Properties

 Label 880.2.bo.j Level $880$ Weight $2$ Character orbit 880.bo Analytic conductor $7.027$ Analytic rank $0$ Dimension $12$ Inner twists $2$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(81,880)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("880.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$880 = 2^{4} \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 880.bo (of order $$5$$, degree $$4$$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$7.02683537787$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$3$$ over $$\Q(\zeta_{5})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{12} - 2 x^{11} + 15 x^{10} - 22 x^{9} + 89 x^{8} - 118 x^{7} + 205 x^{6} - 68 x^{5} + 1061 x^{4} + \cdots + 400$$ x^12 - 2*x^11 + 15*x^10 - 22*x^9 + 89*x^8 - 118*x^7 + 205*x^6 - 68*x^5 + 1061*x^4 - 1490*x^3 + 2760*x^2 - 1600*x + 400 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 440) Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

Coefficients of the $$q$$-expansion are expressed in terms of a basis $$1,\beta_1,\ldots,\beta_{11}$$ for the coefficient ring described below. We also show the integral $$q$$-expansion of the trace form.

 $$f(q)$$ $$=$$ $$q + ( - \beta_{5} - \beta_1) q^{3} + \beta_{8} q^{5} + (\beta_{9} - \beta_{8} + \beta_{7} + \cdots + 1) q^{7}+ \cdots + ( - \beta_{11} - \beta_{10} + \beta_{9} + \cdots - 1) q^{9}+O(q^{10})$$ q + (-b5 - b1) * q^3 + b8 * q^5 + (b9 - b8 + b7 - b2 + 1) * q^7 + (-b11 - b10 + b9 + 3*b8 - 2*b7 + b6 - 1) * q^9 $$q + ( - \beta_{5} - \beta_1) q^{3} + \beta_{8} q^{5} + (\beta_{9} - \beta_{8} + \beta_{7} + \cdots + 1) q^{7}+ \cdots + ( - \beta_{11} - \beta_{10} + \cdots + 4 \beta_1) q^{99}+O(q^{100})$$ q + (-b5 - b1) * q^3 + b8 * q^5 + (b9 - b8 + b7 - b2 + 1) * q^7 + (-b11 - b10 + b9 + 3*b8 - 2*b7 + b6 - 1) * q^9 + (b11 + b6 - b5) * q^11 + (-b10 + b9 - 2*b8 + 3*b7 - b6 + b3 - b2 + 1) * q^13 + (b4 + b1) * q^15 + (-b10 - 2*b8 + 2*b7 - b3 - b2 - b1 + 2) * q^17 + (-b9 + b8 + b7 + b6 + b4 - b3) * q^19 + (-b11 + b10 + b2 - b1) * q^21 + (b7 - b6 - 2*b2 - b1 - 2) * q^23 + b7 * q^25 + (-b11 - b10 + b9 + b7 + 3*b4 + 2*b3 - b2 + 2*b1) * q^27 + (b11 - 2*b8 + b5 + b4 + b3 + 2*b1 + 2) * q^29 + (b11 - 2*b3 - b2) * q^31 + (-b11 + b9 + 2*b8 - 3*b7 - 2*b5 - 2*b4 + b2 - 3*b1 - 4) * q^33 + (b11 + b8 - b7 - b2) * q^35 + (b11 + 3*b8 + b6 - 2*b5 - 2*b3 - 2*b1 - 3) * q^37 + (-2*b11 - b10 + 2*b9 + 6*b8 - b3 - b2 - b1 - 2) * q^39 + (b10 + b9 - b8 - b6 - b5 - 3*b4 + 3*b3 - b1) * q^41 + (-b11 + b10 - 2*b5 - 2*b4 + 3*b2 - 2*b1 - 2) * q^43 + (-b11 + b10 + 2*b7 - 2*b6 - 1) * q^45 + (2*b10 - b8 - 2*b7 - b6 + b4 - b3) * q^47 + (-b11 - 3*b10 + b9 + b8 + b4 - b3 - 3*b2 - b1 - 1) * q^49 + (b11 - 2*b8 + 4*b6 - 2*b5 - b4 - 2*b3 - 3*b1 + 2) * q^51 + (b10 - b9 + 3*b8 - 4*b7 + 2*b6 + b2 - 2) * q^53 + (-b10 + b9 + b8 + b6 - b2 + b1 - 1) * q^55 + (b11 + b10 - b9 - 2*b8 + b7 + 2*b6 - b5 - 3*b3 - 2) * q^57 + (-2*b11 + 3*b8 + b6 + b5 - 3*b4 + b3 - 2*b1 - 3) * q^59 + (-3*b11 + 3*b9 + 5*b7 + b4 - 2*b3 - 2*b1 + 2) * q^61 + (-b10 + 2*b9 + b8 + 3*b7 + b6 + b5 + b1) * q^63 + (-b7 + b6 + b5 + b4 - b2 + b1 + 1) * q^65 + (-2*b11 + 2*b10 - 2*b7 + 2*b6 - b5 - b4 + 2*b2 - 2*b1 - 4) * q^67 + (b10 + 4*b8 - 2*b7 + 4*b6 + 5*b5 + 3*b4 - 3*b3 + 5*b1) * q^69 + (4*b8 - 6*b7 + b4 + b3 + b1 - 6) * q^71 + (2*b9 - 2*b8 + 2*b7 - b5 + b4 - b3 - 2*b2 + 2) * q^73 - b3 * q^75 + (3*b11 - 2*b9 + b8 - 5*b7 - b5 + 2*b4 - b3 - b2 - b1 - 3) * q^77 + (b10 - b9 - 4*b8 + 3*b7 - 8*b6 + 3*b5 - b3 + b2 + 8) * q^79 + (-3*b11 + 10*b8 + b6 + b5 + 2*b4 + b3 + 3*b1 - 10) * q^81 + (-b11 + b10 + b9 - 10*b8 + 5*b7 - b4 - b3 + b2 - b1 + 4) * q^83 + (-b9 + 2*b8 - 3*b7 + 2*b6 - b5 - b1) * q^85 + (-b11 + b10 + 6*b7 - 6*b6 - 3*b5 - 3*b4 - 6*b1 - 2) * q^87 + (-b11 + b10 + 7*b7 - 7*b6 - 3*b5 - 3*b4 - b1 + 2) * q^89 + (-4*b10 - 6*b8 + 5*b7 - 6*b6) * q^91 + (2*b11 + 3*b10 - 2*b9 - 12*b8 + 2*b7 - b3 + 3*b2 - b1 + 4) * q^93 + (-b9 + b8 - b7 + 3*b6 - b5 - b3 + b2 - b1 - 1) * q^95 + (3*b11 + 2*b8 - 2*b7 + 4*b6 - 5*b5 - b3 - 3*b2 - 4) * q^97 + (-b11 - b10 + 2*b9 + 8*b8 - 9*b7 + 8*b6 + b5 + 2*b4 + 3*b3 + 4*b1) * q^99 $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q + q^{3} + 3 q^{5} + 8 q^{7} + 10 q^{9}+O(q^{10})$$ 12 * q + q^3 + 3 * q^5 + 8 * q^7 + 10 * q^9 $$12 q + q^{3} + 3 q^{5} + 8 q^{7} + 10 q^{9} + 4 q^{11} - 7 q^{13} - q^{15} + 7 q^{17} - 3 q^{19} + 4 q^{21} - 36 q^{23} - 3 q^{25} - 8 q^{27} + 13 q^{29} - 2 q^{31} - 19 q^{33} + 2 q^{35} - 22 q^{37} + q^{39} + 7 q^{41} - 6 q^{43} - 20 q^{45} + 2 q^{47} - 19 q^{49} + 33 q^{51} + 3 q^{53} - 4 q^{55} - 25 q^{57} - 19 q^{59} + 22 q^{61} + 2 q^{63} + 12 q^{65} - 22 q^{67} + 21 q^{69} - 44 q^{71} + 17 q^{73} + q^{75} - 38 q^{77} + 43 q^{79} - 85 q^{81} + 15 q^{83} + 18 q^{85} - 50 q^{87} + 2 q^{89} - 59 q^{91} + 5 q^{93} + 3 q^{95} - 20 q^{97} + 79 q^{99}+O(q^{100})$$ 12 * q + q^3 + 3 * q^5 + 8 * q^7 + 10 * q^9 + 4 * q^11 - 7 * q^13 - q^15 + 7 * q^17 - 3 * q^19 + 4 * q^21 - 36 * q^23 - 3 * q^25 - 8 * q^27 + 13 * q^29 - 2 * q^31 - 19 * q^33 + 2 * q^35 - 22 * q^37 + q^39 + 7 * q^41 - 6 * q^43 - 20 * q^45 + 2 * q^47 - 19 * q^49 + 33 * q^51 + 3 * q^53 - 4 * q^55 - 25 * q^57 - 19 * q^59 + 22 * q^61 + 2 * q^63 + 12 * q^65 - 22 * q^67 + 21 * q^69 - 44 * q^71 + 17 * q^73 + q^75 - 38 * q^77 + 43 * q^79 - 85 * q^81 + 15 * q^83 + 18 * q^85 - 50 * q^87 + 2 * q^89 - 59 * q^91 + 5 * q^93 + 3 * q^95 - 20 * q^97 + 79 * q^99

