Properties

Label 1089.6.a
Level 10891089
Weight 66
Character orbit 1089.a
Rep. character χ1089(1,)\chi_{1089}(1,\cdot)
Character field Q\Q
Dimension 222222
Newform subspaces 4141
Sturm bound 792792
Trace bound 77

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Defining parameters

Level: N N == 1089=32112 1089 = 3^{2} \cdot 11^{2}
Weight: k k == 6 6
Character orbit: [χ][\chi] == 1089.a (trivial)
Character field: Q\Q
Newform subspaces: 41 41
Sturm bound: 792792
Trace bound: 77
Distinguishing TpT_p: 22, 55, 77

Dimensions

The following table gives the dimensions of various subspaces of M6(Γ0(1089))M_{6}(\Gamma_0(1089)).

Total New Old
Modular forms 684 231 453
Cusp forms 636 222 414
Eisenstein series 48 9 39

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

331111FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
++++++168168424212612615615642421141141212001212
++--174174484812612616216248481141141212001212
-++-17417471711031031621626767959512124488
--++168168707098981561566565919112125577
Plus space++3363361121122242243123121071072052052424551919
Minus space-3483481191192292293243241151152092092424442020

Trace form

222q2q2+3456q4+72q5+18q7312q8+158q10+252q13+1308q14+53940q161958q17+1960q19+2592q203630q23+131622q254704q26+66570q98+O(q100) 222 q - 2 q^{2} + 3456 q^{4} + 72 q^{5} + 18 q^{7} - 312 q^{8} + 158 q^{10} + 252 q^{13} + 1308 q^{14} + 53940 q^{16} - 1958 q^{17} + 1960 q^{19} + 2592 q^{20} - 3630 q^{23} + 131622 q^{25} - 4704 q^{26}+ \cdots - 66570 q^{98}+O(q^{100}) Copy content Toggle raw display

Decomposition of S6new(Γ0(1089))S_{6}^{\mathrm{new}}(\Gamma_0(1089)) into newform subspaces

