i+2)q5+4iq74q114iq13+q+(i+2)q^{5}+4 i q^{7}-4 q^{11}-4 i q^{13}+\cdots
2880.2.f.r 2880.f 5.b 22 22.99722.997 Q(1)\Q(\sqrt{-1}) None 120.2.f.a 00 00 44 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(i+2)q5+2iq72q11+2iq13+q+(i+2)q^{5}+2 i q^{7}-2 q^{11}+2 i q^{13}+\cdots
2880.2.f.s 2880.f 5.b 22 22.99722.997 Q(1)\Q(\sqrt{-1}) Q(1)\Q(\sqrt{-1}) 1440.2.f.a 00 00 44 00 U(1)[D2]\mathrm{U}(1)[D_{2}] q+(i+2)q54iq132iq17+(4i+3)q25+q+(i+2)q^{5}-4 i q^{13}-2 i q^{17}+(4 i+3)q^{25}+\cdots
2880.2.f.t 2880.f 5.b 22 22.99722.997 Q(1)\Q(\sqrt{-1}) None 120.2.f.a 00 00 44 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(i+2)q5+2iq7+2q11+q+(-i+2)q^{5}+2 i q^{7}+2 q^{11}+\cdots
2880.2.f.u 2880.f 5.b 22 22.99722.997 Q(1)\Q(\sqrt{-1}) None 360.2.f.b 00 00 44 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(i+2)q5+4iq7+4q11+q+(-i+2)q^{5}+4 i q^{7}+4 q^{11}+\cdots
2880.2.f.v 2880.f 5.b 44 22.99722.997 Q(i,5)\Q(i, \sqrt{5}) None 480.2.f.e 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qβ1q5+β2q7β3q11+2β1q13+q-\beta _{1}q^{5}+\beta _{2}q^{7}-\beta _{3}q^{11}+2\beta _{1}q^{13}+\cdots
2880.2.f.w 2880.f 5.b 44 22.99722.997 Q(i,5)\Q(i, \sqrt{5}) Q(5)\Q(\sqrt{-5}) 160.2.c.b 00 00 00 00 U(1)[D2]\mathrm{U}(1)[D_{2}] q+β3q5β1q7+(β1+2β2)q23+q+\beta _{3}q^{5}-\beta _{1}q^{7}+(-\beta _{1}+2\beta _{2})q^{23}+\cdots
2880.2.f.x 2880.f 5.b 88 22.99722.997 Q(ζ24)\Q(\zeta_{24}) None 1440.2.f.j 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β4q5+β5q7+β6q11+β7q13+q+\beta_{4} q^{5}+\beta_{5} q^{7}+\beta_{6} q^{11}+\beta_{7} q^{13}+\cdots

Decomposition of S2old(2880,[χ])S_{2}^{\mathrm{old}}(2880, [\chi]) into lower level spaces

S2old(2880,[χ]) S_{2}^{\mathrm{old}}(2880, [\chi]) \simeq S2new(30,[χ])S_{2}^{\mathrm{new}}(30, [\chi])12^{\oplus 12}\oplusS2new(40,[χ])S_{2}^{\mathrm{new}}(40, [\chi])12^{\oplus 12}\oplusS2new(45,[χ])S_{2}^{\mathrm{new}}(45, [\chi])7^{\oplus 7}\oplusS2new(60,[χ])S_{2}^{\mathrm{new}}(60, [\chi])10^{\oplus 10}\oplusS2new(80,[χ])S_{2}^{\mathrm{new}}(80, [\chi])9^{\oplus 9}\oplusS2new(90,[χ])S_{2}^{\mathrm{new}}(90, [\chi])6^{\oplus 6}\oplusS2new(120,[χ])S_{2}^{\mathrm{new}}(120, [\chi])8^{\oplus 8}\oplusS2new(160,[χ])S_{2}^{\mathrm{new}}(160, [\chi])6^{\oplus 6}\oplusS2new(180,[χ])S_{2}^{\mathrm{new}}(180, [\chi])5^{\oplus 5}\oplusS2new(240,[χ])S_{2}^{\mathrm{new}}(240, [\chi])6^{\oplus 6}\oplusS2new(320,[χ])S_{2}^{\mathrm{new}}(320, [\chi])3^{\oplus 3}\oplusS2new(360,[χ])S_{2}^{\mathrm{new}}(360, [\chi])4^{\oplus 4}\oplusS2new(480,[χ])S_{2}^{\mathrm{new}}(480, [\chi])4^{\oplus 4}\oplusS2new(720,[χ])S_{2}^{\mathrm{new}}(720, [\chi])3^{\oplus 3}\oplusS2new(960,[χ])S_{2}^{\mathrm{new}}(960, [\chi])2^{\oplus 2}\oplusS2new(1440,[χ])S_{2}^{\mathrm{new}}(1440, [\chi])2^{\oplus 2}