Basis of coefficient ring in terms of a root $$\nu$$ of $$x^{12} - 2 x^{11} + 15 x^{10} - 22 x^{9} + 89 x^{8} - 118 x^{7} + 205 x^{6} - 68 x^{5} + 1061 x^{4} + \cdots + 400$$ :

 $$\beta_{1}$$ $$=$$ $$( - 183142278447 \nu^{11} - 2277678635906 \nu^{10} + 1497463471915 \nu^{9} + \cdots - 16\!\cdots\!00 ) / 26\!\cdots\!80$$ (-183142278447*v^11 - 2277678635906*v^10 + 1497463471915*v^9 - 30087268866496*v^8 + 29245002805097*v^7 - 154939442724244*v^6 + 266629054674695*v^5 - 240285553385674*v^4 - 92746660753747*v^3 - 2354762567691180*v^2 + 1742774610010020*v - 1648503774716000) / 2606027312424580 $$\beta_{2}$$ $$=$$ $$( 147497735591 \nu^{11} - 5588599527022 \nu^{10} + 8587750298190 \nu^{9} + \cdots - 66\!\cdots\!00 ) / 13\!\cdots\!90$$ (147497735591*v^11 - 5588599527022*v^10 + 8587750298190*v^9 - 73833360070702*v^8 + 68915346516889*v^7 - 402369327473788*v^6 + 312592108338825*v^5 - 675483717280503*v^4 - 182908370810539*v^3 - 5759913874922060*v^2 + 4256164729559740*v - 6612888446198900) / 1303013656212290 $$\beta_{3}$$ $$=$$ $$( 1378720916147 \nu^{11} - 1842154717364 \nu^{10} + 18603057405925 \nu^{9} + \cdots - 924275028852200 ) / 13\!\cdots\!90$$ (1378720916147*v^11 - 1842154717364*v^10 + 18603057405925*v^9 - 17837336734524*v^8 + 102251116020973*v^7 - 97549393144111*v^6 + 193197001790390*v^5 + 12264590152539*v^4 + 1755990492478992*v^3 - 1215325772161065*v^2 + 3722345652192940*v - 924275028852200) / 1303013656212290 $$\beta_{4}$$ $$=$$ $$( 1378720916147 \nu^{11} - 1842154717364 \nu^{10} + 18603057405925 \nu^{9} + \cdots - 924275028852200 ) / 13\!\cdots\!90$$ (1378720916147*v^11 - 1842154717364*v^10 + 18603057405925*v^9 - 17837336734524*v^8 + 102251116020973*v^7 - 97549393144111*v^6 + 193197001790390*v^5 + 12264590152539*v^4 + 1755990492478992*v^3 - 1215325772161065*v^2 + 2419331995980650*v - 924275028852200) / 1303013656212290 $$\beta_{5}$$ $$=$$ $$( - 1424041493464 \nu^{11} + 3116845670683 \nu^{10} - 20053332036635 \nu^{9} + \cdots + 850171561945900 ) / 13\!\cdots\!90$$ (-1424041493464*v^11 + 3116845670683*v^10 - 20053332036635*v^9 + 32255738450963*v^8 - 107199681059821*v^7 + 163813581245752*v^6 - 220603989140845*v^5 + 24454148736947*v^4 - 1555609447024369*v^3 + 2497996402608885*v^2 - 3408509920704830*v + 850171561945900) / 1303013656212290 $$\beta_{6}$$ $$=$$ $$( - 4121259436790 \nu^{11} + 8425661152027 \nu^{10} - 59541212915944 \nu^{9} + \cdots + 48\!