Label Char Prim Dim AA Field CM Minimal twist Traces A-L signs Sato-Tate qq-expansion
a2a_{2} a3a_{3} a5a_{5} a7a_{7} 3 11
1089.6.a.a 1089.a 1.a 11 174.658174.658 Q\Q None 363.6.a.a 9-9 00 24-24 72-72 - ++ SU(2)\mathrm{SU}(2) q9q2+72q424q572q7153q8+q-9q^{2}+7^{2}q^{4}-24q^{5}-72q^{7}-153q^{8}+\cdots
1089.6.a.b 1089.a 1.a 11 174.658174.658 Q\Q None 3.6.a.a 6-6 00 6-6 4040 - - SU(2)\mathrm{SU}(2) q6q2+4q46q5+40q7+168q8+q-6q^{2}+4q^{4}-6q^{5}+40q^{7}+168q^{8}+\cdots
1089.6.a.c 1089.a 1.a 11 174.658174.658 Q\Q None 11.6.a.a 4-4 00 1919 10-10 - - SU(2)\mathrm{SU}(2) q4q224q4+19q510q7+192q8+q-4q^{2}-2^{4}q^{4}+19q^{5}-10q^{7}+192q^{8}+\cdots
1089.6.a.d 1089.a 1.a 11 174.658174.658 Q\Q None 33.6.a.a 2-2 00 46-46 148-148 - - SU(2)\mathrm{SU}(2) q2q228q446q5148q7+q-2q^{2}-28q^{4}-46q^{5}-148q^{7}+\cdots
1089.6.a.e 1089.a 1.a 11 174.658174.658 Q\Q Q(11)\Q(\sqrt{-11}) 121.6.a.a 00 00 57-57 00 - ++ N(U(1))N(\mathrm{U}(1)) q25q457q5+210q16+1824q20+q-2^{5}q^{4}-57q^{5}+2^{10}q^{16}+1824q^{20}+\cdots
1089.6.a.f 1089.a 1.a 11 174.658174.658 Q\Q Q(3)\Q(\sqrt{-3}) 1089.6.a.f 00 00 00 25-25 ++ - N(U(1))N(\mathrm{U}(1)) q25q452q7+1202q13+210q16+q-2^{5}q^{4}-5^{2}q^{7}+1202q^{13}+2^{10}q^{16}+\cdots
1089.6.a.g 1089.a 1.a 11 174.658174.658 Q\Q Q(3)\Q(\sqrt{-3}) 1089.6.a.f 00 00 00 2525 ++ - N(U(1))N(\mathrm{U}(1)) q25q4+52q71202q13+210q16+q-2^{5}q^{4}+5^{2}q^{7}-1202q^{13}+2^{10}q^{16}+\cdots
1089.6.a.h 1089.a 1.a 11 174.658174.658 Q\Q None 33.6.a.b 11 00 9292 2626 - - SU(2)\mathrm{SU}(2) q+q231q4+92q5+26q763q8+q+q^{2}-31q^{4}+92q^{5}+26q^{7}-63q^{8}+\cdots
1089.6.a.i 1089.a 1.a 11 174.658174.658 Q\Q None 363.6.a.a 99 00 24-24 7272 - ++ SU(2)\mathrm{SU}(2) q+9q2+72q424q5+72q7+153q8+q+9q^{2}+7^{2}q^{4}-24q^{5}+72q^{7}+153q^{8}+\cdots
1089.6.a.j 1089.a 1.a 22 174.658174.658 Q(177)\Q(\sqrt{177}) None 33.6.a.c 5-5 00 58-58 286286 - - SU(2)\mathrm{SU}(2) q+(2β)q2+(24+5β)q4+(24+)q5+q+(-2-\beta )q^{2}+(2^{4}+5\beta )q^{4}+(-24+\cdots)q^{5}+\cdots
1089.6.a.k 1089.a 1.a 22 174.658174.658 Q(3)\Q(\sqrt{3}) Q(3)\Q(\sqrt{-3}) 1089.6.a.k 00 00 00 00 ++ ++ N(U(1))N(\mathrm{U}(1)) q25q4149βq7+116βq13+210q16+q-2^{5}q^{4}-149\beta q^{7}+116\beta q^{13}+2^{10}q^{16}+\cdots
1089.6.a.l 1089.a 1.a 22 174.658174.658 Q(5)\Q(\sqrt{5}) None 363.6.a.h 00 00 196196 00 - ++ SU(2)\mathrm{SU}(2) qβq212q4+98q5+53βq7+q-\beta q^{2}-12q^{4}+98q^{5}+53\beta q^{7}+\cdots
1089.6.a.m 1089.a 1.a 22 174.658174.658 Q(38)\Q(\sqrt{38}) None 121.6.a.c 00 00 3838 00 - ++ SU(2)\mathrm{SU}(2) q+βq2+6q4+19q5+8βq726βq8+q+\beta q^{2}+6q^{4}+19q^{5}+8\beta q^{7}-26\beta q^{8}+\cdots
1089.6.a.n 1089.a 1.a 22 174.658174.658 Q(3)\Q(\sqrt{3}) None 363.6.a.i 00 00 48-48 00 - ++ SU(2)\mathrm{SU}(2) q+4βq2+24q424q5βq726βq8+q+4\beta q^{2}+2^{4}q^{4}-24q^{5}-\beta q^{7}-2^{6}\beta q^{8}+\cdots
1089.6.a.o 1089.a 1.a 22 174.658174.658 Q(313)\Q(\sqrt{313}) None 33.6.a.d 11 00 3838 1818 - - SU(2)\mathrm{SU}(2) q+βq2+(46+β)q4+(2410β)q5+q+\beta q^{2}+(46+\beta )q^{4}+(24-10\beta )q^{5}+\cdots
1089.6.a.p 1089.a 1.a 22 174.658174.658 Q(33)\Q(\sqrt{33}) None 33.6.a.e 1313 00 58-58 146-146 - - SU(2)\mathrm{SU}(2) q+(7β)q2+(5213β)q4+(24+)q5+q+(7-\beta )q^{2}+(5^{2}-13\beta )q^{4}+(-24+\cdots)q^{5}+\cdots