\cdots\!80 ) / 26\!\cdots\!80$$ (-4121259436790*v^11 + 8425661152027*v^10 - 59541212915944*v^9 + 89170244137465*v^8 - 336704821007814*v^7 + 457063610736123*v^6 - 689918741817706*v^5 + 13616587027025*v^4 - 4132370709048516*v^3 + 6233423221570847*v^2 - 9019913477849220*v + 4851240488853980) / 2606027312424580 $$\beta_{7}$$ $$=$$ $$( - 8501715619459 \nu^{11} + 11307265265062 \nu^{10} - 115058351609153 \nu^{9} + \cdots - 31294691684920 ) / 52\!\cdots\!60$$ (-8501715619459*v^11 + 11307265265062*v^10 - 115058351609153*v^9 + 106824415481558*v^8 - 627629736327999*v^7 + 574403718856878*v^6 - 1087597377006087*v^5 - 304299294440168*v^4 - 8922503677298211*v^3 + 6445118484896434*v^2 - 13472749499271300*v - 31294691684920) / 5212054624849160 $$\beta_{8}$$ $$=$$ $$( 8983553542643 \nu^{11} - 18514673951448 \nu^{10} + 135296709681109 \nu^{9} + \cdots - 96\!\cdots\!20 ) / 52\!\cdots\!60$$ (8983553542643*v^11 - 18514673951448*v^10 + 135296709681109*v^9 - 200444349517156*v^8 + 797035334427991*v^7 - 1021363572577072*v^6 + 1796806343199891*v^5 - 187251480952154*v^4 + 9197854157530819*v^3 - 12769463918227072*v^2 + 25215765164103600*v - 9632793522256320) / 5212054624849160 $$\beta_{9}$$ $$=$$ $$( - 18735151134651 \nu^{11} + 22105897203158 \nu^{10} - 244513689144357 \nu^{9} + \cdots - 101022986909080 ) / 52\!\cdots\!60$$ (-18735151134651*v^11 + 22105897203158*v^10 - 244513689144357*v^9 + 185176192786462*v^8 - 1282537360997291*v^7 + 900392010848322*v^6 - 1923375955249163*v^5 - 1436069090473752*v^4 - 19645996427872639*v^3 + 14233625907471066*v^2 - 22183309240541180*v - 101022986909080) / 5212054624849160 $$\beta_{10}$$ $$=$$ $$( 1941584272431 \nu^{11} - 2386060570628 \nu^{10} + 28042643669239 \nu^{9} + \cdots + 56036595164120 ) / 521205462484916$$ (1941584272431*v^11 - 2386060570628*v^10 + 28042643669239*v^9 - 21463507938880*v^8 + 164032721905641*v^7 - 104187147462228*v^6 + 347213949415767*v^5 + 116552466659680*v^4 + 2118274106815911*v^3 - 1306058479840394*v^2 + 5117972342924684*v + 56036595164120) / 521205462484916 $$\beta_{11}$$ $$=$$ $$( 5268988587323 \nu^{11} - 10133555287451 \nu^{10} + 80319172840620 \nu^{9} + \cdots - 94\!\cdots\!00 ) / 13\!\cdots\!90$$ (5268988587323*v^11 - 10133555287451*v^10 + 80319172840620*v^9 - 113591392657021*v^8 + 483465954249437*v^7 - 626945786699369*v^6 + 1127239603091685*v^5 - 517586142711414*v^4 + 5540337336872943*v^3 - 7577240269545315*v^2 + 15884938959386980*v - 9478747747482100) / 1303013656212290
 $$\nu$$ $$=$$ $$-\beta_{4} + \beta_{3}$$ -b4 + b3 $$\nu^{2}$$ $$=$$ $$-\beta_{11} + 4\beta_{8} - 4\beta_{7} + 6\beta_{6} + \beta_{2} - 6$$ -b11 + 4*b8 - 4*b7 + 6*b6 + b2 - 6 $$\nu^{3}$$ $$=$$ $$-\beta_{11} + \beta_{10} + \beta_{9} + \beta_{7} + 7\beta_{4} - 2\beta_{3} + \beta_{2} - 2\beta_1$$ -b11 + b10 + b9 + b7 + 7*b4 - 2*b3 + b2 - 2*b1 $$\nu^{4}$$ $$=$$ $$3\beta_{11} + 9\beta_{9} - 22\beta_{8} + 9\beta_{7} - 46\beta_{6} - \beta_{5} + \beta_{4} - \beta_{3} - 9\beta_{2} + 22$$ 3*b11 + 9*b9 - 22*b8 + 9*b7 - 46*b6 - b5 + b4 - b3 - 9*b2 + 22 $$\nu^{5}$$ $$=$$ $$13\beta_{11} - 13\beta_{10} + 6\beta_{7} - 6\beta_{6} - 25\beta_{5} - 25\beta_{4} - 23\beta_{2} + 30\beta _1 + 8$$ 13*b11 - 13*b10 + 6*b7 - 6*b6 - 25*b5 - 25*b4 - 23*b2 + 30*b1 + 8 $$\nu^{6}$$ $$=$$ $$- 38 \beta_{10} - 78 \beta_{9} + 210 \beta_{8} + 92 \beta_{7} + 210 \beta_{6} + 16 \beta_{5} + \cdots + 16 \beta_1$$ -38*b10 - 78*b9 + 210*b8 + 92*b7 + 210*b6 + 16*b5 - 21*b4 + 21*b3 + 16*b1 $$\nu^{7}$$ $$=$$ $$- 137 \beta_{11} + 94 \beta_{10} - 94 \beta_{9} + 52 \beta_{8} - 146 \beta_{7} + 158 \beta_{6} + \cdots - 158$$ -137*b11 + 94*b10 - 94*b9 + 52*b8 - 146*b7 + 158*b6 + 458*b5 + 248*b3 + 231*b2 - 158 $$\nu^{8}$$ $$=$$ $$- 385 \beta_{11} + 689 \beta_{10} + 385 \beta_{9} - 1336 \beta_{8} - 1523 \beta_{7} + 295 \beta_{4} + \cdots - 1908$$ -385*b11 + 689*b10 + 385*b9 - 1336*b8 - 1523*b7 + 295*b4 - 200*b3 + 689*b2 - 200*b1 - 1908 $$\nu^{9}$$ $$=$$ $$889 \beta_{11} + 1369 \beta_{9} - 1390 \beta_{8} + 1369 \beta_{7} - 2170 \beta_{6} - 3933 \beta_{5} + \cdots + 1390$$ 889*b11 + 1369*b9 - 1390*b8 + 1369*b7 - 2170*b6 - 3933*b5 + 2293*b4 - 3933*b3 - 1369*b2 - 1640*b1 + 1390 $$\nu^{10}$$ $$=$$ $$6191 \beta_{11} - 6191 \beta_{10} + 17038 \beta_{7} - 17038 \beta_{6} - 2279 \beta_{5} - 2279 \beta_{4} + \cdots + 28184$$ 6191*b11 - 6191*b10 + 17038*b7 - 17038*b6 - 2279*b5 - 2279*b4 - 9853*b2 + 1260*b1 + 28184 $$\nu^{11}$$ $$=$$ $$- 8470 \beta_{10} - 13392 \beta_{9} + 16194 \beta_{8} - 3794 \beta_{7} + 16194 \beta_{6} + \cdots + 20700 \beta_1$$ -8470*b10 - 13392*b9 + 16194*b8 - 3794*b7 + 16194*b6 + 20700*b5 - 34375*b4 + 34375*b3 + 20700*b1