1089.6.a.q 1089.a 1.a 33 174.658174.658 3.3.193425.1 None 363.6.a.k 1-1 00 5858 117117 - - SU(2)\mathrm{SU}(2) qβ1q2+(6+β1+2β2)q4+(17+6β1+)q5+q-\beta _{1}q^{2}+(6+\beta _{1}+2\beta _{2})q^{4}+(17+6\beta _{1}+\cdots)q^{5}+\cdots
1089.6.a.r 1089.a 1.a 33 174.658174.658 3.3.54492.1 None 11.6.a.b 00 00 24-24 84-84 - - SU(2)\mathrm{SU}(2) q+β2q2+(282β14β2)q4+(8+)q5+q+\beta _{2}q^{2}+(28-2\beta _{1}-4\beta _{2})q^{4}+(-8+\cdots)q^{5}+\cdots
1089.6.a.s 1089.a 1.a 33 174.658174.658 3.3.193425.1 None 363.6.a.k 11 00 5858 117-117 - - SU(2)\mathrm{SU}(2) q+β1q2+(6+β1+2β2)q4+(17+6β1+)q5+q+\beta _{1}q^{2}+(6+\beta _{1}+2\beta _{2})q^{4}+(17+6\beta _{1}+\cdots)q^{5}+\cdots
1089.6.a.t 1089.a 1.a 44 174.658174.658 Q[x]/(x4)\mathbb{Q}[x]/(x^{4} - \cdots) None 363.6.a.m 9-9 00 42-42 14-14 - - SU(2)\mathrm{SU}(2) q+(2β1)q2+(12+6β1+β2)q4+q+(-2-\beta _{1})q^{2}+(12+6\beta _{1}+\beta _{2})q^{4}+\cdots
1089.6.a.u 1089.a 1.a 44 174.658174.658 Q[x]/(x4)\mathbb{Q}[x]/(x^{4} - \cdots) None 363.6.a.m 99 00 42-42 1414 - - SU(2)\mathrm{SU}(2) q+(2+β1)q2+(12+6β1+β2)q4+q+(2+\beta _{1})q^{2}+(12+6\beta _{1}+\beta _{2})q^{4}+\cdots
1089.6.a.v 1089.a 1.a 55 174.658174.658 Q[x]/(x5)\mathbb{Q}[x]/(x^{5} - \cdots) None 121.6.a.e 4-4 00 29-29 102-102 - - SU(2)\mathrm{SU}(2) q+(1+β1)q2+(21β1+β3)q4+q+(-1+\beta _{1})q^{2}+(21-\beta _{1}+\beta _{3})q^{4}+\cdots
1089.6.a.w 1089.a 1.a 55 174.658174.658 Q[x]/(x5)\mathbb{Q}[x]/(x^{5} - \cdots) None 99.6.a.h 4-4 00 100100 1818 ++ - SU(2)\mathrm{SU}(2) q+(1+β1)q2+(213β1+β4)q4+q+(-1+\beta _{1})q^{2}+(21-3\beta _{1}+\beta _{4})q^{4}+\cdots
1089.6.a.x 1089.a 1.a 55 174.658174.658 Q[x]/(x5)\mathbb{Q}[x]/(x^{5} - \cdots) None 99.6.a.h 44 00 100-100 1818 ++ - SU(2)\mathrm{SU}(2) q+(1β1)q2+(213β1+β4)q4+q+(1-\beta _{1})q^{2}+(21-3\beta _{1}+\beta _{4})q^{4}+\cdots
1089.6.a.y 1089.a 1.a 55 174.658174.658 Q[x]/(x5)\mathbb{Q}[x]/(x^{5} - \cdots) None 121.6.a.e 44 00 29-29 102102 - - SU(2)\mathrm{SU}(2) q+(1β1)q2+(21β1+β3)q4+(6+)q5+q+(1-\beta _{1})q^{2}+(21-\beta _{1}+\beta _{3})q^{4}+(-6+\cdots)q^{5}+\cdots
1089.6.a.z 1089.a 1.a 66 174.658174.658 6.6.\cdots.1 None 363.6.a.o 00 00 5050 00 - ++ SU(2)\mathrm{SU}(2) q+(β1+3β2)q2+(14+β37β4+)q4+q+(-\beta _{1}+3\beta _{2})q^{2}+(14+\beta _{3}-7\beta _{4}+\cdots)q^{4}+\cdots
1089.6.a.ba 1089.a 1.a 66 174.658174.658 Q[x]/(x6)\mathbb{Q}[x]/(x^{6} - \cdots) None 363.6.a.p 00 00 4848 00 - ++ SU(2)\mathrm{SU}(2) q+β1q2+(28+β2)q4+(8+β2+β4+)q5+q+\beta _{1}q^{2}+(28+\beta _{2})q^{4}+(8+\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots
1089.6.a.bb 1089.a 1.a 88 174.658174.658 Q[x]/(x8)\mathbb{Q}[x]/(x^{8} - \cdots) None 11.6.c.a 8-8 00 70-70 292292 - - SU(2)\mathrm{SU}(2) q+(1+β1)q2+(11β1+β2)q4+q+(-1+\beta _{1})q^{2}+(11-\beta _{1}+\beta _{2})q^{4}+\cdots
1089.6.a.bc 1089.a 1.a 88 174.658174.658 Q[x]/(x8)\mathbb{Q}[x]/(x^{8} - \cdots) None 1089.6.a.bc 00 00 00 00 ++ ++ SU(2)\mathrm{SU}(2) qβ4q2+(19β1)q4β2q5+β7q7+q-\beta _{4}q^{2}+(19-\beta _{1})q^{4}-\beta _{2}q^{5}+\beta _{7}q^{7}+\cdots