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$$.

 $$n$$ $$111$$ $$177$$ $$321$$ $$661$$ $$\chi(n)$$ $$1$$ $$1$$ $$-\beta_{6}$$ $$1$$

Embeddings

For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.

For more information on an embedded modular form you can click on its label.

comment: embeddings in the coefficient field

gp: mfembed(f)

Label   $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
81.1
 0.945349 − 2.90948i 0.421568 − 1.29745i −0.866917 + 2.66810i −1.51700 − 1.10216i 0.359793 + 0.261405i 1.65720 + 1.20403i 0.945349 + 2.90948i 0.421568 + 1.29745i −0.866917 − 2.66810i −1.51700 + 1.10216i 0.359793 − 0.261405i 1.65720 − 1.20403i
0 −0.584258 + 1.79816i 0 0.809017 0.587785i 0 0.846938 + 2.60661i 0 −0.464972 0.337822i 0
81.2 0 −0.260543 + 0.801870i 0 0.809017 0.587785i 0 −1.46997 4.52411i 0 1.85194 + 1.34551i 0
81.3 0 0.535784 1.64897i 0 0.809017 0.587785i 0 0.386966 + 1.19096i 0 −0.00499969 0.00363249i 0
401.1 0 −2.45455 1.78334i 0 −0.309017 + 0.951057i 0 0.700550 0.508979i 0 1.91748 + 5.90141i 0
401.2 0 0.582157 + 0.422962i 0 −0.309017 + 0.951057i 0 3.38507 2.45940i 0 −0.767041 2.36071i 0
401.3 0 2.68141 + 1.94816i 0 −0.309017 + 0.951057i 0 0.150443 0.109303i 0 2.46759 + 7.59446i 0
641.1 0 −0.584258 1.79816i 0 0.809017 + 0.587785i 0 0.846938 2.60661i 0 −0.464972 + 0.337822i 0
641.2 0 −0.260543 0.801870i 0 0.809017 + 0.587785i 0 −1.46997 + 4.52411i 0 1.85194 1.34551i 0
641.3 0 0.535784 + 1.64897i 0 0.809017 + 0.587785i 0 0.386966 1.19096i 0 −0.00499969 + 0.00363249i 0
801.1 0 −2.45455 + 1.78334i 0 −0.309017 0.951057i 0 0.700550 + 0.508979i 0 1.91748 5.90141i 0
801.2 0 0.582157 0.422962i 0 −0.309017 0.951057i 0 3.38507 + 2.45940i 0 −0.767041 + 2.36071i 0
801.3 0 2.68141 1.94816i 0 −0.309017 0.951057i 0 0.150443 + 0.109303i 0 2.46759 7.59446i 0
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 81.3 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.c even 5 1 inner

Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 880.2.bo.j 12
4.b odd 2 1 440.2.y.b 12
11.c even 5 1 inner 880.2.bo.j 12
11.c even 5 1 9680.2.a.cx 6
11.d odd 10 1 9680.2.a.cy 6
44.g even 10 1 4840.2.a.be 6
44.h odd 10 1 440.2.y.b 12
44.h odd 10 1 4840.2.a.bf 6

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
440.2.y.b 12 4.b odd 2 1
440.2.y.b 12 44.h odd 10 1
880.2.bo.j 12 1.a even 1 1 trivial
880.2.bo.j 12 11.c even 5 1 inner
4840.2.a.be 6 44.g even 10 1
4840.2.a.bf 6 44.h odd 10 1
9680.2.a.cx 6 11.c even 5 1
9680.2.a.cy 6 11.d odd 10 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{3}^{12} - T_{3}^{11} + T_{3}^{9} + 79 T_{3}^{8} - 19 T_{3}^{7} + 500 T_{3}^{6} - 311 T_{3}^{5} + \cdots + 400$$ acting on $$S_{2}^{\mathrm{new}}(880, [\chi])$$.

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T^{12}$$
$3$ $$T^{12} - T^{11} + \cdots + 400$$
$5$ $$(T^{4} - T^{3} + T^{2} + \cdots + 1)^{3}$$
$7$ $$T^{12} - 8 T^{11} + \cdots + 121$$
$11$ $$T^{12} - 4 T^{11} + \cdots + 1771561$$
$13$ $$T^{12} + 7 T^{11} + \cdots + 22801$$
$17$ $$T^{12} - 7 T^{11} + \cdots + 234256$$
$19$ $$T^{12} + 3 T^{11} + \cdots + 3025$$
$23$ $$(T^{6} + 18 T^{5} + \cdots + 9505)^{2}$$
$29$ $$T^{12} - 13 T^{11} + \cdots + 1296$$
$31$ $$T^{12} + 2 T^{11} + \cdots + 8880400$$
$37$ $$T^{12} + \cdots + 219662041$$
$41$ $$T^{12} + \cdots + 1401828481$$
$43$ $$(T^{6} + 3 T^{5} + \cdots + 75284)^{2}$$
$47$ $$T^{12} - 2 T^{11} + \cdots + 990025$$
$53$ $$T^{12} - 3 T^{11} + \cdots + 50625$$
$59$ $$T^{12} + 19 T^{11} + \cdots + 101761$$
$61$ $$T^{12} + \cdots + 4935905536$$
$67$ $$(T^{6} + 11 T^{5} + \cdots - 19900)^{2}$$
$71$ $$T^{12} + \cdots + 4157154576$$
$73$ $$T^{12} - 17 T^{11} + \cdots + 10523536$$
$79$ $$T^{12} + \cdots + 220938496$$
$83$ $$T^{12} + \cdots + 115379784976$$
$89$ $$(T^{6} - T^{5} + \cdots + 179771)^{2}$$
$97$ $$T^{12} + \cdots + 1613062564096$$