1089.6.a.bd 1089.a 1.a 88 174.658174.658 Q[x]/(x8)\mathbb{Q}[x]/(x^{8} - \cdots) None 121.6.a.h 00 00 256256 00 - ++ SU(2)\mathrm{SU}(2) q+β1q2+(192β2+β6)q4+(33+)q5+q+\beta _{1}q^{2}+(19-2\beta _{2}+\beta _{6})q^{4}+(33+\cdots)q^{5}+\cdots
1089.6.a.be 1089.a 1.a 88 174.658174.658 Q[x]/(x8)\mathbb{Q}[x]/(x^{8} - \cdots) None 1089.6.a.be 00 00 00 106-106 ++ - SU(2)\mathrm{SU}(2) q+β1q2+(52+β2)q4+(3β1β3+)q5+q+\beta _{1}q^{2}+(5^{2}+\beta _{2})q^{4}+(-3\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots
1089.6.a.bf 1089.a 1.a 88 174.658174.658 Q[x]/(x8)\mathbb{Q}[x]/(x^{8} - \cdots) None 1089.6.a.be 00 00 00 106106 ++ - SU(2)\mathrm{SU}(2) q+β1q2+(52+β2)q4+(3β1+β3+)q5+q+\beta _{1}q^{2}+(5^{2}+\beta _{2})q^{4}+(3\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots
1089.6.a.bg 1089.a 1.a 88 174.658174.658 Q[x]/(x8)\mathbb{Q}[x]/(x^{8} - \cdots) None 11.6.c.a 88 00 70-70 292-292 - ++ SU(2)\mathrm{SU}(2) q+(1β1)q2+(11β1+β2)q4+(9+)q5+q+(1-\beta _{1})q^{2}+(11-\beta _{1}+\beta _{2})q^{4}+(-9+\cdots)q^{5}+\cdots
1089.6.a.bh 1089.a 1.a 1010 174.658174.658 Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots) None 33.6.e.a 9-9 00 11-11 470470 - ++ SU(2)\mathrm{SU}(2) q+(1+β1)q2+(19β1+β2)q4+q+(-1+\beta _{1})q^{2}+(19-\beta _{1}+\beta _{2})q^{4}+\cdots
1089.6.a.bi 1089.a 1.a 1010 174.658174.658 Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots) None 33.6.e.b 7-7 00 3333 78-78 - - SU(2)\mathrm{SU}(2) q+(1+β1)q2+(15β1+β2β3+)q4+q+(-1+\beta _{1})q^{2}+(15-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots
1089.6.a.bj 1089.a 1.a 1010 174.658174.658 Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots) None 363.6.a.s 00 00 198-198 00 - ++ SU(2)\mathrm{SU}(2) q+β6q2+(18+β1)q4+(20β1+)q5+q+\beta _{6}q^{2}+(18+\beta _{1})q^{4}+(-20-\beta _{1}+\cdots)q^{5}+\cdots
1089.6.a.bk 1089.a 1.a 1010 174.658174.658 Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots) None 33.6.e.b 77 00 3333 7878 - ++ SU(2)\mathrm{SU}(2) q+(1β1)q2+(15β1+β2β3+)q4+q+(1-\beta _{1})q^{2}+(15-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots
1089.6.a.bl 1089.a 1.a 1010 174.658174.658 Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots) None 33.6.e.a 99 00 11-11 470-470 - - SU(2)\mathrm{SU}(2) q+(1β1)q2+(19β1+β2)q4+(1+)q5+q+(1-\beta _{1})q^{2}+(19-\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots
1089.6.a.bm 1089.a 1.a 1212 174.658174.658 Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots) None 1089.6.a.bm 00 00 00 00 ++ ++ SU(2)\mathrm{SU}(2) q+β6q2+(14+β3)q4+(β1β2)q5+q+\beta _{6}q^{2}+(14+\beta _{3})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots
1089.6.a.bn 1089.a 1.a 2020 174.658174.658 Q[x]/(x20)\mathbb{Q}[x]/(x^{20} - \cdots) None 99.6.f.d 00 00 00 472-472 ++ ++ SU(2)\mathrm{SU}(2) q+β1q2+(15+β2)q4+(β1β8+)q5+q+\beta _{1}q^{2}+(15+\beta _{2})q^{4}+(-\beta _{1}-\beta _{8}+\cdots)q^{5}+\cdots
1089.6.a.bo 1089.a 1.a 2020 174.658174.658 Q[x]/(x20)\mathbb{Q}[x]/(x^{20} - \cdots) None 99.6.f.d 00 00 00 472472 ++ - SU(2)\mathrm{SU}(2) q+β1q2+(15+β2)q4+(β1+β8)q5+q+\beta _{1}q^{2}+(15+\beta _{2})q^{4}+(\beta _{1}+\beta _{8})q^{5}+\cdots

Decomposition of S6old(Γ0(1089))S_{6}^{\mathrm{old}}(\Gamma_0(1089)) into lower level spaces